Antenna Array Signal Processing for Multistatic Radar Systems

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Antenna Array Signal Processing for Multistatic Radar Systems

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magniﬁcus prof.dr.ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op vrijdag 12 juli 2013 om 10:00 uur

door

Francesco BELFIORI

Laurea Specialistica in Ingegneria delle Telecomunicazioni Universit`adegli studi di Roma “La Sapienza” geboren te Roma, Itali¨e

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Dit proefschrift is goedgekeurd door de promotor: Prof.ir. P. Hoogeboom

Samenstelling promotiecomissie:

Rector Magnificus, voorzitter Prof. ir. P. Hoogeboom, Technische Universiteit Delft, promotor Prof. Dr. L. Ferro-Famil, Universitéde Rennes 1 Prof. Dr. A. Yarovoy, Technische Universiteit Delft Prof. Dr.-Ing. J. Ender, UniversitätSiegen - Fraunhofer FHR Prof. Dr. F. Le Chevalier, Technische Universiteit Delft - Thales Dr. W. van Rossum, TNO

This research was supported by TNO under contract DenV-017.

ISBN 978-94-6191-782-9 Antenna Array Signal Processing for Multistatic Radar Systems. Dissertation at Delft University of Technology. Copyright c 2013 by Francesco Belﬁori.

All rights reserved. No parts of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the author.

Author e-mail: [email protected]

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A mia madre

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Contents

1 Introduction 1 1.1 Passive Coherent Locator (PCL) systems ...... 4 1.2 The Multiple-Input Multiple-Output radar concept ...... 5 1.3 Outline of the Thesis ...... 7

2 Antenna theory and array pattern synthesis 9 2.1 Main antenna parameters ...... 9 2.1.1 Directivity ...... 10 2.1.2 Eﬃciency ...... 10 2.1.3 Gain ...... 11 2.2 Antenna array pattern synthesis ...... 11 2.2.1 Linear array pattern synthesis ...... 14 2.2.2 Circular array pattern synthesis ...... 17 2.3 Pattern synthesis in non ideal arrays ...... 20 2.3.1 Mutual coupling ...... 20 2.3.2 Illumination errors ...... 21 2.4 Summary ...... 22

3 Digital beamforming for PCL 23 3.1 Digital processing scheme ...... 23 3.2 Mutual coupling compensation ...... 24 3.2.1 Analytical description ...... 24 3.2.2 Optimisation approach for the C matrix evaluation ...... 26 3.3 DBF for circular arrays ...... 27 3.3.1 Phase modes theory ...... 27 3.3.2 Proposed algorithm ...... 29 3.3.3 Array pattern comparisons ...... 31 3.4 Direct path interference suppression ...... 34 3.5 Summary ...... 35

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viii Contents

4 PCL radar description and experimental results 37 4.1 Overview of the PCL system ...... 37 4.2 Antenna array analysis ...... 39 4.2.1 Array element characterisation ...... 39 4.2.2 Circular array characterisation ...... 41 4.3 PCL receiver ...... 43 4.3.1 Dynamic range analysis ...... 44 4.3.2 Digital down conversion ...... 46 4.4 Experimental results ...... 47 4.4.1 MC compensation ...... 47 4.4.2 Direct path interference suppression ...... 49 4.4.3 Range/Doppler processing ...... 51 4.4.4 CFAR detector and plots extraction ...... 52 4.5 System future improvements ...... 54 4.6 Summary ...... 54

5 Coherent MIMO array theory 57 5.1 Coherent MIMO array pattern synthesis ...... 57 5.1.1 Fourier-like transform representation of a MIMO array pattern 60 5.2 Waveform diversity/orthogonality concept ...... 62 5.3 Eﬀect of the illumination errors on the pattern synthesis ...... 64 5.3.1 Simulated results ...... 70 5.4 Summary ...... 72

6 MIMO signal processing: RADOCA test board and experimental results 75 6.1 RADOCA MIMO radar description ...... 76 6.1.1 Antenna and PCB design ...... 78 6.2 Board calibration ...... 80 6.2.1 Experimental results ...... 82 6.3 Moving target detection in TDM MIMO radars ...... 84 6.3.1 Doppler speed impact ...... 86 6.3.2 Multi domain signal analysis ...... 87 6.3.3 Eﬀect of the random selection of the active transmitter . . . . 91 6.4 High resolution techniques applied to coherent MIMO arrays . . . . . 94 6.4.1 The MUltiple SIgnal Classiﬁcation (MUSIC) method . . . . . 94 6.4.2 2D-MUSIC algorithm description ...... 95 6.4.3 Simulated and Experimental Results ...... 98 6.5 Summary ...... 101

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Contents ix

7 Conclusion and outlook 103 7.1 Conclusions ...... 104 7.2 Recommendations and future work ...... 106

A PCL system measurements 109 A.1 Receiver channel gains ...... 109 A.2 Channel noise ﬁgures ...... 110 A.3 Element patterns ...... 111

B Illumination error eﬀects on the synthesis of MIMO array pattern 115

C Basic theory of FMCW 121

List of Acronyms and Symbols 123

Bibliography 136

Summary 137

Samenvatting 139

Author’s publications 141

About the author 143

Acknowledgements 145

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x Contents

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List of Figures

1.1 Sketch of an analog beamformer based on phase shifter components. .2 1.2 Basic digital beamforming scheme...... 3

2.1 Generic antenna array geometry...... 12 2.2 Linear antenna array geometry scanning on the xOz plane...... 14 2.3 Normalised array pattern behaviors along the azimuthal plane (θ = 90o). 17 2.4 Circular antenna array geometry...... 18 2.5 3D view of the array factor for an 8-elements UCA (linear scale). . . . 19 2.6 Array factor for an 8-elements UCA along the azimuthal (θ = 90o, left) and the elevation (φ = 0o, right) planes...... 19

3.1 Digital signal processing scheme of the PCL radar...... 24 3.2 First kind Bessel functions of diﬀerent orders...... 29

3.3 Normalised UCA pattern and mask function fd(φ) of the desired pattern behavior...... 30 3.4 Results of the proposed side lobe reduction method for a (a) UCA with radius r = 0.48λ, (b) UCA with radius r = 0.36λ...... 31 3.5 Results of the phase modes side lobe reduction method for a (a) UCA with radius r = 0.48λ, (b) UCA with radius r = 0.36λ...... 32 3.6 Comparison between the phase modes and the proposed DBF technique syntheses of a circular array pattern with radius r = 0.36λ and SLL=−19dB...... 33

4.1 Block diagram of the PCL system...... 38 4.2 TNO circular array for passive radar applications...... 39 4.3 Simulated element pattern gain of a stand alone dipole considered as a single radiating element using CST: (a) 3D plot and (b) cut along the elevation plane (φ = 90◦)...... 40

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xii LIST OF FIGURES

4.4 Simulated element pattern gain of a single dipole in the circular array configuration using CST: (a) 3D plot and (b) cut along the azimuthal plane (θ = 90◦)...... 40 4.5 Comparison between the measured element patterns for three different array channels and the CST simulated data...... 41 4.6 Array construction model used in the CST simulator...... 42 4.7 Simulated circular array pattern gain using CST: (a) 3D plot and (b) “blue line”: cut along the azimuthal plane (θ = 90◦) “red line”: cut along the elevation plane (φ = 90◦)...... 42 4.8 Rack of the PCL system analog receiver: (a) front view (b) internal view. 43 4.9 Block diagram of a receiving channel...... 44 4.10 FM bandwidth input signals measured with the 6-th dipole of the array. 46 4.11 Representation of: a uniformly (a) and a sparsely (b) filled FM band. 47 4.12 (a) Sxx scattering parameters for the 8 channels of the array , (b) S1x scattering parameters with respect to the first element of the array. . . 48 4.13 (a) Relative (with respect to first array channel) phase shifts after digital conversion, (b) Measured signal amplitudes after digital conversion. 48 4.14 Cartesian reference system comparison between the un-/calibrated and the theoretical patterns in dB scale for (a) transmission point 1 and (b) transmission point 2...... 49 4.15 Effect of the DBF nulling procedure on the array pattern behavior. . . 50 4.16 Matched filter output Range-Doppler map...... 52 4.17 GO-CFAR Time vs Range output map (a) and Overlapping of the CFAR detections with the ADSB available tracks data (b)...... 53 4.18 GO-CFAR Doppler Velocity vs Range output map (a) and Overlapping of the CFAR detections with the ADSB available tracks data (b). . . . 53

5.1 Periodical array configuration of transmitting and receiving elements. 58 5.2 Different MIMO pattern contributions and realised pattern synthesis. . 61 2 2 5.3 Error affected array pattern comparisons for (a) ∆ = σδ = 0.01, (b) 2 2 2 2 ∆ = 0.01 and σδ = 0.1, (c) ∆ = σδ = 0.1...... 70 5.4 Analysis of the upper bound conditions for the average error patterns 2 2 2 2 for (a) ∆ = σδ = 0.001, (b) ∆ = 0.01 and σδ = 0.1...... 72

6.1 X-Band radar test board with MIMO functionality developed at TNO. 77 6.2 Details of the USB 2.0 connector (a), boxed test board (b) and radar system layout while connected to the data acquisition notebook (c). . 77 6.3 Virtual element relative positions of the MIMO array board...... 78 6.4 Layout of λ/4 (8mm) spaced microstrip fed quasi-Yagi antenna. . . . . 79 6.5 Scattering parameter measurements of the λ/4 spaced elements. . . . 79

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LIST OF FIGURES xiii

6.6 Required spacings of the receiver elements for increasing number of the transmitters...... 81 6.7 Measured and expected phase behavior of the reference scatterers. . . 82 6.8 Measured and average (a) phase offset and (b) fractional amplitude values for the reference scatterers...... 82 6.9 Effect of the calibration on the pattern synthesis (a) first scatterer (b) second scatterer...... 83 6.10 Effect of the tapering on the calibrated and un-calibrated patterns (a) first scatterer (b) second scatterer...... 83 6.11 Example of a FMCW transmission scheme for a TDM MIMO array. . 85 6.12 FMCW Range/Doppler processing (a) FMCW Range/Doppler processing with a 3 stages MTI canceler (b)...... 86 6.13 TDM MIMO 3D matrix data structure...... 88 o 6.14 Ambiguity functions of a target with status vector v0 = [50m, 20 , 3m/s] in a sequential TDM transmission mode: Range/Doppler (a) and An- gle/Doppler (b) maps...... 89 o 6.15 Angle/Doppler map for a target with status vector v0 = [50m, 20 , 3m/s] in a conventional FMCW radar with transmitted pulse length of NT T . 90 o 6.16 Ambiguity functions of a target with status vector v0 = [50m, 20 , 3m/s] in a random TDM transmission mode: range/Doppler (a) and azimuth/Doppler (b) maps...... 91 o 6.17 Ambiguity functions of two targets with status vectors v0 = [50m, 20 , 3m/s] o and v1 = [50m, 35 , 10m/s] in a sequential (a) and random (b) TDM transmission mode...... 92 6.18 Effect of the number of integrated sweeps on the sidelobes level: (a) 16 MIMO sweeps (b) 128 MIMO sweeps...... 92 6.19 Data matrix samples and scanning window procedure...... 96 6.20 Simulated scenario with 6 targets spaced by 0.6m in range and 5o in angle: DBF processing (a) 2D-MUSIC processing (b)...... 98 6.21 Cut at the 20.6m range bin for the 3 scatterers case (a); cut at the 20m range bin for the 2 scatterers case (b)...... 99 6.22 Cut at the 5o angular bin for the 3 scatterers case (a); cut at the 0o angular bin for the 2 scatterers case (b)...... 99 6.23 Scenario for the measured data set collection with highlighted targets. 100 6.24 Real data scenario: DBF processing (a) 2D-MUSIC processing (b). . . 101

A.1 Set-up of the gain measurements...... 109 A.2 Set-up of the noise ﬁgure measurements...... 110

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xiv LIST OF FIGURES

A.3 Element pattern measurement setup: reference transmitter (a), PCL

array ARx and reference transmitter AT x (b), measurements geometry (c) and rotating platform with scaled plane (d) ...... 113

C.1 Transmitted and received sawtooth modulated signals ...... 121

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List of Tables

3.1 Azimuthal resolution performance ...... 32 3.2 Angular resolution comparison for different SLL taperings ...... 32 3.3 Illumination efficiency comparison for different SLL taperings . . . . . 33

4.1 ICS-554B digitiser board speciﬁcations ...... 38 4.2 Average power levels at the input of the analog receiver ...... 45

6.1 Main to Maximum Sidelobe Level ...... 93 6.2 Radar parameters selection for the simulated scenario ...... 98 6.3 Target positions for the simulated scenario ...... 99

A.1 Gain values of the receiver channels ...... 110 A.2 Noise figure values ...... 111 A.3 Noise figure dependency with the attenuators configuration ...... 111

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xvi LIST OF TABLES

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Chapter 1

Introduction

The basic tasks of a radar system conceive the detection of a target and the estimation of its range, i.e. the distance from the radar. This information is retrieved by transmitting a probing signal inside the scene of interest, and by analysing the signal that is reflected by the object. In the case of classical monostatic radars, a single antenna is used at both the transmitting and the receiving sections. When the angular information is needed, the antenna is mechanically rotated and the direction of arrival of the target is obtained. Modern radars employ transceiver sections that are composed by multiple radiators, which are referred to as array of antennas, in order to enhance the overall system capabilities. With respect to single antenna-based radars, one of the main advantages offered by such systems is the possibility of combining the signals received by the different channels and retrieving the angular information belonging to various directions [1]. This allows for non mechanical scanning of the beams. A higher flexibility for surveillance tasks exploitation can then be achieved. Aside from the targets of interest, the radar scenario is characterised by the presence of unwanted signals that can degrade the detection performance of the desired echoes. Those signals can be generated by either environmental reflections (clutter, multipath) or intentional interferers (jammer). The latter class of signals are normally referred to as Electronic Counter Measure (ECM) and they are present in military scenarios with the aim of deceiving the sensor, increasing the noise floor of the radar or saturating the related receiver. Since these disturbances are usually located in well defined sectors and the degrees of freedom provided by the multiple antennas allow the synthesis of directional nulls in the array radiation pattern, several Electronic Counter Counter Measure (ECCM) techniques can be adopted to suppress or mitigate the impact of the interfering signals on the radar system [2].

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2 1. Introduction

Figure 1.1: Sketch of an analog beamformer based on phase shifter components.

Early array based radar systems used to perform pattern synthesis by means of analog components, such as phase shifters1 (PS) or variable time delay lines (TDL) [2,3], electronically controlled by a computer unit. As shown in Fig.1.1, the signals are then summed at the receiver level, which yields a single beam, and digitally converted before being available to the radar signal processor. The choice about using either PS or TDL, aside from the inherent cost of the systems based on the latter ones, is driven by the transmitted pulse characteristics with respect to the array fill time [4]. In order to really benefit from all the array elements, the signal has indeed to be present on each of them before summation. If TDL are considered, this condition can be satisfied by a proper adjustment of each acquisition channel delay. In the case of PS, the signal duration has to be greater than the time needed by the electromagnetic wave to cover the array extension. By considering a linear array geometry, about which more details are provided in Ch.2, it can be written that: L sin θ τ T = , (1.1) c being L the array length, θ the angle of arrival of the signal and c the speed of light. The quantities τ and T represent the pulse duration and the array fill time respectively. Since the pulse duration is inversely proportional to its bandwidth B,

by means of a proportionality term kB, (1.1) can also be written as: c B . (1.2) kBL sin θ

1The wording phased arrays was indeed introduced to refer to these type of analog systems. Nowadays it is kept and it is more generally referred to any class of antenna arrays which perform signal processing at an element level.

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Figure 1.2: Basic digital beamforming scheme.

If we divide both sides of (1.2) by the carrier frequency fc, we obtain: B λ , (1.3) fc kBL sin θ where λ is the wavelength. Expression (1.3) highlights the dependency between the signal fractional bandwidth B and the array system characteristics. If (1.3) is satis- fc ﬁed, the system is considered operating under narrow band assumption and PS can be used in place of TDL, which are then exploited in the case of wideband arrays. Thanks to the evolution of the radar electronics, state of the art systems can apply digital conversion at an element level (see Fig.1.2). In this case, each receiving channel has an independent front-end and an Analog to Digital Converter (ADC). Maximum freedom is then provided to the signal processing section for the application of the digital processing schemes, that are conventionally referred to as Digital Beam Form- ing (DBF) algorithms. In the digital domain, the antenna array can electronically be steered to any direction. Multiple and closely spaced antenna beams can be synthesised and independently pointed and shaped. A more accurate control of both the sidelobes behavior and the directional nulling is obtained thanks to calibration techniques that can directly be implemented in the digital domain [2]. With respect to surveillance operations, the DBF processing allows following the trajectory of the detected targets by means of narrow beams, while the sensed area being illuminated with a wide beam. Since the two operations are carried on at the same time, on the one hand, the performance of the radar tracker is improved, on the other hand, there is no reduction of the update rate of the sensed area. The electronic steering

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4 1. Introduction

capability also represents an essential requirement in case of wideband and/or near ﬁeld applications2 [5, 6]. Latest developments of sensing techniques have led to the realisation of novel radar concepts for security, safety and surveillance applications based on phased array technology [7–9]. A growing interest in that sense is represented by the deﬁnition of proper array processing approaches for passive and Multiple-Input Multiple-Output (MIMO) radars.

1.1 Passive Coherent Locator (PCL) systems

Active monostatic radars work by transmitting a known signal and receiving the reflection of illuminated objects. As a consequence, while they detect a target, they can also be detected by hostile sensing systems because of their own transmission. To improve the covertness of the operation, bistatic systems were deployed already in the early days of radar development, with the transmitter located far from the receiver. While such a configuration allowed protecting the receiver, the transmitter could still be detected and damaged by the enemy. Thanks to the use of transmitters of opportunity, such as radio, mobile phone and TV broadcasters, a Passive Coherent Locator (PCL) does not produce any emissions and is inherently covert. The target location is retrieved in terms of a bistatic range, which is the sum of the distance from the transmitter to the illuminated object and from this object to the receiver. Given the bistatic range, the object is located on an ellipse having as focal points the transmitter and the receiver. To resolve the object position, the direction of arrival of the reflected signal is needed. For this purpose, passive radars typically contain an antenna array and the target bearing angle is retrieved by means of array signal processing [10]. A crucial issue which influences the system performance relates to the capability of separating the relatively small signal reflected by the object and the direct signal produced by the emitter of opportunity. The large difference in strength between these two signals makes the design of passive radar system rather cumbersome [11]. Furthermore, the accuracy also depends on the emitted waveform and the related ambiguity function characteristics [12]. The covertness characteristic and the bistatic observation geometry, the latter one particularly suitable against stealth targets [13], have stimulated the research about PCL for military purposes. More recently air and vessel traffic control applications have also been considered [14–16]. Experimental PCL programs have been developed in several research institutes and industries in the world. Among them, the Lockheed Martin Silent Sentry in USA, the french HA-100 developed by Thales, the CORA PCL system designed at the

2The distinction between the near and the far ﬁeld systems will be presented in Ch.2.

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1.2 The Multiple-Input Multiple-Output radar concept 5

Fraunhofer institute in Germany and the italian AULOS realised by Selex-ES. TNO - Defence, Safety and Security has been actively working on passive radar systems since 2002 [17]. Different experimental systems have been designed and manufactured for research purposes. The latest demonstrator is based on a circular array configuration that, with respect to linear array systems, offers the benefit of an omnidirectional coverage [18]. As a consequence, the direct signal is always present since there is not a physical separation between the channels which are aimed at acquiring the surveillance and the reference signals. The two channels are indeed synthesised by means of DBF techniques, that are also used to perform a preliminary suppression of the direct signal. With respect to this system, the following research objectives have been addressed:

• The identiﬁcation of a proper calibration technique for the PCL system, accounting for both the analog and the digital sections of the receiver. For the application of any DBF scheme, it is indeed essential to have a complete understanding of the antenna conﬁguration and the RF chain of the radar.

• The derivation of a novel DBF method for the synthesis of the reference and the surveillance beams. Since the target direction of arrival estimation depends on the angular resolution provided by the array, this parameter has represented a driving point for the selection of the preferred approach. A comparison with existing technique, aimed at showing the beneﬁts of the proposed method, has been carried out. The eﬀective direct signal nulling capability that is achievable by means of DBF has also been evaluated.

• The assessment of the PCL system by means of real data acquisition and performance validation. To that aim, the entire signal processing chain has been implemented and the detection performance compared with ground truth data sets.

1.2 The Multiple-Input Multiple-Output radar concept

Unlike phased array radars, where the radiating elements transmit a scaled version of the same waveform, the MIMO paradigm is based on the possibility of employing multiple emitters in order to transmit probing signals that are orthogonal to each other [19]. At the receiver side, these uncorrelated waveforms can be separated to enable processing of each independent transmitter/receiver pair. The orthogonality among the probing signals can be achieved in diﬀerent domains [20]. The most obvious way is by allocating each emitter to a separate time slot, in the so called Time Division Multiplexing (TDM); drawbacks of this method are the scarce capability of dealing with fast moving targets and the increased requirement in data

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6 1. Introduction

handling (the transmitted waveforms must separately be digitised). Another approach is based on the Frequency Division Multiplexing (FDM), in which case each waveform belongs to a different sub-band. Here the main issue is represented by the difficulty to ensure the desired coherency between pulses which are located at different frequencies. The last category is represented by the Code Division Multiplexing (CDM), that is an inheritance of the wireless communications where the MIMO paradigm was firstly applied. In this case digital codes with low cross-correlation profiles are exploited to modulate the basic waveform. MIMO radars can also be classified on the basis of the transmitters and receivers spatial distribution. The case of widely separated radiators is normally referred to as statistical MIMO [21]. Such systems exploit the intrinsic angular diversity of the system layout in order to obtain uncorrelated reflections of the target. The processing of the multiple responses helps in mitigating the rapid signal fluctuations of the target Radar Cross Section (RCS). An improved target detection and estimation performance is then achieved [22,23]. The other class of MIMO radars, namely coherent MIMO radars, is denoted by the presence of antenna elements placed in proximity to each other. By assuming each transmitter/receiver couple excited by the same target scattering response, i.e. the target response keeps its coherency among the multiple transmitted waveforms [24–26], the different contributions can be coherently combined leading to the synthesis of an extended number of virtual array channels. Array signal processing techniques based on the exploitation of these additional channels ensure a better angular resolution of the radar system and an increased number of detectable targets [27]. The RADOCA radar demonstrator, where RADOCA stands for RAdar DOme CAm- era, is the result of one of the research projects led at TNO in the framework of coherent MIMO systems. The idea consists of combining a camera with a radar in order to perform the detection and classification of slow moving targets in private environments. To this aim, the radar has to provide the information (azimuth and range) about the target to the camera, that can then be steered towards the object and finalize its identification. Design requirements in terms of: system size, angular resolution and spatial adaptivity for clutter mitigation have driven the choice to the realisation of a TDM based MIMO radar. The research activity within this framework has focused on:

• The theoretical characterisation of the coherent MIMO radar concept by the assessment of advantages and disadvantages with respect to conventional phased array based radars. Speciﬁcally, a proper dimensioning of the MIMO system, in both ideal and non ideal conditions, has been studied and the expected performance for the angular resolution and the array pattern sidelobes behavior have been retrieved.

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1.3 Outline of the Thesis 7

• The estimation of a calibration procedure aimed at compensating for the array element mismatching. As in the case of phased arrays, the application of DBF techniques and the correct behavior of the radar depend on a proper calibration of the array antenna section. An approach that exploits the MIMO conﬁguration has been studied to this purpose.

• The analysis of the limiting factors which are introduced by the selected TDM scheme. Their impact on the target identiﬁcation have been analysed and a transmitter selection procedure aimed at overcoming this limitation has been proposed.

• The evaluation of high resolution array processing techniques for radar performance enhancement. Thanks to the exploitation of the extended number of degrees of freedom provided by the coherent MIMO array, a novel technique has been implemented and the better range/angle discrimination capability has been assessed.

1.3 Outline of the Thesis

The remainder of the thesis is organised as follows:

Chapter 2 introduces the principles of general antenna and array antenna theory. The main concepts to assess and to describe the array pattern behavior are presented. Causes of pattern degradation, i.e. mutual coupling and element illumination errors, are explained and referred throughout the text to characterise the radar systems under investigation.

Chapter 3 focuses on the algorithm for the mutual coupling compensation of the circular array which is used as a PCL sensor. A set of internal and external measurements are used for the compensation procedure and the related signal processing operations are illustrated. An array pattern shaping technique is also illustrated. The performance of the proposed method is then compared with the phase modes technique and the speciﬁc beneﬁts are highlighted.

Chapter 4 presents the PCL radar that has been the object of the digital beamforming research on circular arrays. The antenna section of the system is analysed and the design choices of the receiver are depicted. The techniques illustrated in Ch.3 are then applied and assessed by means of experimental validations. Also, the entire signal processing chain, leading to target detection and plot extraction, is presented and the radar performance is compared with Automatic Dependent Surveillance Broadcast (ADSB) ground truth data.

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8 1. Introduction

Chapter 5 discusses the topic of digital beamforming in connection with the coherent MIMO theory. The procedure leading to the design of this kind of radar is presented and the concept of waveform diversity is introduced. Then, the characteristics of the MIMO array pattern and the degradation due to the presence of element illumination errors are addressed. The higher sensitivity to the illumination errors of the MIMO arrays, with respect to conventional linear arrays, is described and proven by the retrieved analytical formalism.

Chapter 6 describes the RADOCA radar demonstrator that has been realised and the results of the signal processing techniques which have been developed: the calibration procedure, the transmission approach aimed at extending the unambiguous Doppler interval for the TDM based MIMO radars and the novel high resolution technique. Both simulated and experimental results are presented and discussed.

Chapter 7 summarises the main achievements of the research activity described in this thesis and provides an overview of the challenges which can still be the objective of further analyses, both from hardware and signal processing perspectives.

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Chapter 2

Antenna theory and array pattern synthesis

The chapter is concerned with the description of the main antenna and array antenna parameters that will be used throughout the text. In the first section, the basic definitions of the antenna radiating properties are considered. Then, specific attention is given to the introduction of the array pattern concepts with respect to the linear and the circular shape configurations. With the aim of characterising the effect of the non ideal behavior of the array elements, the consequences due to the presence of mutual element interactions and aperture illumination errors are considered in the last section of the chapter.

2.1 Main antenna parameters

The classical definition of antenna is provided by the “IEEE Standard Definitions of Terms for Antennas (IEEE Std 145-1983)” [28] where it is defined as “the part of a transmitting or receiving system which is designed to radiate or to receive electromagnetic waves”. It then results to be the transitional structure between the free-space and the guided propagations of an electromagnetic wave. From the circuital point of view, by exploiting the Thevenin representation of a guided propagation channel, the antenna can be described by means of the impedance [29]:

ZA = (RL + Rr) + jXA, (2.1)

being RL the resistance associated to the dielectric and conduction losses of the antenna structure, Rr the radiation resistance and XA is the reactance which represents the imaginary part of the impedance. Any design is performed in order to obtain,

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10 2. Antenna theory and array pattern synthesis

under ideal conditions, the conjugate matching between the antenna characteristic impedance and the internal impedance of the source. In this way, the maximum power is delivered to the antenna. Besides its function as a receiving or transmitting energy device, most of the applications require the optimization of the radiated energy into some speciﬁc directions, while it has to be minimized into others. Here the main parameters which are used to describe the directional behavior of an antenna are introduced, since they will be referred to later in the thesis. A more detailed and extensive description can be found in [29–32].

2.1.1 Directivity The directivity function D(θ, φ) of an antenna is deﬁned as the ratio between the radiation intensity U(θ, φ)1 in a given direction and the radiation intensity averaged all over the directions. Being the average radiation intensity equal to the total power radiated by the antenna divided by 4π, it follows that

U(θ, φ) 4πU(θ, φ) D(θ, φ) = = , (2.2) U0 Prad

1 R where U0 = 4π Ω U(θ, φ)dΩ and Ω is the solid angle. From (2.2) it is clear that, in the case of an isotropic radiator, the directivity is unity as the quantities U(θ, φ) and

U0 are equal to each other. Under the far ﬁeld assumption2, the directivity can also be expressed in terms of the electric ﬁeld component as:

4πE(θ, φ)2 D(θ, φ) = R 2 . (2.3) Ω E(θ, φ) dΩ

2.1.2 Efficiency A number of efficiencies can be related to an antenna; the overall efficiency η is normally taken as the combination of all of them and it is written as:

η = ηrηcηd, (2.4)

where ηr is the reﬂection eﬃciency, which depends on the mismatch between the transmission line and the antenna, ηc and ηd are the conduction and the dielectric

1The radiation intensity represents the power radiated by an antenna per unit solid angle [30]. 2 2D2 The far ﬁeld region is assumed at a distance greater than λ being D the diameter of the sphere which includes the antenna and λ the wavelength. This approximation keeps its validity at the frequency bands of VHF and above. At lower frequencies, the starting distance of the far ﬁeld region is dictated by the most stringent value between 10D and 10λ.

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2.2 Antenna array pattern synthesis 11

eﬃciencies respectively and they are related to the dissipation losses. The eﬃciency represents a quality factor of the antenna performance as it indicates

how much of the input power Pin is eﬀectively radiated by the antenna:

Prad = ηPin. (2.5)

2.1.3 Gain A parameter which takes into account both the directional and the efficiency properties of an antenna is the gain, which is defined as “the ratio between the radiation intensity in a given direction and the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically”. Being the radiation intensity corresponding to an isotropic radiator equal to the input accepted power divided by 4π and by considering (2.5) we have: 4πU(θ, φ) 4πU(θ, φ) G(θ, φ) = = η . (2.6) Pin Prad The relation between the antenna gain and the antenna directivity can then be written as: G(θ, φ) = ηD(θ, φ). (2.7) The gain is then equal to the directivity in the case of an ideal radiator which presents no losses, i.e. efficiency equal to unit. It must also be said that the IEEE standard definition does not usually include the reflection efficiency in (2.7), limiting therefore the efficiency to the dielectric and the conduction contributions.

2.2 Antenna array pattern synthesis

Multiple independent radiating elements can be arranged into a certain geometrical configuration in order to improve the performance of the transceiver section. These antenna configurations are usually referred to as “arrays”. The main advantage provided by the antenna arrays is represented by their electronic scanning capability. Furthermore, an opportune tapering of the excitation coefficients of the different elements can be used to control the shape and the sidelobes of the array pattern as it will be shown in Sec.2.2.1 and Sec.2.2.2. The array pattern control also conceives the possibility of simultaneously steering the main beam in a certain direction while a null is placed towards the direction of an interfering/jamming signal. The behavior of the array pattern mainly depends on five parameters [29]: • geometry, i.e. the spatial configuration of the array

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12 2. Antenna theory and array pattern synthesis

Figure 2.1: Generic antenna array geometry.

• spacing between the multiple elements

• amplitude excitation of each element

• phase excitation of each element

• element pattern of the radiators

The resulting electric ﬁeld excited by a radiating element in a given point of the space depends on the distance from the element itself and the related angular coordinates. If the point is taken at a very far distance from the element, then the electric ﬁeld

can be represented as the product between an angular function, fn(θ, φ), which is referred to as the element pattern and a radiation term which has spherical wave dependance with the range [4]. By considering the geometry illustrated in Fig.2.1, which represents a generic distribution and composition of array elements, the electric far ﬁeld produced the by the n-th element can be written as:

e−jkRn En(θ, φ, r) = fn(θ, φ) , (2.8) Rn

being k the free space wave number and:

p 2 2 2 Rn = (x − xn) + (y − yn) + (z − zn) (2.9)

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2.2 Antenna array pattern synthesis 13

the distance between the n-th array element and the point where the electric field is measured. If this distance is considered in the far field of the array3 the related electric field wavefront can be assumed to be planar and (2.9) can be approximated by:

Rn = R − rˆ · ~rn, (2.10)

wherer ˆ is the versor to the point where the electric field is measured and ~rn is position vector of the n-th array element. The origin of the reference system can be arbitrarily chosen. According to (2.10), the expression in (2.8) can be rewritten as: e−jkR E (θ, φ, r) = f (θ, φ) ejk(ˆr·~rn). (2.11) n n R The total electric field can then be retrieved by superposition of all the element contributions: N e−jkR X E(θ, φ, r) = f (θ, φ)ejk(ˆr·~rn). (2.12) R n n=1 Since the angular properties of the electric field in (2.12) are measured on a sphere e−jkR of constant radius, the term R can be neglected and (2.12) can be written as a function of the angular variables only. Thus, if all the elements share the same

pattern characteristic and diﬀerent complex excitations an are considered for the multiple elements of the array, (2.12) becomes:

N X jk(ˆr·~rn) P (θ, φ) = f(θ, φ) ane (2.13) n=1

which represents the array pattern. The aim of the an tapering coeﬃcients is to perform both the array pattern shaping and steering. More details about the weights selection are provided in Sec.2.2.1 and Sec.2.2.2 with respect to linear and circular array conﬁgurations. These geometries are of particular interest since they are the chosen structures for the design of the radar systems that are illustrated in Ch.3 and Ch.6. According to (2.13), the array pattern can be seen as the product between two main components: the element pattern and the array factor:

N X jk(ˆr·~rn) F (θ, φ) = ane (2.14) n=1 which describes the geometrical characteristics of the array.

3 2L2 The array far ﬁeld region is considered to start at a distance R = λ , being L the largest dimension of the array. However, it is pointed out in [4, 33, 34] that, in order to measure very low 10L2 sidelobes and array patterns with deep nulled regions, the more stringent limit of R = λ should be taken as reference.

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14 2. Antenna theory and array pattern synthesis

2.2.1 Linear array pattern synthesis

The linear array structure, or uniform linear array (ULA) when the an coefficients have the same amplitudes, foresees a deployment of the antenna elements on a straight line, as it is shown in Fig.2.2 for an array of N elements. According to this geometry, the steering capability of the array is limited to the xOz plane (φ = 0), whereas the angular performance on the xOy plane is dictated by the behavior of the element pattern only. The analysis of the array factor for this configuration can be done by taking for simplicity a phase reference at the first element, then (2.14) takes the form:

N−1 X −jknd sin (θ) F (θ) = ane , (2.15) n=0

where d is the inter-element spacing between the radiators. The series in (2.15) has a known expression4 and it can then be rewritten as (the tapering coeﬃcients are assumed equal to one):

−j 2π Nd sin(θ) −j π Nd sin(θ) j π Nd sin(θ) −j π Nd sin(θ) 1 − e λ e λ e λ − e λ F (θ) = = −j 2π d sin(θ) −j π d sin(θ) j π d sin(θ) −j π d sin(θ) 1 − e λ e λ e λ − e λ sin π Nd sin(θ) jφref λ = e π (2.16) sin λ d sin(θ)

Figure 2.2: Linear antenna array geometry scanning on the xOz plane.

−jAx 4PA−1 e−jax = 1−e . a=0 1−e−jx

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2.2 Antenna array pattern synthesis 15

and it is also valid: sin π Nd sin(θ) sin π Nd sin(θ) jφref λ jφref λ F (θ) = e π = e N π sin λ d sin(θ) N sin λ d sin(θ) hπ i ≈ ejφref Nsinc Nd sin(θ) , (2.17) λ where the contribution of the array gain N, which depends on the total elements number, has been highlighted. When the complex excitations are chosen to synthesise the main beam towards a jknd sin(θ0) speciﬁc direction θ0, which is obtained by selecting an = e , it can easily be retrieved that (2.16) becomes:

sin π Nd(sin(θ) − sin(θ )) jφref λ 0 F (θ) = e π . (2.18) sin λ d(sin(θ) − sin(θ0))

Grating lobes By analysing (2.18) it is clear that the element contributions can coherently add up together at diﬀerent angles. Those angles correspond to the zeros of the denominator: π d| sin(θ) − sin(θ )| = pπ with p = 1, 2, ... (2.19) λ 0 and, as a result, multiple beams of the same amplitude, usually referred to as grating lobes, can arise in the ﬁeld of view of the array. This occurrence can be avoided by properly choosing the inter element spacing d. For a given maximum pointing angle

θ0, if only a single beam, i.e. the main beam, has to be synthesised, the following condition must hold: d N − 1 1 < , (2.20) λ N 1 + | sin(θ0)| which is a conservative constraint as it imposes that the entire grating lobe must be outside of the scanning region of interest.

Beamwidth and sidelobes The pattern beamwidth, which corresponds to the physical angular resolution of the array, can be referred to either the Half Power Beamwidth (HPB) or to the First Null Beamwidth (FNB). The former is measured at the -3dB intersection points from the array pattern main peak, which for large arrays5 and by considering the boresight

5For a generic array length the expression which provides the 3dB beamwidth is: πNd √ sin( λ sin(θ3dB )) πd = 0.5. However, it is shown in [4] that for N ≥ 3 the beamwidth variation N sin( λ sin(θ3dB )) with respect to (2.21) is less than 5% and it becomes lower than 1% for N ≥ 7.

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16 2. Antenna theory and array pattern synthesis

pointing direction are given by: λ θ = sin−1 ±0.443 , (2.21) 3dB Nd the latter, by considering (2.18), is given by the solution of: π π d(sin(θ) − sin(θ )) = (2.22) λ 0 N which after few steps6 results to be: −1 λ θFNB = sin . (2.23) Nd cos(θ0) Equation (2.23) also highlights the resolution degradation which is introduced by the pattern steering. By combining (2.21) and (2.23), the relation between the HPB and the FNB is retrieved:

θHPB ' 0.886θFNB. (2.24)

A useful descriptor of the array pattern behavior is the Side Lobe Level (SLL), which represents the ratio between the highest side lobe and the main beam amplitudes. In the case of large arrays, the SLL is independent of the main beam angle [35] and, if a uniform excitation is applied throughout the elements, a -13.2dB level is obtained. The SLL can be decreased by applying non uniform tapering masks at the cost of both a reduced illumination eﬃciency:

PN 2 1 ( n=1 |an|) ηi = (2.25) N PN 2 n=1 |an| and a degraded angular resolution. Any novel technique that is implemented in order to improve the SLL of an antenna array should also be analysed by taking into account these eﬀects. Fig.2.3 provides an example of all the concepts that have just been introduced. Three normalised pattern behaviors, belonging to a 16 elements linear array, are illustrated. The ﬁrst plot shows the uniform illumination case with an inter-element spacing d = λ/2. The FNB and the HPB are depicted. In the second curve, while keeping the uniform illumination, the array spacing has been increased to the value of d = λ leading to the synthesis of a grating lobe at θ = 90o. In the last plot, a Chebishev tapering mask [36] providing an SLL=-30dB has been applied instead of a uniform one. The broadening of the main beam can be noticed and a resulting illumination

eﬃciency ηi = 0.86 is obtained.

6 πd πd λ [sin[(θ − θ0) + θ0]] ≈ λ [sin(θ − θ0) cos(θ0) + sin(θ0) − sin(θ0)] πd = λ sin(θFNB ) cos(θ0).

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2.2 Antenna array pattern synthesis 17

Figure 2.3: Normalised array pattern behaviors along the azimuthal plane (θ = 90o).

2.2.2 Circular array pattern synthesis

The main advantage of using a circular array conﬁguration is represented by its symmetry on the plane where the array is deployed. As a result, the pattern characteristics do not present an high variation while the beam is electronically steered. For this reason, the circular arrays are particularly suited for applications that require a 360o coverage as it is for direction ﬁnding systems, auxiliary antennas, communication bridges and so on. In Fig.2.4 the typical geometry of an N elements circular array is shown. By following similar steps to the ones which have led to the representation of the array factor

for the linear array case, the Rn distance between the n-th array element and the observation point in the far ﬁeld region is equal to:

p 2 2 Rn = R + a − 2aR cos ξn, (2.26)

being a the array radius and R the distance between the array center and the point

where the electric ﬁeld is measured. Considering that R a, Rn can be approximated in the following way:

Rn ' R − a cos ξn = R − a(ˆar · aˆn)

= R − a(ˆax cos φn +a ˆy sin φn)

·(ˆax sin θ cos φ +a ˆy sin θ sin φ +a ˆz cos θ)

= R − a sin θ cos(φ − φn), (2.27)

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18 2. Antenna theory and array pattern synthesis

R q Rn

xn y fn an n 1 2 f x

Figure 2.4: Circular antenna array geometry.

2π where φn = N (n − 1). The complex excitation coeﬃcients that are used to perform both the shaping and the steering of the array pattern can explicitly be written as:

jαn wn = Ine . (2.28)

By considering (2.15), (2.27) and (2.28), the array factor in the circular array case is then given by: N X j[ka sin θ cos(φ−φn)+αn] F (θ, φ) = Ine . (2.29) n=1

The synthesis of the array pattern towards a speciﬁc direction (θ0, φ0) can be obtained by selecting αn = −ka sin θ0 cos(φ0 − φn) and it consequently follows that:

N X jka[sin θ cos(φ−φn)−sin θ0 cos(φ0−φn)] F (θ, φ) = Ine . (2.30) n=1 The pattern of the array factor for an 8-elements Uniform Circular Array (UCA),

having therefore ∀In = 1, is presented in Fig.2.5, whereas the cuts along the azimuthal and the elevation planes are shown in Fig.2.6 The ﬁrst sidelobe in the UCA case shows a relative amplitude of −7.9dB, which is the typical value for this class of arrays. A traditional way to perform the analysis and the pattern shaping of UCA systems is

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2.2 Antenna array pattern synthesis 19

Figure 2.5: 3D view of the array factor for an 8-elements UCA (linear scale).

Figure 2.6: Array factor for an 8-elements UCA along the azimuthal (θ = 90o, left) and the elevation (φ = 0o, right) planes.

based on the phase modes theory, which will be presented in Sec.3.3.1. By exploiting that representation, in [37,38] an extensive analysis of the parameters selection, which allows avoiding distortions of the synthesised pattern, is conducted. Speciﬁcally in [38], the condition to prevent the grating lobes is proven to be:

λ d < (2.31) 2

being d the element spacing on the circle.

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2.3 Pattern synthesis in non ideal arrays

The array pattern analyses, which have been presented in Sec.2.2.1 and Sec.2.2.2, are based on the ideal behavior of the array manifolds. However, real arrays are aﬀected by diﬀerent sources of errors that introduce degradations in terms of sidelobes level, pointing accuracy and angular resolution of the synthesised pattern. Although it is possible to compensate for some of these errors, as it is described in Sec.2.3.1 and with more details in Sec.3.2, proper design choices are required in order to overcome the physical limitations produced by the random error distributions of the system, which cannot be corrected. This case is analysed in Sec.2.3.2 and it is extended in Ch.5 for a particular type of arrays.

2.3.1 Mutual coupling

The expression retrieved in (2.13) is based on the assumption that the element pattern is the same for all the radiators. However, the gain of an isolated element may substantially vary when the same element is placed inside an array. This gain variation also depends on the specific location of the radiator: the behavior at the edges of the structure is quite different from the one in the center. For this reason, a reliable evaluation of the array pattern behavior cannot be exempted from the assessment of the mutual electromagnetic influences, which are usually referred to as Mutual Coupling (MC) [39,40], among the array radiating elements. The element pattern affected by MC can be written as the product between the

expected ideal pattern fi(θ, φ) and a spatial factor that accounts for the coupled element contributions [4]:

" # X −jk(~rm−~rn)ˆr fn(θ, φ) = fi(θ, φ) 1 + Snme , (2.32) m

being Snm the scattering coefficient [41]. The pattern in (2.32) is measured in a controlled environment and by transmitting with the n-th element while all the other elements are closed on matched loads. The total coupling effect is quantified by collecting all the scattering contributions in the so called MC matrix [42, 43], which is then used to retrieve the ideal behavior of the array pattern [44–47]. Due to its dependance on several parameters, it is preferable to perform the direct measurement of the MC matrix instead of predicting its coefficient values. In Ch.3 a novel technique aimed at estimating the MC matrix is presented with respect to the case of a circular array in an interfering environment.

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2.3 Pattern synthesis in non ideal arrays 21

2.3.2 Illumination errors An array illumination distribution, which is aimed at providing a very low sidelobes array pattern, may result in a poor SLR because of the presence of amplitude and phase errors introduced by the array imperfections [2, 4]. This type of errors, which are caused by the tolerance and quantization limits of the array devices (feeding network, phase shifters, element orientations and positions, ...), can be treated as a random and uncorrelated process7. The sidelobes level degradation is produced by the random sidelobes that are generated and that add to the expected ones. If the errors for the N elements array are assumed to be independent but identically distributed, and by referring to the linear array case, the AF aﬀected by illumination errors can be written from (2.15) as:

N−1 X −j(knd sin θ+δφn) Fe(θ) = an(1 + δn)e , (2.33) n=0

where δn and δφn are the fractional amplitude and phase errors associated to the n-th element respectively. The AF is now a random variable and it depends on the

statistical distributions of δn and δφn. The mean value of the AF is:

N−1 N−1 X −jknd sin θ −jδφn X −jknd sin θ −jδφn hFe(θ)i = ane e + hδni e e , (2.34) n=0 n=0 where the second addend in the sum is equal to zero if the presence of systematic errors is avoided, i.e. the random processes are not biased. The ﬁrst contribution represents the product between the ideal AF and the characteristic function8 evaluated in ω = 1. For a uniform phase error distribution: 1 p(δφ ) = rect (δφ), (2.36) n ∆φ ∆φ (2.33) can then be written as:

sin(∆φ) hF (θ)i = F (θ) . (2.37) e ∆φ With respect to the ﬁeld intensity, which is proportional to the array factor as shown in (2.13), it is clear from (2.37) that the eﬀect of the illumination errors only consists

7For an extended analysis, the correlated errors case could also be considered and it would result in higher sidelobes at ﬁxed locations [2]. 8The characteristic function is deﬁned as: Z −jωx −jωx C(ω) = e = e px(x)dx. (2.35) .

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of a little attenuation of the expected ideal pattern. In the case of the power pattern, which is related to the radiation intensity through (2.2)-(2.3), its representation can be retrieved by taking the average value of the product between (2.33) and its complex conjugate value:

D 2E ∗ |Fe(θ)| = hFe(θ) · Fe (θ)i . (2.38)

The solution of (2.38) has been ﬁrstly retrieved in [48], then further investigated in [49, 50]. Here the ﬁnal expression is provided:

D 2E 2 2 2 |Fe(θ)| = |F (θ)| + δn + δφn ηi. (2.39)

An extension to the case of virtually synthesised arrays is retrieved in Ch.5, where also more details about the analytical solution are given. The average power pattern that is shown in (2.39) is the sum of two contributions: the ideal power pattern and a term depending on both the amplitude and the phase error distributions. It can be observed that it is independent of the angular coordinates whereas it is directly

proportional to the illumination eﬃciency ηi. According to the mentioned characteristics, the second term in (2.39) introduces a uniform rise of the sidelobes level all over the angular domain of the pattern; the eﬀect is however of minor relevance in the main beam and in the near sidelobe regions [49]. It is also of interest to observe that, by referring to (2.25) which shows a 1/N dependency with the array elements number, the larger the number of elements, the lower will be the degradation of the sidelobes produced by the illumination errors.

2.4 Summary

The aim of this chapter was to provide the basic theoretical notions that allow describing the behavior of an antenna in both the isolated and the array configuration cases. Attention has been given to the characterisation of the array pattern synthesis for the linear and the circular array structures. At first, the ideal pattern behaviors have been retrieved and the expected performance in terms of beamwidth, characteristic sidelobes level and shape have been discussed. Secondly, the main causes of pattern degradation at both the antenna level (MC) and the system front end (illumination errors) have been presented. These analyses pave the way for the system investigations in Ch.3, Ch.5 and Ch.6 where real radar demonstrators based on the above mentioned configurations are considered.

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Chapter 3

Digital beamforming for PCL

The signal processing steps required by a radar system are multiple and they have to deal with the receiver chain at different levels. A first distinction can be done on the basis of the analog and the digital sections that are involved. The first one, which is mainly based on the front-end system architecture, will be analysed in the next chapter. Here the attention is focused on the description of the digital processing blocks that represent the back-end part of the system. A further distinction is required. The digital section can indeed be considered as composed by two different macro blocks: the one belonging to the DBF processing, which is tailored on the specific array characteristics, and the one related to the conventional signal processing steps of the radar system. In this chapter, the entire attention is given to the analysis of the implemented DBF procedures for the PCL system, which represents the core of the research activity. However, in order to fully characterise the system performance, also the remaining signal processing steps have been implemented and they will be shown in Ch.41.

3.1 Digital processing scheme

A sketch of the digital processing steps that are involved in the PCL system operations is presented Fig.3.1. The sub-division into the two macro-blocks referred to as the DBF and the speciﬁc radar signal processing is also highlighted. With respect to the DBF part, the ﬁrst operation is aimed at compensating for the MC interactions among the antennas of the circular array. The non ideal behavior of the receiver elements is corrected by means of the estimation of the MC matrix. This operation is considered as a part of the DBF section since it allows the application of the beamforming algorithms, which otherwise would not provide the expected performance.

1This chapter is based on articles [J1], [C8], [C9] and [R1] (a list of the author’s publications is included at the end of this dissertation, p. 141).

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24 3. Digital beamforming for PCL

Figure 3.1: Digital signal processing scheme of the PCL radar.

Specifically, a method for the sidelobes shaping is proposed and the related results are compared with a well established technique, which is especially tailored for circular array patterns. The pattern shaping technique, in conjunction with the digital steering, is used to retrieve the reference and the surveillance channels of the system. While the surveillance beam is synthesised, a digital null is placed in the direction of the reference transmitter. The spatial nulling is part of the Direct Path Interference (DPI) suppression, which is aimed at reducing the jamming effect of the direct signal in the surveillance channel, and it represents the last step of the processing referred to as the DBF. The overall signal processing chain is then completed by: a digital filtering operation, based on the Least Mean Squared (LMS) principle, which integrates the spatial DPI nulling; the Matched Filter (MF), based on the cross correlation between the surveillance and the reference channels; the Constant False Alarm Rate (CFAR) thresholding that provides the output target detections.

3.2 Mutual coupling compensation

Most of the MC compensation techniques require either a detailed knowledge of the electrical characteristics of the antenna [51], or the possibility to measure them in a controlled environment, e.g. an anechoic chamber, [52, 53]. The former case, as it is highlighted in Sec.4.2.1, cannot be considered due to the lack of information about the commercial components of the reference system; the latter one, due to the size of the entire structure, is not applicable either. The compensation technique that is proposed in this section, in order to overcome the mentioned issues, is based on measurements aimed at obtaining a preliminary estimation of the MC matrix. Then, a further reﬁnement is obtained by means of an optimisation approach.

3.2.1 Analytical description In real arrays, the element pattern is aﬀected by the neighboring elements and, if we refer to a circular array, it is an angular function of the element position. By recalling

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3.2 Mutual coupling compensation 25

the characterisation presented in Ch.2, the far-ﬁeld array pattern for a N-element circular array can be written as:

N X jkr cos(φ−φn) P (φ) = anfn(φ − φn)e . (3.1) n=1 The dependency with the elevation angle θ is omitted for simplicity. Similarly to [42], the total received voltage at the m-th element can be written as a weighted sum of the contributions of all the array elements:

N X vm(φ) = cmmEmfi(φ − φm) + cmnEnfi(φ − φn) n,n6=m N X = cmnEnfi(φ − φn), (3.2) n=1

being Em the electric ﬁeld which excites the m-th element port and fi the ideal element pattern. The mutual coupling coeﬃcient cmn therefore represents the proportionality term that relates the induced voltage on channel m to the total voltage on channel n. The desired voltage on channel m is then given by:

d vm(φ) = Emfi(φ − φm). (3.3)

jkr cos(φ−φm) If we compare (3.2) and (3.3) and by taking into account that Em = Em0 e we obtain the same expression as [42] for the linear case which relates the desired voltage signal and the real (aﬀected by mutual coupling) one. By means of matrix notation it can be written as:

     d  v1 c11 c12 . . . c1N v1 d  v2   c21 c22 . . . c2N   v2    =   ·   , (3.4)  .   . . . .   .   .   . . . .   .  d vN cN1 cN2 . . . cNN vN or in a more compact way as: vd = C−1v. (3.5) The MC matrix C can be written as a function of the antenna scattering parameters S [4, 41]: C = S + I, (3.6) where I is the identity matrix. The evaluation of the coupling coeﬃcients in (3.5) can be performed in an analytical or numerical way, depending on the antenna type and the array conﬁguration [29].

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26 3. Digital beamforming for PCL

If we refer to real systems, the eﬀect of the feeding network and the analog/digital front-end must also be considered, since it introduces discrepancies with respect to the conventional representation. By considering the cables section as a reciprocal and isolated structure, its contribution on the MC matrix can be modeled by a diagonal matrix T of the transmission coeﬃcients2. From (3.6) we have:

C = T(S + I). (3.7)

Equation (3.7) fully describes the matrix term which must be applied in order to compensate for the non ideal behavior of the analog section of the system. Since the presented correction is applied in the digital domain, e.g. after digital conversion of the received signals, the eﬀect of the phase and amplitude errors introduced by the digital receiver should also be taken into account. The ﬁnal correction matrix can then be expressed as the following product:

C = P[T(S + I)], (3.8)

where P is the digital section compensation matrix.

3.2.2 Optimisation approach for the C matrix evaluation The expression retrieved in (3.8) is valid when no other signal sources, which can generate local interferences to the radiation pattern, are present at the array location. However, the environment in which the TNO passive radar is located, the top of the tower at The Hague laboratory, is heavily affected by multipath due to the presence of several large metallic structures. Moreover, the FM signals coming from the local radio stations produce additive interferences and, as a consequence, an inaccurate measurement of the main components of the MC matrix. For this reason, the C matrix coefficients have been refined by means of an optimisation approach. As proposed in [54], a reference transmitter has been moved around the PCL, at distances ensuring the far field condition, and the signals from the known positions have been acquired. For a far field monochromatic source, the received data vector can be written as: x(t) = C[sa(t) + n(t)], (3.9) where a(t) is the amplitude of the received signal and n(t) the noise realisation vector. The quantity s represents the steering vector of the array that, on the azimuthal plane

and for an angle of arrival φm, takes the form:

s = [ejkr cos(φm), ejkr cos(φm−φ1), ..., ejkr cos(φm−φN−1)]T , (3.10)

2The transmission coefficients represent the attenuation and the phase offset values to which the signals propagating in the cables are affected.

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3.3 DBF for circular arrays 27

T where (·) is the transposed operator. As mentioned before, the φm value is known. By considering M transmission points, all of them characterised by the same C matrix, the following objective function can be written:

M X 2 O(C, a1, a2, ..., aM ) = kxm − Csmamk (3.11) m=1 which represents a non linear system of equations whose unknowns are the signal am-

plitudes [a1, a2, ..., aM ] and the coupling matrix elements in C. The xm vector is the collected data vector having the reference transmitter at the m-th location around the array. A Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi Newton method [55, 56] has been applied to minimise the objective function in (3.11). In order to facilitate the optimisation process, the values of C have been initialised according to the preliminary estimation provided by (3.8).

3.3 DBF for circular arrays

In passive radar applications the requirement on the SLL can be a very stringent constraint, when considering that the ratio between the reference signal and a target echo can be in the order of 90dB or more. Thus the patterns obtained in the previous section are not able to satisfy it. A further reduction can be achieved by means of a non uniform tapering on the array channels. Several DBF techniques for circularly shaped phased arrays are based on phase mode excitations theory [57–60]. Such theory aims at synthesising a virtual uniform linear array that can then be weighted with conventional tapering functions. However, the synthesis of the linear array results in a degradation of the pattern beamwidth and often in an illumination efficiency loss. If the second consequence can still be tolerated in PCL radars, thanks to the power strength of the signal which are exploited, a further deterioration of the angular resolution of the system should be avoided. To this aim a novel sidelobes shaping technique has been developed. The regions of interest of the circular array pattern are identified by an optimisation mask, as it is proposed in [54]. Then, the closed form analytical expression for the optimal beamforming vector is retrieved. The phase modes theory is briefly presented in Sec.3.3.1 whereas in Sec.3.3.2 the proposed technique is discussed and the comparisons of the two methods are illustrated.

3.3.1 Phase modes theory A well known technique for the array pattern shaping of circular and cylindrical arrays is based on the phase modes theory. The array pattern of a circular array is a periodic function in the interval [0, 2π] and this characteristic allows representing it in terms

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28 3. Digital beamforming for PCL

of a complex Fourier series. Referring to (3.1) we can write:

∞ ∞ X X jpφ P (φ) = = Pp(φ) = Cpe , (3.12) p=−∞ p=−∞ being: Z π 1 −jpφ Cp = P (φ)e dφ. (3.13) 2π −π Each term of the series in (3.12) is normally referred to as phase mode of the radiation pattern [1] and it has a 2pπ phase variation as φ varies from 0 to 2π. From (3.12) it

follows that, in order to synthesise a directional far field pattern Pp(φ), a p-th order jpφ phase mode e must be produced in the far field. The Cp coefficients can generally be evaluated as a sum of the an excitations, but that sum cannot be solved in a closed form for all the an. However, a specific set of symmetrical excitation currents can be identified [4] and computed as:

∞ ∞ X p X jpφn an = an = Ape . (3.14) p=−∞ p=−∞

The terms of the sum in (3.14) are referred to as the phase mode excitation currents. By combining (3.1) and (3.14), the p-th phase mode pattern takes the form:

N X jpφn jkr cos(φ−φn) Pp(φ) = Ape e . (3.15) n=1 By introducing the Bessel function approximation for the array factor exponential term and neglecting a constant term of no interest, (3.15) can be rewritten as:

p jpφ Pp(φ) ≈ Apj Jp(kr)e , (3.16)

where Jp(·) is the ﬁrst kind Bessel function of order p. The behavior of the Bessel functions, which is shown in Fig.3.2, also introduces a limitation on the maximum number of phase modes that can be excited on the array. Decreasing rapidly to zero when the order of the function exceeds its argument, the maximum phase mode order is estimated as the maximum value of the argument which is: P = bkrc.

The Ap coefficients can now be selected in order to synthesise the far field pattern of the array. By choosing the coefficients as:

e−jpφ0 Ap = p , (3.17) j Jp(kr) the array pattern resembles the pattern of a linear array [57]. The only diﬀerence is that, whereas in the linear case the azimuth scanning angle φ is related to a sin(·)

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3.3 DBF for circular arrays 29

FirstkindBesselfunctions 1 J (x) 0 J (x) 1 J (x) 2 J (x) 3 0.5 J (x) 4 J (x) 5

-0.5 0 2 4 6 8 10 X

Figure 3.2: First kind Bessel functions of diﬀerent orders.

function, providing therefore a possible steering sector of 180◦, in this case the scanning capability has no angular restrictions over the 360◦. This result is in accordance with the circular shape of the array. Referring to the N excitations that must be applied to the circular array, they can be evaluated by combining (3.14) and (3.17) and by considering the upper bound of the eﬀective number of phase modes that can be excited, it results:

P X ejp(φn−φ0) an = p . (3.18) j Jp(kr) p=−P

The tapering introduced by (3.18) produces a virtual transformation of the circularly shaped array into a linear array structure, resulting in a SLL of −13dB. A secondary eﬀect resides in the possibility of over imposing a conventional tapering window in order to further reduce the SLL.

3.3.2 Proposed algorithm The array factor of the UCA that has been introduced in Ch.2, can be written according to (3.10) in the compact form:

F (φ) = sH a(φ), (3.19)

where a(φ) = [ejkr cos(φ), ejkr cos(φ−φ1), ..., ejkr cos(φ−φN−1)]T (3.20) represents the array manifold and the superscript (·)H is the Hermitian operator. The angular behavior of the array factor is characterised by the presence of three diﬀerent

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30 3. Digital beamforming for PCL

Figure 3.3: Normalised UCA pattern and mask function fd(φ) of the desired pattern behavior.

regions: the sidelobe, the transition and the main beam regions. In accordance with

the angular location of these sectors, it is possible to deﬁne a mask function fd(φ) that describes a desired array factor behavior. An example is given in Fig.3.3 where the generic UCA pattern for an 8 elements array with r = 0.48λ is also plotted. The aim of a digital beamforming procedure is to identify the steering vector that, at the same time, minimises the contribution from the side lobes and focuses the energy into the main beam region without a considerable degradation of the angular resolution. If the mask function is taken as the objective of the pattern synthesis, the previous conditions can be expressed by the following minimisation:

H 2 O(s) = min{ks a(φ) − fd(φ)k }. (3.21) s

The eﬀect of the minimisation in the sidelobes region can be emphasised by a diagonal matrix of weights Λ; thus (3.21) can be rewritten as:

H H H O(s) = min{[s a(φ) − fd(φ)]Λ[s a(φ) − fd(φ)] } (3.22) s

and by omitting the dependency with the angle φ:

H H H H H H O(s) = min{s aΛa s − s aΛfd − fdΛa s + fdΛfd }. (3.23) s

This approach, for the sidelobe shaping of a UCA pattern, was proposed in [54]. In that case, the steering vector was obtained by applying a numerical optimisation approach similar to the one presented in Sec.3.2.2. Here, a closed form expression for the optimal beamformer is retrieved. As a function of the steering vector s, which is the only unknown in the second term of (3.22), the desired minimisation argument is obtained by imposing the equality to

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3.3 DBF for circular arrays 31

zero of the gradient [61, 62]:

H H ∇s∗ O(s) = aΛa s − aΛfd . (3.24)

From (3.24), and by writing: aΛaH = R, (3.25) the ﬁnal expression of the UCA steering vector takes the form:

−1 H s = R aΛfd . (3.26)

3.3.3 Array pattern comparisons Different Λ functions have been applied, according to (3.26), providing different sidelobe reduction (SLR) levels. Results of the DBF algorithm, for two circular arrays with different radius lengths, are presented in Fig.3.4, whereas the 3dB beamwidth apertures of the synthesised patterns, with respect to the unweighted UCA excitations, are summarised in Tab.3.1. The radius of r = 0.36λ has been chosen as a comparison term as it shows, among the analysed cases, the best angular resolution of the array pattern. It is interesting to observe that for r = 0.36λ the implemented DBF algorithm produces a slightly better angular resolution than the uniformly weighted case. On the other hand, an array radius of 0.48λ is still preferable w.r.t. the mutual coupling for the reasons that will be discussed in Sec.4.2. The phase mode weights, with additional tapering windows, have also been applied to the circular arrays with different radius presented in the previous paragraph. In Fig.3.5 the obtained array patterns are shown whereas a comparison between the

0 0

-10 -10

-20 -20

-30 -30

-40 -40

-50 -50

Normalisedpattern[dB] -60 Normalisedpattern[dB] -60 UCA Pattern UCA Pattern -70 19dBSLR -70 19dBSLR 23dBSLR 23dBSLR 27dBSLR 27dBSLR -80 -80 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Azimuthangle[°] Azimuthangle[°] (a) (b)

Figure 3.4: Results of the proposed side lobe reduction method for a (a) UCA with radius r = 0.48λ, (b) UCA with radius r = 0.36λ.

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32 3. Digital beamforming for PCL

Table 3.1: Azimuthal resolution performance Uniform Tapering Proposed Tapering SLR −8dB −19dB −23dB −27dB r = 0.36λ 57.6o 41.6o 45o 50.2o r = 0.48λ 43o 43o 46.7o 51.2o

angular resolutions realised with the phase mode excitations and the tapering of the proposed DBF algorithm is listed in Tab.3.2. In both cases, for the diﬀerent values of the radius length, and for all the obtained SLL reductions the proposed DBF method provides better angular resolutions than the phase modes technique. A visual example of the resolution improvement is illustrated in Fig.3.6. The array patterns synthesised with the phase modes algorithm and the proposed DBF technique, in the case of r = 0.36λ and for an SLL=−19dB, are shown. In order to further asses the validity of the proposed pattern synthesis

0 0

-10 -10

-20 -20

-30 -30

-40 -40

-50 -50

Figure 3.5: Results of the phase modes side lobe reduction method for a (a) UCA with radius r = 0.48λ, (b) UCA with radius r = 0.36λ.

Table 3.2: Angular resolution comparison for diﬀerent SLL taperings SLL reduction Array radius Algorithm −19dB −23dB −27dB Phase Modes 53.2o 56.2o 59o r = 0.36λ Proposed DBF 41.6o 45o 50.2o Phase Modes 55.7o 58.4o 60.9o r = 0.48λ Proposed DBF 43o 46.7o 51.2o

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3.3 DBF for circular arrays 33

Figure 3.6: Comparison between the phase modes and the proposed DBF technique syntheses of a circular array pattern with radius r = 0.36λ and SLL=−19dB.

method, the taper eﬃciency of the array weights is also evaluated in the two cases.

Being the illumination eﬃciency ηi deﬁned as:

PN 2 ( n=1 |an|) ηi = , (3.27) PN 2 N n=1 |an|

the results for all the considered configurations are shown in Tab.3.3. With reference to the depicted values, the proposed algorithm shows an improvement in terms of angular resolution “gain” which is, on average, equal to 14.4%; at the same time, the illumination efficiency is, also on average, 5.3% lower than the phase modes one. For the application purpose, due to the poor directivity of the circular array pattern, an improvement of the angular resolution is preferable. The quality of the proposed method is then confirmed. For the following processing steps, the tapering mask that ensures an SLL reduction of -19dB has been used.

Table 3.3: Illumination eﬃciency comparison for diﬀerent SLL taperings SLL reduction Array radius Algorithm −19dB −23dB −27dB Phase Modes 0.97 0.97 0.98 r = 0.36λ Proposed DBF 0.82 0.89 0.93 Phase Modes 0.81 0.83 0.84 r = 0.48λ Proposed DBF 0.82 0.81 0.76

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34 3. Digital beamforming for PCL

3.4 Direct path interference suppression

The Direct Path Interference (DPI) reduction is based on two diﬀerent steps: the synthesis of an adapted pattern with a null in the direction of the reference illuminator and a digital ﬁlter which provides the further reduction of the DPI signal. If the absence of targets is initially considered and according to [2]:

x(t) = [v1, v2, ..., vI ]a(t) + n(t) = Va(t) + n(t), (3.28)

T where x(t) = [x1(t), x2(t), . . . , xN (t)] is the N channels received signal data vector, vi represents the steering vector related to the i-th interference, a(t) is the vector of the interference amplitudes and n(t) the vector of noise realisations. The interference source directions are then collected into the V matrix which is not necessarily a full rank matrix. The modeling of the environment depends on the representation of the data covariance matrix:

M = < x(t)xH (t) >=< [Va(t) + n(t)][aH (t)VH + nH (t)] > H H 2 H 2 = V < a(t)a (t) > V + σnI = VPV + σnI, (3.29)

2 being P the covariance matrix of the interference sources complex amplitudes and σn the noise variance, which is assumed to have a gaussian distribution. The interference rejection in the array subspace is achieved by including the inverse of (3.29) into the surveillance channel signal acquisition:

H −1 xs(t) = s M x(t). (3.30)

The expression of M−1 can be evaluated in a closed form. By applying the Sherman- Morrison-Woodbury3 formula, from (3.29) we have:

" −1 # −1 1 VP 1 H H M = 2 I − 2 I + 2 V VP V σn σn σn

1 h 2 H −1 H i = 2 I − VP σnI + V VP V σn 1 h 2 −1 H −1 H i = 2 I − V σnP + V V V . (3.31) σn Thanks to the broadcasting channel selection procedure, which will be shown in Sec.4.3.2, the presence of a single source of interference can be assumed. As a conse-

3(A + UVT )−1 = A−1 − A−1U(I + VT A−1U)−1VT A−1.

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3.5 Summary 35

quence, (3.31) can be simpliﬁed:

" 2 −1 # −1 1 σn H H M = 2 I − v 2 + v v v σn σI   1 vvH = 2 I − 2  σ σn H n 2 + v v σI 1 INR H = 2 I − H vv , (3.32) σn 1 + INRv v

2 where σI is the interference (broadcaster) power and INR is the Interference to Noise Ratio. Experimental results of the DPI suppression by means of pattern nulling are presented in Ch.4.

3.5 Summary

The chapter has introduced the digital processing chain of a PCL system with DBF capabilities. The core of the analysis has regarded:

• an advanced calibration procedure for the circular array in an interfering environment. The novelty of the technique is represented by the exploitation of two sequential steps: a measurement phase and an optimisation algorithm. The former comprises both internal and external data acquisitions, aimed at retrieving a preliminary evaluation of the system non ideal behavior. The latter exploits that estimation in order to obtain a reﬁned version of the MC matrix.

• an original DBF method for the array pattern shaping. The related results have been compared with the phase modes approach, an algorithm speciﬁcally tailored for circular arrays. The proposed tapering technique ensured better results in terms of angular resolution of the synthesised patterns, whereas a negligible reduction of illumination eﬃciency has been calculated.

The steps regarding the signal processing, which is required by the passive radar system, will be taken into account in Ch.4, together with the experimental results that have been achieved. However, a relevant consideration about the proposed DBF steps can already be drawn: the achieved angular resolution, when only DBF is applied, is obviously below the standard expected from a surveillance radar system. An obvious improvement from this point of view can be represented by the exploitation of high resolution techniques based on either monopulse or spectral estimation approaches.

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36 3. Digital beamforming for PCL

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Chapter 4

PCL radar description and experimental results

The chapter provides a functional description of the PCL system that has been designed and developed at TNO. A detailed analysis of the antenna array is conducted from both the element pattern and the array configuration perspectives. The FM analog receiver is then presented and the multiple RF components are depicted. Considerations about the degradation of the receiver noise figure, which can affect the passive radar system in presence of strong input signals, are highlighted. Experimental results, obtained by applying the MC compensation and pattern shaping techniques that have been presented in Ch.3, are illustrated. At last, the remaining steps of the signal processing chain, which lead to the target detection and the plot extraction, are considered. Suggestions for future system improvement and final remarks about the PCL design are outlined in the concluding section of the chapter1.

4.1 Overview of the PCL system

The PCL system, which is the object of the research study, can be described by taking into account the three main sections into which it is divided and that are illustrated in Fig.4.1. The antenna section, which performs the acquisition of the FM signals and is deeply described in Sec.4.2, consists of a circular array of 8 half-wavelength dipoles. Each dipole has an independent receiving channel; all the amplifying and ﬁltering stages are integrated into Printed Circuit Board (PCB) inside the analog receiver rack (Sec.4.3). The rack also contains the power supply component and the

1This chapter is based on articles [J1], [C8], [C9] and [R1] (a list of the author’s publications is included at the end of this dissertation, p. 141).

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38 4. PCL radar description and experimental results

ReceiverunitCh1 1 Ch1 Ch2 Ch3 ICS-554B Ch4 Data AcquisitionBoard1

ReceiverunitCh4 Clock 4

ReceiverunitCh5 5 Ch5 Ch6

Antenna Array Ch7 ICS-554B Ch8 Data AcquisitionBoard2

ReceiverunitCh8 Clock 8

A/DConversionon Samplingclockunit PCboard

PowerSupply

AnalogReceiver

Figure 4.1: Block diagram of the PCL system.

clock unit. The sampling clock is buﬀered and split into two (amplitude and phase equal) signals for both the four-channel ICS-554B digitiser PC boards [63]. The board speciﬁcations are listed in Tab.4.1. The boards are directly mounted on a separate workstation where all the digitised data are collected. The signal processing is then performed on a separate machine.

Table 4.1: ICS-554B digitiser board speciﬁcations Type ICS-554B Input impedance 50Ω SMA Full scale input level 1.2Vpp 5.56dBm in 50Ω Number of bits 14 Analog bandwidth 2-200MHz -3dB bandwidth Minimum sampling rate 30MHz Maximum sampling rate 100MHz Clock input level -3...+6dBm

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4.2 Antenna array analysis 39

4.2 Antenna array analysis

The analysis of the array characteristics regards both the single radiating element, the element behavior in the array setup and the array pattern synthesis taking into account the overall structure. The antenna array in Fig.4.2 consists of 8 half-wavelength dipoles, produced by Aldena [64], that are placed in a circular configuration. The dipole bandwidth defined with respect to a return loss of 10dB is about 19% centered at the operating frequency within the FM band (88-108MHz). Each dipole is equipped with a Gamma match [29] that allows a fine tuning of the input impedance to optimise the matching at the reference frequency. This feature is useful when the antenna is inserted into an array environment because the MC affects the antenna input impedance. The dipoles have been tuned to operate at 96.8MHz, the broadcast frequency of Radio 3 in the Netherlands, which has been selected as emitter of opportunity due to its high transmitted power (100kW).

4.2.1 Array element characterisation

Since the exact characteristics of the selected antenna were not disclosed by the manu- facturer, simulations were carried out using a Finite Diﬀerence Time Domain (FDTD) based commercial software package: CST Microwave Studio [65]. A dipole of radius r = 0.003λ and length l = 0.45λ, where λ = 309.93cm at the frequency of 96.8MHz, was considered for the simulations. The dipole was fed with an ideal discrete edge port with 50Ω input impedance. Fig.4.3.(a) shows the calculated radiation pattern of the dipole oriented along the z-axis. The cut along the elevation plane, considered for φ = 90◦, is presented in Fig.4.3.(b). The antenna is matched with a return loss of 10dB in the frequency band 91.9-105MHz centered at 97.85MHz (13% band), and it has a maximum gain of 2.02dB.

Figure 4.2: TNO circular array for passive radar applications.

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40 4. PCL radar description and experimental results

0 −30 30

−60 60

0 −10 −90 90

−120 120

−150 150 180

(a) (b)

Figure 4.3: Simulated element pattern gain of a stand alone dipole considered as a single radiating element using CST: (a) 3D plot and (b) cut along the elevation plane (φ = 90◦).

The stand alone behavior depicted in Fig.4.3 changes when the radiating element is part of an array. A discriminating factor is represented by the array radius: the shorter is the radius with respect to the wavelength, the more directive the element pattern, but the higher is the MC. The last effect introduces a degradation in the element pattern behavior that has to be evaluated before applying any digital beamforming scheme. Different array configurations have been investigated by taking into account both the EM behavior of the structure and the following signal processing steps, as discussed in Ch.3. The multiple aspects have been analysed and as a result of this trade-off a radius a = 0.48λ was chosen. The simulated element radiation

0 −30 30

−60 60

0 −10 −90 90

−120 120

−150 150 180

(a) (b)

Figure 4.4: Simulated element pattern gain of a single dipole in the circular array conﬁguration using CST: (a) 3D plot and (b) cut along the azimuthal plane (θ = 90◦).

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4.2 Antenna array analysis 41

-2

-4

-6

-8 Channel8 -10 Channel4 Channel6 -12 SimulatedPattern

-14

-16

Normalised elementpattern[dB] -18

-20 0 50 100 150 200 250 300 350 Azimuth angle[°]

Figure 4.5: Comparison between the measured element patterns for three diﬀerent array channels and the CST simulated data.

pattern, in the array configuration, is shown in Fig.4.4.(a). Due to the mutual interaction of the elements, the maximum gain of the single dipole changes from 2.02dB to 4.5dB. The simulation has been performed with a simplified geometry: the feeding network has not been taken into account and the dipoles have been fed with ideal lumped ports. In order to asses the validity of the simulation, measurements aimed at evaluating the element pattern of the real array system have been conducted at the reference frequency of 96.8MHz. The element pattern of the array elements has been characterised in an open air far-field measurement setup, by placing the array on a rotating platform and using a biconical dipole antenna as reference transmitter. A detailed description of the procedure is described in Appendix A whereas the results are presented in Fig.4.5. Three different array elements have been considered. The related element patterns have been aligned along the same pointing angle for an easy comparison. A good matching with the element pattern obtained with the CST simulation can be observed.

4.2.2 Circular array characterisation A preliminary analysis of the array pattern synthesis has also been performed at an early stage of the PCL system design. As the absolute gain of the element embedded in the array antenna could not be measured at the time of the element pattern characterisation, because a standard gain antenna was not available, an investigation aimed at qualifying the eight elements array gain was carried out. The ﬁnal array model used in the simulation is shown in Fig.4.6. It includes: a central mast with a metallic tripod, a circular ring that holds the dipoles and part of the concrete surface which supports the entire structure. At the PCL current location, the base of the system is surrounded by a square steel frame and this component has

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42 4. PCL radar description and experimental results

Figure 4.6: Array construction model used in the CST simulator.

also been introduced in the simulation. The inclusion of the mast was driven by the EM analysis of the array. It was noticed that the effect of the tripod on the element patterns resulted in a de-pointing of the array pattern towards the ground. Cause of the misalignment was the resonating effect of the tripod itself at the working frequency of the PCL. The extension of the mast above the plane of the array solved the de-pointing issue by reestablishing the correct radial pointing of the array pattern. The increase of the single dipole gain, which has been presented in Sec.4.2.1, is also influenced by the presence of the mast. Fig.4.7 presents the result of the simulated array pattern synthesis. The realised antenna pattern gain has a maximum equal to 9.6dB and if we consider the gain of the single element (4.5dB), it can be concluded that no more than 3 elements effec-

0 −30 30

−60 60

0 −10 −90 90

−120 120

−150 150 180

(a) (b)

Figure 4.7: Simulated circular array pattern gain using CST: (a) 3D plot and (b) “blue line”: cut along the azimuthal plane (θ = 90◦) “red line”: cut along the elevation plane (φ = 90◦).

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4.3 PCL receiver 43

tively produce a contribution to the array pattern synthesis. The simulated circular array pattern in Fig.4.7 is taken as reference in Sec.4.4.1 for the validation of the MC compensation algorithm presented in Ch.3.

4.3 PCL receiver

The signals received by the antennas are independently amplified and filtered by the 8-channel analog receiver in Fig.4.8. The analog chain was designed to be flexible and reliable in different working environments, also in presence of relatively strong unwanted signals. Main characteristic of the receiver is the frequency agility in the whole FM radio band (88-108MHz). Since the system does not perform analog down conversion to a lower frequency and the entire FM radio band is digitally converted, any transmitting channel can be acquired without any performance degradation. The sampling clock has been chosen in order to obtain a high sampling frequency, which is optimal for the digital processing, and to preserve the spectral purity during the

baseband conversion. A sampling frequency of fs = 80MHz proved to be a good choice for two reasons: from the theoretical point of view, the signal spectrum is

located between fs and the Nyquist frequency (fN = 120MHz) such that the under sampling also provides the down conversion to the baseband, and from the practical point of view, 80MHz components can be found off-the-shelf. The building blocks of each analog receiving channel are shown in Fig.4.9. They consist of: (1) a variable attenuator providing a maximum attenuation of 10dB, which can be introduced if very strong signals are expected at the input of each channel (this attenuator is not used in the current setup), (2) a 20MHz bandpass filter centered around 98MHz, that prevents intermodulation of strong incoming out-of-band signals with signals inside the FM-band; (3) a 10dB pre-attenuator that can be used to reduce the total gain of the receiver if the input signals were causing saturation of the ADC (this pre- attenuator is normally switched off); (4) a low noise amplifier, which provides 22dB

(a) (b)

Figure 4.8: Rack of the PCL system analog receiver: (a) front view (b) internal view.

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44 4. PCL radar description and experimental results

ON/OFF ON/OFF -10dB -10dB 22dB -6dB -10dB 22dB -6dB ATT ATT ATT ATT ATT 1 2 3 4 5 6 7 8 9 10

Figure 4.9: Block diagram of a receiving channel.

gain; (5) a high-pass filter with a cut-off frequency of 88MHz, which suppresses the signals on the low side of the FM-band; (6) a fixed 6dB attenuator, that isolates the high and low pass filter; (7) a low pass filter with a cut-off frequency of 108MHz, which suppresses the signals on the high side of the FM-band; (8) a 10dB post-attenuator to control the gain of the receiver. It does not severely influence the noise figure of the system; (9) a 22dB gain amplifier and (10) a fixed 6dB attenuator that has three purposes: preventing the digitiser from being damaged by too strong signals from the amplifier; improving the S11 at the output of the receiver and providing a short circuit protection to the receiver output.

4.3.1 Dynamic range analysis Passive radar systems are known for the needed relatively large Dynamic Range (DR). Transmitters of opportunity are used for the detection and the bistatic ranging of the targets and these transmitters are typically broadcast stations for television and radio. The direct signal from the transmitter of opportunity is much larger than the scattered signal from the object to be detected. Moreover, whereas in active radar systems the transmitted signal is known, in passive radar systems this signal is unknown and needs to be sampled just as the target signal. The receiver DR must be higher than the maximum Signal to Noise Ratio (SNR),

which is the ratio of the maximum received power Smax to the level of equivalent input thermal noise power N. For a wideband receiver, such that of TNO passive

radar, which is in principle sensitive to all FM broadcast stations, Smax is the sum of the power received from these stations: S DR = max , (4.1) N

with N = kT0BF where k is the Boltzmann constant, T0 is the standard temperature of 270K, B is the receiver bandwidth, F is the system noise ﬁgure. The Smax in (4.1) is computed as: ! X Smax = max Si , (4.2) time i

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4.3 PCL receiver 45

being: 2 PiGi(θ, φ)Gr(θ, φ)λ Si = 2 2 , (4.3) (4π) LRi

and it is calculated with respect to the transmitter parameters: gain Gi as a function of elevation θ and azimuth φ angles, transmitted power Pi, distance to the receiver Ri and atmospheric losses L. Considering the large amount of broadcast stations operating in urban environment (Fig.4.10), it appears from (4.3) that a high DR is required for any passive radar system. The DR of the signal is defined as the ratio (linear scale) or difference (dB scale) between the highest signal level and lowest signal level. Throughout the radar system these levels can change. This means that the DR can be different at the antenna from the DR at the ADC. In the following it is assumed that the DR of the hardware is sufficient in order not to influence the DR at the ADC input: 1dB compression levels are not reached and no third order intermodulation products are larger than the noise level. Then for the passive radar system at TNO, being the total FM band sampled at 80Ms/s and 14 bits and representing each bit a factor of two in amplitude or a factor of four (6dB) in power, a theoretical maximum DR of 84dB is available.

Power consideration about the broadcasting stations in the FM bandwidth The maximum signal level at the ADC input corresponds to the total power received in the FM-band at the passive radar location, a 40m high tower at TNO premises in The Hague. Multiple transmitters and multiple stations operate in the working band. In order to evaluate the impact of all these transmitters on the signal level, an oscilloscope was used to estimate the amplitude of the signals received from each dipole. The measurement of the 6-th channel is presented in Fig.4.10 where also the reference transmitter power has been highlighted. The average power levels have been measured for all the array channels and their values are listed in Tab.4.2. With reference to the analog channel analysis illustrated in Sec.4.3, the minimum gain provided

by the receiving channel is Gmin ≈6.5dB. According to the values in Tab.4.2 and by considering that the maximum input power to the ADC, in order to avoid clipping eﬀects, is 8dBm (by direct estimation) we concluded that at the current array location both available attenuators in the receiver had to be switched on during the data acquisition. From the radar point of view, this constraint has a high impact on the system per-

Table 4.2: Average power levels at the input of the analog receiver Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Ch. 6 Ch. 7 Ch. 8 Power (dBm) 2.54 1.34 2.46 2.73 2.78 -2.82 -6.49 0.38

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46 4. PCL radar description and experimental results

-45dBm

-10 -43dBm

-20

-30

-40

-50

Power[dBm] -60

-70

-80

-90

-100 85 90 95 100 105 110 Frequency [Mhz]

Figure 4.10: FM bandwidth input signals measured with the 6-th dipole of the array.

formance as the noise ﬁgure of the whole system is degraded to the value of 17dB. As a consequence, the detection sensitivity is also decreased due to the additional noise that is introduced. However, since the receiver hardware could not be modiﬁed, the reduced sensitivity was tolerated.

4.3.2 Digital down conversion Due to physical limitations in data handling and storage capacity of the digital section of the current system, the digitiser boards work in Digital Down Conversion (DDC) mode. The DDC performs a down sampling of the digitised signal by selecting a speciﬁc channel (96.8MHz carrier of FM3 radio from Lopik) within the ﬁltered spectrum. The output sampling rate of the DDC is 250ks/s that, by considering the 80Ms/s input data rate of the ADC, yields a decimation factor of 320. The introduced decimation is equivalent to a processing gain of 25dB that approximately corresponds to a gain in SNR and in DR of 25dB or 4 bits2. Therefore, the theoretically achievable DR after the DDC is 109dB (18 bits). A setback is that the suppression level of the

out-of-band signals, FDDC , although large is still ﬁnite. The out-of-band signals are suppressed at the DDC output by about 70dB (measured signal level relative to an injected out-of-band signal). By assuming a completely and

2A rigorous analysis should take into account that the noise component, after the ﬁltering stages described in Sec.4.3, has a uniform distribution only within the selected 20MHz of the FM spectrum. Indeed, the behavior outside the mentioned bandwidth depends on the combined response of both the low-pass and the high-pass ﬁlters. However, the residual out-of-band noise signal is weaker than the one inside, therefore the 25dB SNR gain can be assumed a conservative value.

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4.4 Experimental results 47

Power 1 P

88MHz 108MHz f

Nc channels (a) (b)

Figure 4.11: Representation of: a uniformly (a) and a sparsely (b) ﬁlled FM band.

uniformly ﬁlled FM band, Fig.4.11.(a), the maximum power reduction factor Fpow is given by:

FDDC (BFM − Bchannel) + Bchannel Bchannel Fpow = ≈ , (4.4) BFM BFM

where Bchannel is the bandwidth occupied by a single channel, selected by the DDC, and BFM is the whole FM bandwidth. However, the power distribution within the band of interest is not uniform, Fig.4.11.(b), and Nc separate equal-power channels can be distinguished. According to that, (4.4) becomes:

FDDC (Nc − 1) + 1 1 Fpow = ≈ . (4.5) Nc Nch

The Nc value was estimated by considering all the stations for which the received power, measured at the input of the analog receiver, was greater or equal to the

Lopik value minus 3dB. In our case this yields Nc = 20 and a reduction factor of about 13dB. Thus, after the DDC, the thermal noise is reduced by a factor of 320 while the maximum expected power is reduced by a factor 20. This corresponds to an increase in DR of a factor 16 (12dB) or 2 bits and not the expected increase of 4 bits from noise consideration alone. As a consequence, the actually available DR after the DDC is 96dB (16 bits).

4.4 Experimental results

4.4.1 MC compensation The experimental validation of the proposed technique for the MC compensation is based on a set of internal and external measurements. By referring to the ﬁrst ones, a network analyzer has been used to get the preliminary estimation of C, as

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48 4. PCL radar description and experimental results

-5

-10

-15

-20

-25 S -30 12 S 13 S -35 14 S 15 -40 S 16

Scatteringparameter[dB] S -45 17 S 18 -50

-55 90 92 94 96 98 100 102 104 106 108 110 Frequency[Mhz] (a) (b)

Figure 4.12: (a) Sxx scattering parameters for the 8 channels of the array , (b) S1x scattering parameters with respect to the ﬁrst element of the array.

it is presented in (3.7), with respect to the S matrix component. Since it was not possible to directly measure the scattering parameters at the input of the antenna elements, the contribution of the cables is included in the measurements that are shown in Fig.4.12. The plots highlight an overall behavior which is below -10dB in the bandwidth 88MHz-102MHz and below -8dB in the bandwidth 102MHz-108MHz. A frequency agility of the array elements could then be appreciated in the band of interest for the passive radar application. The estimation of the P matrix has been retrieved by connecting a stable transmitter to an 8-channels splitter. The output signals of the splitter have directly fed the

(a) (b)

Figure 4.13: (a) Relative (with respect to ﬁrst array channel) phase shifts after digital conversion, (b) Measured signal amplitudes after digital conversion.

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4.4 Experimental results 49

0 0 UncalibratedPattern UncalibratedPattern CalibratedPattern CalibratedPattern -5 TheoreticalPattern -5 TheoreticalPattern

-10 -10

-15 -15

-20 -20

Normalised pattern[dB] Normalised pattern[dB] -25 -25

-30 -30

-35 -35 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Azimuth angle[°] Azimuth angle[°] (a) (b)

Figure 4.14: Cartesian reference system comparison between the un-/calibrated and the theoretical patterns in dB scale for (a) transmission point 1 and (b) transmission point 2.

digital receiver. The amplitudes and relative phases of the measured digital signals are plotted in Fig.4.13. It can be observed that the amplitude variations among the different channels represents a negligible effect, which is in the order of 0.8dB at the reference frequency, whereas the measured relative phase shifts, which are produced by the sampling with two parallel boards, show an higher variation which is both frequency and channel dependent. The measurements in Fig.4.12 and Fig.4.13 have been used to initialise the algorithm for the minimisation of the objective function in (3.11). A total number of 6 locations around the array have been chosen and some results of the overall compensation are illustrated in Fig.4.14 for two different transmission points. Effects of the calibration include the removal of the pattern asymmetries and the reduction of the SLL to the expected theoretical value of -8dB. If we compare the obtained figures, differences between the compensated diagrams mostly affect the region far from the main beam pointing. Such discrepancies depend on both the variability of the multipath interferences with respect to the angular position of the transmitter, and the convergency of the optimisation algorithm that is mostly influenced by the main beam region, where the signal amplitudes are stronger.

4.4.2 Direct path interference suppression

As already pointed out in Ch.3, the whole DPI suppression procedure consists of two steps: the synthesis of a spatial null into the surveillance beam pattern in the direction of the reference transmitter; the application of a digital ﬁlter for the removal of the residual direct signal component inside the surveillance channel. The result of the achieved suppression level, thanks to the DBF nulling, is presented in Fig.4.15. The

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50 4. PCL radar description and experimental results

-10

25dB -20

-30

-40

Normalisedpattern[dB] -50

-60 UncalibratedPattern CalibratedPattern CalibratedPattern+SLR CalibratedPattern+SLR+Nulling -70 0 50 100 150 200 250 300 350 Azimuthangle[°]

Figure 4.15: Eﬀect of the DBF nulling procedure on the array pattern behavior.

figure also shows the calibrated array pattern, obtained by electronic steering, in the uniform excitations case and with the pattern shaping method proposed in Sec.3.3.2. The effective suppression provided by the DBF nulling, due to the width of the array pattern, is in the order of 25dB. For conventional processing scenarios, which at best allow using 1s of integration time for an effective bandwidth of 50kHz, the autocorrelation function of an FM signal is characterised by range/Doppler sidelobes at a level of 40-50dB. Given that the direct signal itself can be 80-90dB higher than the expected reflection from a real target, it is clear that a suppression of 25dB is not enough for the PCL system.

The further suppression of the residual reference signal xr(t), that according to the used notation can be expressed as:

H xr(t) = v x(t), (4.6)

in the surveillance channel xs(t), can be achieved by a digital filtering subtraction. The implemented filtering procedure is based on an adaptive Gradient Least Mean Squared (GLMS) filter [66–68] and, since the interference is not constant, the filter has to continuously adapt its coefficients to the interference variation. In the following description of the filter the discrete-time notation is used, with k as the time index. T At time instant k, the N tap delayed inputs xk = [xk, . . . , xk−N+1] of the reference T signal are fed to the filter with weights wk = [wk(0), . . . , wk(N − 1)] . The output

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4.4 Experimental results 51

signal at time k is then:

N−1 X ∗ H yk = wk(n)xk−n = wk xk. (4.7) n=0

If we define the error signal ek as the difference between the filtered signal yk and the desired signal dk ≡ xr(t):

H ek = dk − wk xk = dk − yk, (4.8) the interference cancelation is realised when (4.8) is minimal. In order to minimise

the error power, the weights vector wk is adapted according to the LMS optimisation algorithm: ∂ek H wk+1 = wk − δ ek = wk + δxk ek. (4.9) ∂wk

∂ek 1 2 Where the product ek represents the gradient of the function e and the scalar ∂wk 2 k term δ is called the learning rate of the filter. This learning rate depends on the variability of the signal which must be removed. Experimental tests have shown that a learning rate δ = 0.005 and a number of filter taps N = 48 are suitable values for the data set under test. Typical additional suppression provided by the filter with the mentioned characteristics is in the order of 30-40dB.

4.4.3 Range/Doppler processing The next step in the processing chain of the PCL is represented by the exploitation of the reference signal in order to perform the target detection inside the surveillance channel. By applying the conventional Matched Filter (MF) theory, the range/- Doppler maps of the target positions can be retrieved. In this section a brief summary of the theory is presented, whereas a more detailed description can be found in the referred radar literature [69, 70]. The optimum detector, in presence of white Gaussian noise, is represented by a ﬁlter with impulse response h(t) of the form:

∗ h(t) = Gas (T − t), (4.10)

being s(t) the signal we want to detect, T the delay of the ﬁlter, which is equivalent

to the signal duration, and Ga the arbitrary gain of the ﬁlter. In both the active and the passive radar cases, the signal to be detected is a delayed and Doppler shifted

copy of the reference signal xr(t):

j2πfD t s(t) = xr(t − τ)e . (4.11)

The ﬁlter output can then be evaluated as a function of the introduced delay and

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52 4. PCL radar description and experimental results

150

100

Bistatic range[km] 50

0 -200-150 -100 -50 0 50 100 150 200 Dopplerfrequency [Hz]

Figure 4.16: Matched ﬁlter output Range-Doppler map.

the Doppler shift; after normalisation it can be written as:

Z +∞ 2 2 ∗ −j2πfD t Z(τ, fD) = |z(τ, fD)| = xs(t)xr(t − τ)e dt . (4.12) −∞

The formulation in (4.12) shows that the MF receiver is equivalent to the Fourier transform of the product between the surveillance channel signal and a delayed conjugate version of the reference signal. The practical software implementation makes use of this equivalence. In Fig.4.16 the output of the MF is presented for an acquired data set of 1s duration. Multiple targets can be distinguished, with Doppler components not equal to zero, and they have been included highlighted in the dash-line circles. On the other hand, zero-Doppler detections can also be noticed in the ﬁgure and they are associated to multipath reﬂections of the direct signal coming from static objects.

4.4.4 CFAR detector and plots extraction The amplitude values of (4.12) have been passed through a CFAR detector based on the Greatest-Of (GO) principle [71]. The reference window size, in both range and Doppler dimensions, and the detection threshold were empirically estimated over diﬀerent range/Doppler maps at the output of the MF. The estimation led to a [17x17] window, having therefore M=8 cells on each side of the cell under test, with a

threshold κ0 = 6dB. The threshold value has been chosen to maintain the detection probability in view of the reduced sensitivity of the system caused by the degraded noise ﬁgure. The higher false alarm rate was tolerated. The outputs of the CFAR algorithm are shown in Fig.4.17.(a) and Fig.4.18.(a) for the range/time and range/Doppler cases respectively. The detection performance

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4.4 Experimental results 53

160 160

140 140

120 120

100 100

80 80

60 60

Bistatic range[km] Bistatic range[km]

40 40

20 20

0 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Time[s] Time[s] (a) (b)

Figure 4.17: GO-CFAR Time vs Range output map (a) and Overlapping of the CFAR detections with the ADSB available tracks data (b).

160 160

140 140

120 120

100 100

80 80

Bistatic range[km] 60 Bistatic range[km] 60

40 40

20 20

0 0 -400 -300 -200 -100 0 100 200 300 400 -400 -300 -200 -100 0 100 200 300 400 Dopplervelocity [m/s] Dopplervelocity [m/s] (a) (b)

Figure 4.18: GO-CFAR Doppler Velocity vs Range output map (a) and Overlapping of the CFAR detections with the ADSB available tracks data (b).

was compared with the track data provided by an Automatic Dependent Surveillance Broadcast (ADSB) transponder and recorded at the same time of the experiment. This technology is not yet available on all ﬂights that explains why only some of the detected tracks match with the information included in the ADSB ﬁles. The comparisons between the detections and the ground truth data are illustrated in Fig.4.17.(b) and Fig.4.18.(b). A good match of the radar plots with the track overlay can be distinguished for the entire extension of the available data set.

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54 4. PCL radar description and experimental results

4.5 System future improvements

The PCL demonstrator is the third generation of passive radar systems that have internally been studied at TNO during the last years. The main difference with the previous systems is represented by the use of the same antenna array to perform the acquisition of both the reference and the surveillance channels. This characteristic has driven the design choices which have been illustrated in this chapter and which have led to the current system configuration. Some limiting factors have also been mentioned and those can be considered as objectives for future improvements of the current system. Specifically:

• A complete exploitation of the available agile receiver depends on the data throughput. The upgrade of the data acquisition Local Area Network (LAN) would allow the simultaneous collection of multiple baseband signals. A multilateral system could then be realised, with an expected gain in terms of radar coverage and resolution in both the range and the angular domains.

• With respect to the previous issue, the system agility does also depend on the array elements. The current dipoles are indeed tuned at the reference frequency of 96.8MHz. Still showing a good behavior over the full FM-band, wideband radiating elements would be recommended in order to avoid variability of the overall system performance due to the selection of diﬀerent broadcasters.

• The noise ﬁgure of the PCL system is currently degraded by the introduction of the double attenuation step, which is needed in order to avoid the clipping of the ADC. This degradation has a direct impact on the radar sensitivity. State- of-the-art PC digitiser boards could be installed into the PCL working station to overcome this limitation.

4.6 Summary

This chapter has provided a top-down description and a performance assessment of the PCL radar system that has been realised at TNO. A detailed study of the antenna section has been presented. The analysis resulted, by means of simulations and direct measurements, in the characterisation of the radiating properties of the antenna elements in both the stand alone and the array conﬁgura- tions. Then, the 8-channel analog receiver has been considered. The receiver RF chain, aimed at correctly selecting the FM bandwidth and properly amplifying the input signals for the ADC, has been illustrated. The impact of the digital signal decimation on the DR has been discussed by highlighting the diﬀerence among the expected and the realised improvements.

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4.6 Summary 55

The experimental validation of the system has firstly been based on the capability of retrieving the proper pattern characteristics of the circular array under analysis. The proposed MC compensation technique has been capable of restoring the pattern symmetry and the theoretical SLL of a circular array. The consistency of the result has been confirmed by the application of the proposed pattern shaping method and the DPI spatial nulling, which have shown the expected performance in both cases. The final validation of the PCL operation followed after the implementation of a complete back-end processing section to the system. Assessed processing techniques have been taken into account, since the main interest of the research was not driven by the investigation of novel algorithms. However, the implementation of the mentioned processing blocks has been a crucial part for a complete evaluation of the PCL system capabilities.

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56 4. PCL radar description and experimental results

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Chapter 5

Coherent MIMO array theory

The distinction between the statistical and the coherent MIMO arrays has been introduced in Ch.1. Here the attention is focused on the analysis of the latter case with respect to the synthesised virtual array pattern. The procedure to select the mutual positions between the transmitting and the receiving elements, which is needed in order to avoid the presence of grating lobes, and the design choices aimed at obtaining the required angular resolution are discussed. The concepts of signal orthogonality and waveform diversity, as a preliminary condition for the exploitation of the MIMO approach, are also presented. In the last section of the chapter, the MIMO array pattern aﬀected by illumination errors is analysed and the analytical representation, in a closed form expression, is retrieved. Simulated results are shown and a comparison with the case of a conventional ULA system is illustrated1.

5.1 Coherent MIMO array pattern synthesis

A coherent MIMO array consists of a set of transmitting and receiving elements that are placed in proximity of each other. According to this configuration and by assuming a far field target to have the same RCS response to the probing signals coming from the multiple transmitters, at the receiver side, the different transmitter- receiver channels can be coherently combined. An array pattern associated to an extended virtual array can then be synthesised [24, 27, 72]. To better clarify this assertion, let us refer to a single target scenario and to the

MIMO array conﬁguration which is shown in Fig.5.1. A receiving linear array of NR elements is considered and it is placed in one of the interleaving spaces of a periodic

sequence of transmitting linear arrays. Each of the transmitting arrays consists of NT

1This chapter is based on the article [J2] and on research material currently in preparation for submission (a list of the author’s publications is included at the end of this dissertation, p. 141).

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58 5. Coherent MIMO array theory

elements. DT is the distance between two sequential transmitting arrays and MT is the total number of arrays acting as transmitters. The receiver elements spacing is

dR, whereas the one between two transmitters is dT . The target echo at the j-th receiver can be represented as:

N M ! XT T xj(t) = aR,j(θ) aT,i(θ)si(t) γ + n(t) (5.1) i=1

and then collected into the NR × 1 vector:

H xR(t) = γaR(θ)aT (θ)s(t) + n(t), (5.2)

where γ is the complex response of the target RCS, aR(θ) and aT(θ) are the receiving and the transmitting steering vectors2 respectively, n(t) represents the additive noise contribution and:

s(t) = [s1(t), s2(t) . . . sNT MT (t)] (5.3) is the vector of the transmitted waveforms. The virtual array synthesis depends on the capability of identifying the signals belonging to the diﬀerent emitters. Probing signals, which are orthogonal with each other in a certain domain, are then employed at transmission. This characteristic is usually referred to as waveform diversity or waveform orthogonality [73–76] and further details about this concept are provided in Sec.5.2. Once all the emitter contributions have been separated and by neglecting the noise term, the angular dependency of (5.2) is represented by the combined steering vector:

H a(θ) = aR(θ) ⊗ aT (θ), (5.4)

Figure 5.1: Periodical array conﬁguration of transmitting and receiving elements.

2Here the transmitting steering vector has to be meant as a result of the signal processing which is performed at the receiver side. There is indeed no focusing, i.e. no steering, of the beam during the transmission.

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5.1 Coherent MIMO array pattern synthesis 59

where ⊗ represents the Kronecker product. As a consequence, the virtual array pattern behavior depends on the mutual positioning of the antenna elements. By exploiting the exponential notation, as it has been done in Ch.2 for the ULA case, and with respect to the structure in Fig.5.1, we have:

NT −1 2π jθref X −j ndT sin(θ) FT (θ) = e [ e λ n=0

NT −1 −j 2π D sin(θ) X −j 2π nd sin(θ) + e λ T e λ T + ... n=0

NT −1 −j 2π D (M −1) sin(θ) X −j 2π nd sin(θ) + e λ T T e λ T ] n=0

NT −1 jθ X −j 2π nd sin(θ) = e ref [ e λ T n=0

MT −1 X −j 2π mD sin(θ) · e λ T ], (5.5) m=0

where ejθref is the arbitrary phase reference of the array and a pointing direction o θ0 = 0 is assumed. By looking at the retrieved expression of the array factor in transmission, it is interesting to observe that it can be described as the combination of two contributions:

a ﬁrst term that is associated to the spacing of transmitter elements dT , as for any linear array, and a second term which is related to the periodicity distance DT among the multiple transmitter arrays. According to this analysis, (5.5) can be rewritten as:

π π sin [ λ NT dT sin(θ)] sin [ λ MT DT sin(θ)] FT (θ) = π · π . (5.6) sin [ λ dT sin(θ)] sin [ λ DT sin(θ)] Similarly, the array factor associated to the receiver array is given by:

π sin [ λ NRdR sin(θ)] FR(θ) = π , (5.7) sin [ λ dR sin(θ)] leading to the ﬁnal expression of the MIMO array factor which is:

F (θ) = FT (θ) · FR(θ) π π π sin [ λ NT dT sin(θ)] sin [ λ MT DT sin(θ)] sin [ λ NRdR sin(θ)] = π · π · π . (5.8) sin [ λ dT sin(θ)] sin [ λ DT sin(θ)] sin [ λ dR sin(θ)]

The expression presented in (5.8) refers to a MIMO array based on linear radiating

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60 5. Coherent MIMO array theory

elements. The related behavior depends on the periodicity parameters (dR,dT , DT ) and, if the aim is to resemble to characteristic of a conventional linear array, they have to be properly selected. Since the achievable angular resolution is dictated by the combined aperture of the diﬀerent arrays and the appearance of grating lobes must be avoided, two conditions have to be imposed on (5.8). At ﬁrst and by referring to

the conﬁguration in Fig.5.1, if we consider a dR spacing larger dT , then grating lobes are generated in the receiver array pattern and they must be compensated by the nulls of the transmitting array pattern: ( π N d sin(θ) = kπ λ T T → d = N d . (5.9) π R T T λ dR sin(θ) = kπ Secondly, the side-lobes of the receiving array must be attenuated by the periodicity of the transmitting array series: ( π D sin(θ) = kπ λ T → D = N d . (5.10) π T R R λ NRdR sin(θ) = kπ By considering (5.8), (5.9) and (5.10), the expression of the MIMO array factor becomes: π sin [ λ MT NRdR sin(θ)] F (θ) = π sin [ λ dT sin(θ)] π sin [ λ MT NRNT dT sin(θ)] = π . (5.11) sin [ λ dT sin(θ)]

It can be noticed that (5.11) represents the array pattern of a linear array of MT NRNT elements whereas the eﬀective number of elements is equal to NT MT +NR. This result represents the additional gain, in terms of degrees of freedom, provided by the MIMO processing with respect to the conventional array techniques. By considering the

element spacing dT , that is present in (5.11), the achieved 3dB aperture associated to the transmitting and receiving array is given by: λ θ3dB = . (5.12) NRNT MT dT A synthesis result example is shown in Fig.5.2 where the contributions belonging to the diﬀerent patterns have been highlighted. The following physical array parameters

have been chosen: dT = 0.5λ, MT = 2, NR = 8 and NT = 4.

5.1.1 Fourier-like transform representation of a MIMO array pattern The transmitter and receiver arrays can also be seen as two linear ﬁlters aimed at performing spatial sampling of the signal of interest. In the spatial domain the wavelength λ can be considered as the independent variable and according to that and to

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5.1 Coherent MIMO array pattern synthesis 61

Figure 5.2: Diﬀerent MIMO pattern contributions and realised pattern synthesis.

the geometry in Fig.5.1, the sampling function which represents the array behavior of the receiver antennas can be expressed via a sequence of Dirac pulses of the form:

N −1 XR sR(λ, θ) = δ(λ − nrdR sin(θ) − λRref ), (5.13)

nr =0

where λRref is a spatial delay associated with the position of the array. In the transmitters section the periodicity related to the term DT can be represented as a convo- lution product between two pulse sequences:

N −1 XT sT (λ, θ) = δ(λ − ntdT sin(θ) − λTref )

nt=0 M −1 XT ∗ δ(λ − mDT sin(θ)), (5.14) m=0

being λTref a common spatial delay reference for the transmitter sections. According to (5.13) and (5.14), and considering the linear characteristic of the domain, the impulse response of the overall system is:

sMIMO(λ, θ) = sR(λ, θ) ∗ sT (λ, θ), (5.15)

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62 5. Coherent MIMO array theory

that can also be represented in a transformed domain by means of the Fourier operator: Z F{·} = e−jΘλdλ. (5.16)

Thanks to the analytical properties of both the Dirac sequences and the Fourier transform, (5.13) and (5.14), after a few passages, can be rewritten as:

Θ sin( NRdR sin(θ)) −jΘλRref 2 SR(Θ, θ) = e Θ (5.17) sin( 2 dR sin(θ)) and: Θ sin( NT dT sin(θ)) −jΘλTref 2 ST (Θ, θ) = e Θ sin( 2 dT sin(θ)) Θ sin( 2 MT DT sin(θ)) · Θ , (5.18) sin( 2 DT sin(θ)) 2π that are equivalent to (5.6) and (5.7) for Θ = λ .

5.2 Waveform diversity/orthogonality concept

Although the topic of MIMO radars has started to gain a large interest in the last years, it is useful to clarify the concept of waveform diversity, which is the basic property of the transmitted waveforms in a MIMO system. The term waveform diversity refers to the property of the radar probing signals to be separable, i.e. orthogonal, in a certain domain. By associating a specific waveform to each of the transmitters and by exploiting this orthogonality feature, the contributions coming from the different emitters can be retrieved at the receiver side. A further clarification is needed. The signal model under the coherent case assumption, as it has been presented in (5.2), refers to a far field point scatterer. By considering that the condition of separability between the waveforms is applied at the receiver, from the theoretical point of view and in the most general case, it can be written: Z ∗ 0 0 0 0 si(ξ(t − τ)) · sj (ξ (t − τ ))dt = δijχi(τ, τ , ξ, ξ ), (5.19) T

where χi is the complex ambiguity function [70,77] related to the i-th waveform and 1 − v /c ξ = D (5.20) 1 + vD/c is the speed stretching factor [78]. The radial speed of the target is represented by

vD. It is known that the result of the integral in (5.19) is independent of the actual

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5.2 Waveform diversity/orthogonality concept 63

values (ξ, τ) and it can be expressed by means of the relative values ∆τ = τ − τ 0 and ∆ξ = ξ − ξ0 [79]: Z ∗ si(t) · sj (∆ξ(t − ∆τ))dt = δijχi(∆τ, ∆ξ) (5.21) T which is usually just simply written as: Z ∗ si(t) · sj (ξ(t − τ))dt = δijχi(τ, ξ). (5.22) T The requirement expressed by (5.22) is often replaced by the less stringent orthogonality condition among the transmitted waveforms: Z ∗ si(t)sj (t)dt = δijχi(0, 0), (5.23) T that does not take into account for the delays and the speed components introduced by the target reﬂections [80]. To include these contributions and by means of the following narrow band assumption:

s(ξ(t − τ)) ≈ s(t − τ)ej2πfD t, (5.24)

the expression in (5.23) can be rewritten as: Z ∗ j2πfD t si(t)sj (t + τ)e dt = δijχi(τ, fD). (5.25) T As correctly pointed out in [81], by considering for simplicity in the explanation the case of zero Doppler speed, the following equivalence holds: Z ∗ −1 ∗ si(t)sj (t + τ)dt = F Si(f) · Sj (f) , (5.26) T where F −1 represents the inverse Fourier transform. It is clear from (5.26) that the orthogonality condition between the two signals is achieved by having non overlapping spectra of the waveforms in the frequency domain. A “softer” constraint can be obtained by limiting the validity of (5.26) within the time interval of the target response. To this aim, in [81] a method based on the application of a weighting function3 is proposed.

3In this case (5.25) becomes: Z ∗ j2πfD t h(τ)si(t)sj (t + τ)e dt = δij χi(τ, fD), (5.27) T where h(τ) may represent either a delay dependant weighting function or, as in the case of the referred paper, a pattern nulling provided by the diﬀerent observing angles of the target of interest.

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64 5. Coherent MIMO array theory

If (5.25) is valid, the contribution of the m-th transmitter can be retrieved from (5.2): Z ∗ 0 0 xm(t) = xR(t)sm(ζ )dζ , (5.28) ζ

and by iterating the procedure for all the waveforms, the NRNT MT × 1 received MIMO vector can be synthesised. Since the behavior of the virtual array depends on the capability to separate the channels at the receiver side, a combined pattern degradation due to the non ideal separation among the channels is expected. It is worth of mention that the analysis presented in this paragraph has considered MIMO transmissions without a focusing capability of the transmitting array, i.e. omnidirectional transmissions. If agility on transmission is available, hybrid techniques which combine spatially orthogonal beams and signal orthogonality can be implemented [20].

5.3 Eﬀect of the illumination errors on the pattern synthesis

It has been shown in Ch.2 that the array pattern synthesis, and the behavior of the related SLL, is subjected to a series of errors which depends on the subsystem components. The presence of these errors degrades the expected performance of the array in the way that has been presented in Sec.2.3.2. In addition to the consequences which follow from the non ideal separation of the multiple channels, MIMO arrays are also inﬂuenced by the illumination errors. Their impact on the pattern synthesis is here after illustrated. The omnidirectional antenna element case is considered in the following text; the terms “array pattern” and “array factor” are then used in an equivalent way. By referring to the linear array case and by means of the same notation which has been used in Ch.2, the MIMO array factor can be written as:

F (θ) = FT (θ) · FR(θ) N−1 X −j(kndT sin θ+δn) = an(1 + ∆n)e n=0 M−1 X −j(kmdR sin θ+δm) · bm(1 + ∆m)e . (5.29) m=0

Here N represents the number of transmitters and M the number of receivers4. Ac-

cordingly, the fractional amplitude errors are ∆n and ∆m whereas the phase error

4 The equivalence with Fig.5.1 is obtained by considering NT = 1 and MT = NR.

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5.3 Eﬀect of the illumination errors on the pattern synthesis 65

components are written as δn and δm. The effect of the illumination errors on the pattern sidelobes is related to the behavior of the power pattern, which is obtained by multiplying (5.29) with its complex conjugate value. By rearranging the different series which are present in the expression, we obtain: |F (θ)|2 = F (θ) · F ∗(θ) N−1 M−1 N−1 M−1 X X X X ∗ ∗ = anan0 bmbm0 (1 + ∆n)(1 + ∆n0 )(1 + ∆m)(1 + ∆m0 ) n=0 m=0 n0=0 m0=0 0 0 · e−jk[(n−n )dT +(m−m )dR] sin(θ)ej(δn−δn0 )ej(δm−δm0 ). (5.30) Due to the random characteristic of the expression in (5.30), as in the conventional array case, the pattern behavior depends on the statistical distributions of the amplitude and phase illumination errors. In order to retrieve the expected performance of the virtual array sidelobes, the mean value estimation of (5.30) must be computed. Four different contributions can be distinguished in accordance with the multiple combinations of the series indexes (n, n0, m and m0). The overall average array pattern can indeed be written as: D E D E D E 2 2 2 |F (θ)| = |F (θ)| (n6=n0) + |F (θ)| (n=n0) (m6=m0) (m=m0) D E D E 2 2 + |F (θ)| (n6=n0) + |F (θ)| (n=n0) . (5.31) (m=m0) (m6=m0) Let us now consider the first term in (5.31). By referring to the inequalities of the indexes and to (5.30), being

h(1 + ∆n)(1 + ∆n0 )(1 + ∆m)(1 + ∆m0 )i = 1, (5.32) it results: N−1 M−1 N−1 M−1 D 2E X X X X D ED E ∗ ∗ j(δn−δn0 ) j(δm−δm0 ) |F (θ)| (n6=n0) = anan0 bmbm0 e e (m6=m0) n=0 m=0 n0=0 m0=0 (n6=n0) (m6=m0) 0 0 · e−jk[(n−n )dT +(m−m )dR] sin(θ), (5.33) since the absence of systematic errors is assumed, i.e. the random distributions of the illumination errors have mean values equal to zero5. The mean values in (5.33) can

be evaluated by applying the change of variable y = δn − δn0 (in a similar way for the other contribution), that allows writing: D E Z ∞ ej(δn−δn0 ) = ejyp(y)dy. (5.34) −∞ 5 0 0 According to this assumption we have h(1 + ∆i)i = 1 for i = n, n , m, m .

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66 5. Coherent MIMO array theory

The probability density function p(y) must be deﬁned in accordance with the one of 6 δi, that here is assumed to be gaussian for ∀i. In this case, being δn and δn0 two statistically independent random variables and with the same normal distribution 2 N (0, σδ ), p(y) results [82]:

2 − y 1 4σ2 p(y) = √ e δ . (5.35) 2σδ π By combining (5.34) and (5.35):

∞ 2 Z − y D j(δ −δ 0 )E 1 jy 4σ2 e n n = √ e e δ dy 2σδ π −∞ ∞ 2 Z − y 1 4σ2 = √ cos(y)e δ dy, (5.36) 2σδ π 0 and by recalling that [83]: √ Z ∞ 2 −a2x2 π − p cos(2px)e dx = e a2 , (5.37) 0 2a after few steps we obtain the following ﬁnal expression:

2 D j(δ −δ 0 )E −σ e n n = e δT (5.38)

and similarly: 2 D j(δ −δ 0 )E −σ e m m = e δR . (5.39)

The subscripts (·)T and (·)R have been introduced to distinguish among the transmitter and the receiver components respectively. The results in (5.38) and (5.39) can now be used to simplify the expression in (5.33):

N−1 M−1 N−1 M−1 D 2E −(σ2 +σ2 ) X X X X ∗ ∗ δR δT |F (θ)| (n6=n0) = e anan0 bmbm0 (m6=m0) n=0 m=0 n0=0 m0=0 (n6=n0) (m6=m0) 0 0 · e−jk[(n−n )dT +(m−m )dR] sin(θ). (5.40)

By considering the argument of the series in (5.40), it can be noticed that it represents the diﬀerence between the ideal MIMO array pattern and the mixed terms which are

2 δi − 2 1 2σ 6p(δ ) = √ e δi . i σ 2π δi

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5.3 Eﬀect of the illumination errors on the pattern synthesis 67

denoted by the other combinations of the indexes in (5.30). We can then write:

   N−1 M−1 D 2E −(σ2 +σ2 )  2 X X 2 2 δT δR  |F (θ)| (n6=n0) = e |F (θ)|i − |an| |bm| 0  (m6=m )  n=0 m=0  | {z } (n=n0) (m=m0) M−1 " N−1 # X 2 2 X 2 − |bm| |FT (θ)|i − |an| m=0 n=0 | {z } (n6=n0) (m=m0)   N−1 " M−1 #  X 2 2 X 2  − |an| |FR(θ)|i − |bm|   n=0 m=0  | {z } (n=n0) (m6=m0) " N−1 M−1 2 2 −(σδ +σδ ) 2 X X 2 2 = e T R |F (θ)|i + |an| |bm| n=0 m=0 M−1 N−1 # 2 X 2 2 X 2 − |FT (θ)|i |bm| − |FR(θ)|i |an| , (5.41) m=0 n=0

where the subscript (·)i refers to the ideal pattern behavior. For the transmitter and the receiver array components in (5.41), the same representation, as the diﬀerence between the ideal pattern and the residual terms, has been used. By following ana- logue steps, the other addends in (5.31) can be evaluated; for (n = n0) and (m = m0) we obtain

D E N−1 M−1 2 2 2 X X 2 2 |F (θ)| (n=n0) = (1 + ∆T )(1 + ∆R) |an| |bm| , (5.42) (m=m0) n=0 m=0

2 2 being ∆T and ∆R the mean square values of the fractional amplitude errors for the transmitter and the receiver arrays respectively.

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68 5. Coherent MIMO array theory

The remaining terms are represented by:

M−1 N−1 N−1 D 2E −σ2 X 2 X X ∗ jk (n−n0)d sin(θ) δT 2 [ T ] |F (θ)| (n6=n0) = e (1 + ∆R) |bm| anan0 e (m=m0) m=0 n=0 n0=0 (n6=n0) M−1 " N−1 # 2 −σδ 2 X 2 2 X 2 = e T (1 + ∆R) |bm| |FT (θ)|i − |an| (5.43) m=0 n=0 and:

N−1 M−1 M−1 D 2E −σ2 X 2 X X ∗ jk (m−m0)d sin(θ) δR 2 [ R] |F (θ)| (n=n0) = e (1 + ∆T ) |an| bmbm0 e (m6=m0) n=0 m=0 m0=0 (m6=m0) N−1 " M−1 # 2 −σδ 2 X 2 2 X 2 = e R (1 + ∆T ) |an| |FR(θ)|i − |bm| . (5.44) n=0 m=0 The expressions in (5.41), (5.42), (5.43) and (5.44) can now be used to evaluate the analytical form of the average array pattern in (5.31). All the steps involved in the pattern evaluation are depicted and explained in Appendix B, here the ﬁnal expression of the normalised pattern is presented:

D 2E 2 |F (θ)| ' |F (θ)|i + NORM NORM M−1 h i P |b |2 σ2 + ∆2 m δR R 2 m=0 + |FT (θ)|i N−1 M−1 2 P P |an||bm| n=0 m=0 N−1 h i P |a |2 σ2 + ∆2 n δT T 2 n=0 + |FR(θ)|i . (5.45) N−1 M−1 2 P P |an||bm| n=0 m=0 Three main terms can be distinguished. Whereas the first one is the ideal behavior of the normalised MIMO array pattern, the other two contributions can be described as weighted sums of the ideal patterns belonging to the transmitter and the receiver arrays. The “weighting coefficients” result to be dependant of the receiver array errors distribution, for what it concerns the ideal transmitter array pattern, and in a reciprocal way for the receiver array side. This result differs from what has been observed in Ch.2 for a conventional linear array. In the ULA case it was indeed possible to retrieve an expression of the average pattern that was completely angle independent. With respect to the MIMO system, this can

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5.3 Eﬀect of the illumination errors on the pattern synthesis 69

only be done in terms of an inequality condition that therefore yields to an upper bound for (5.45). N−1 2 M−1 2 2 P 2 P If we consider that |FT (θ)|i ≤ |an| and |FR(θ)|i ≤ |bm| , from (5.45) n=0 m=0 it can straightforwardly be written:

D 2E 2 |F (θ)| ≤ |F (θ)|i + NORM NORM M−1 h i 2 P |b |2 σ2 + ∆2 N−1 ! m δR R X m=0 + |an| N−1 M−1 2 n=0 P P |an||bm| n=0 m=0 N−1 h i 2 P |a |2 σ2 + ∆2 M−1 ! n δT T X n=0 + |bm| (5.46) N−1 M−1 2 m=0 P P |an||bm| n=0 m=0 which, in the particular case of uniform illumination masks and after few simplification steps, leads to: h i h i N σ2 + ∆2 + M σ2 + ∆2 D 2E 2 δR R δT T |F (θ)| ≤ |F (θ)|i + . (5.47) NORM NORM NM A further assumption can be taken with respect to the statistical characteristics of the illumination errors. If the moments of the distributions are assumed to be identical at both the receiver and the transmitter sides, then the final representation of the upper bound for the average power pattern is obtained: h i (N + M) σ2 + ∆2 D 2E 2 δ |F (θ)| ≤ |F (θ)|i + . (5.48) NORM NORM NM By referring to the expressions in (5.46), (5.47) and (5.48), some considerations must be drawn. The approximation is based on the maximum value that can be assumed by the transmitter and receiver array patterns. Since this value refers to the pointing direction of the two patterns, the offset between (5.45) and (5.46) increases in the sidelobes region far from the main lobe. As a consequence, yet being a conservative approximation for the average power pattern behavior, the imposed limit may result into an over dimensioned constraint for the system. This risk can be avoided by a deeper analysis of the individual array patterns which can help in identifying a better approximation for the upper bound in (5.48). An example is provided in the following section where simulated array patterns based on the presented analysis are also shown.

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70 5. Coherent MIMO array theory

5.3.1 Simulated results

The reference structure for the simulation is a MIMO array with N = M = 6. The

receiver elements spacing is dR = 0.5λ whereas the spacing of the transmitters, according to (5.10), is dT = 3λ. The term of comparison is represented by a ULA with a total number of elements equal to N · M = 36. Similar error distributions are assumed at both the receiver and the transmitter sides; the same applies to the conventional linear array. A Monte Carlo approach [84] has been used to generate the array patterns aﬀected by the illumination errors. Some results with diﬀerent values for the moments of the error distributions are plotted in Fig.5.3. Each plot illustrates the normalised behaviors of: the “Ideal MIMO” array pattern; the “Average Error MIMO” pattern, obtained by evaluating the mean

(a) (b)

(c)

2 2 2 Figure 5.3: Error aﬀected array pattern comparisons for (a) ∆ = σδ = 0.01, (b) ∆ = 0.01 and 2 2 2 σδ = 0.1, (c) ∆ = σδ = 0.1.

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5.3 Eﬀect of the illumination errors on the pattern synthesis 71

of all the patterns produced in the Monte Carlo runs; the “Theoretical Error MIMO”, which represents the analytical expression in (5.45) and the “Theoretical Error ULA”, which depicts the effect of (2.39) on the reference ULA. All the different sub-figures confirm the validity of (5.45). The plots obtained by averaging the Monte Carlo runs indeed fit with the closed form expression that has been retrieved. It was described in Sec.2.3.2 that the presence of illumination errors introduces a uniform raise of the array pattern sidelobes in the ULA case. This effect can be observed in all the plots of Fig.5.3 and it is due to the fact that the error contributions in (2.39) are completely independent of the array pattern. If we refer to the MIMO case, and specifically to (5.45), this condition does not hold. As a consequence, the appearance of “coherent” sidelobes can be noticed. The locations of these sidelobes coincide with the ones of the grating lobes of the transmitting array , which can be computed by means of (2.19) p | sin(θ) − 1| = with p = 1, 2, 3. (5.49) 3 o o o and they are equal to: θ1 = 19.5 , θ2 = 41.8 and θ3 = 90 . The raise of the grating lobes is explained by the fact that the illumination errors introduce a de-pointing of the transmitter and receiver array patterns. The impact of this de-pointing is negligible for what it concerns the main beam of the MIMO pattern. On the other hand, the nulls of the receiver array pattern, which are supposed to compensate for the grating lobes of the transmitting antennas, are also shifted. This pointing offset produces a non ideal cancellation of the mentioned grating lobes and, consequently, a considerable degradation of the synthesised MIMO array pattern. This consideration allows further analysing the expressions retrieved in Sec.5.3. It resulted that the level of the sidelobes, in the region which is far from the pointing direction of the array, is mainly dictated by the weighted7 grating lobes produced by the array with a larger element spacing. According to that it is reasonable to assume 2 |FR(θ)|i = 0 in (5.45) and by following the same steps we have: h i σ2 + ∆2 D 2E 2 δ |F (θ)| ≤ |F (θ)|i + . (5.50) NORM NORM M The upper bound in (5.50) has been written with respect to the transmitter array, since it is the one with a larger element spacing in the considered example; in the opposite case it is obviously valid the substitution M → N for (5.50). The inequalities in (5.48) and (5.50) are compared in Fig.5.4. By referring to (5.45) and to Fig.5.4, a number of considerations can be drawn: • the inequality in (5.50) represents a less stringent upper bound than the one proposed in (5.48); it can indeed be observed that the requirement imposed

7The weighting depends on the tapering which is applied to the array.

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72 5. Coherent MIMO array theory

(a) (b)

2 2 Figure 5.4: Analysis of the upper bound conditions for the average error patterns for (a) ∆ = σδ = 2 2 0.001, (b) ∆ = 0.01 and σδ = 0.1.

by (5.48) overestimates the level of the sidelobes which are produced by the illumination errors;

• (5.50) does not require the a-priori knowledge of the original array pattern behavior, that was the key condition for the approximation of (5.45). However the proper ﬁtting of the curves at the grating lobe locations suggests a correct evaluation of the performance of the synthesised MIMO array pattern.

• whereas the angular resolution of a MIMO array depends on the product between the transmitter and receiver number of elements, the sidelobes behavior of the same array, when illumination errors are considered, is only inversely proportional to the number of elements of the array with a lower spacing.

• as a consequence of the previous statement and by referring to the same number of both physical and virtual array elements, the sidelobes performance of a conventional linear array have been proved to be always better than the ones that can be achieved by the equivalent MIMO array structure.

5.4 Summary

The chapter has dealt with the analysis of the coherent MIMO arrays with particular focus towards: the array pattern synthesis, the waveform diversity concept and the theoretical characterisation of the illumination errors eﬀect on the pattern synthesis. Speciﬁcally, the virtual array concept has been introduced. The design choices that are required for the dimensioning of such type of systems, in order to obtain well

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5.4 Summary 73

defined performance in terms of angular resolution, have been highlighted. With respect to the synthetic array retrieval, the duality between the element space and the Fourier/wavelength domain has also been shown. By referring to the waveform diversity, and the related orthogonality concept, a clarification has been pointed out. It has been remarked that, even though the requirement about the probing signals separation is applied on the transmission side, from a theoretical point of view, the consistency of the MIMO processing is based on the capability of separating the signals at the receiver side. Therefore, a rigorous formalism should imply obtaining the orthogonality among the waveforms at reception. Finally, a complete investigation about the impact of the illumination errors on the MIMO arrays has been presented. Analytical expressions aimed at estimating the expected pattern behaviors have been retrieved in closed forms. The study has allowed defining some relevant characteristics of the MIMO arrays and it has revealed differences with respect to the conventional ULA systems. Among them, it has been demonstrated that, whereas coherent MIMO arrays provide better angular resolution with a fewer number of physical elements, when illumination errors are considered, a degraded performance in terms of the achieved sidelobes level is expected.

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74 5. Coherent MIMO array theory

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Chapter 6

MIMO signal processing: RADOCA test board and experimental results

The chapter presents the radar test board that has been realised within the RADOCA project at TNO and the studies which have characterised its experimental validation. The studies were aimed at evaluating the highest performance which could be achieved by the MIMO radar demonstrator in both the Doppler, the range and the azimuth domains. At first, the design choices are illustrated; the antenna section is described with specific interest towards the positioning of the antenna elements. This analysis is undertaken from both the RF and the mutual location perspectives. As described in Ch.3, an issue that must be accounted for an array based radar regards the definition of a reliable calibration technique. With respect to the realised design and by considering the MIMO characteristic, a method and the related performance are presented. The description then leads to the detection of the slow moving targets, which is the main objective of the radar. Due to the transmission scheme that is used to implement the waveform diversity, a limitation is introduced in terms of the maximum unambiguous Doppler speed that can be measured. A transmitters selection technique to overcome this issue is suggested and the simulated outcome is illustrated. The last section of the chapter is dedicated to the study of high resolution techniques. By referring to the MUSIC method, the validation of such techniques has been confirmed also in the case of MIMO arrays. Furthermore, a novel two-dimensional algorithm has been developed and both simulated and experimental results are shown. Final remarks and a summary of the main

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76 6. MIMO signal processing: RADOCA test board and experimental results

achievements are depicted in the last section of the chapter1.

6.1 RADOCA MIMO radar description

The design of the MIMO radar demonstrator, from an antenna section point of view, was aimed at both achieving the required performance in terms of angular resolution and obtaining a test board that could work as a conventional phased array. This second characteristic was considered of particular interest for two reasons: it could effectively demonstrate the added value of the MIMO processing by directly compar- ing the different configurations; it increases the system robustness in case of failure of one of the transmitters, i.e. the absence of grating lobes within the scanning region is ensured (yet with a reduced angular resolution). According to these premises, the MIMO radar demonstrator in Fig.6.1 has been realised. The board consists of 2 transmitter pairs, one per each side of the array, and of 8 receiving channels which are placed in the middle. The radar operates at X-band in FMCW mode. The waveform can be adjusted in terms of bandwidth and pulse duration: the maximum sweep rate and the maximum transmitted bandwidth are 20MHz/10µs and 1.6GHz respectively. The sampling frequency of the ADC is set to 1.4MHz. The MIMO orthogonality condition is realised in the time domain by sequentially switching on the transmitters. Short range applications were addressed during the design phase of the radar and the related requirement resulted in a maximum transmitted power of 9dBm. A direct benefit is represented by the possibility to use a standard USB 2.0 to power the system, which is shown in Fig.6.2.(a). The low data rate that characterises the FMCW system allows using the same connection for the data acquisition. Thanks to all the mentioned features, the dimensions of the system could be reduced, Fig.6.2.(b), and a conventional notebook, Fig.6.2.(c), can be used to control the radar. The transmitter and the receiver spacings are equal to λ/2. In order to have a correct spacing of the MIMO element channels, λ/4 is the distance between the inner transmitters and the outer receivers. More details about the antenna section design are provided in Sec.6.1.1. The selected receiver elements spacing is in contrast with the analysis in Ch.5 about the dimensioning of the real arrays for the realisation of the MIMO system. A distance of λ should indeed be used. However, the actual design allows the system to be used in a Single-Input Multiple-Output (SIMO) mode with only one active transmitter, which is one of the requirements for the demonstrator. As a drawback, an overlap of the virtual channels is introduced and it is illustrated in Fig.6.3. Out of 32 virtual available MIMO elements, only 18 channels are effectively

1This chapter is based on articles [C1], [C2], [C3] and [C4] (the author publications list is included at the end of this dissertation, p. 141).

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6.1 RADOCA MIMO radar description 77

Figure 6.1: X-Band radar test board with MIMO functionality developed at TNO.

(a) (b)

(c)

Figure 6.2: Details of the USB 2.0 connector (a), boxed test board (b) and radar system layout while connected to the data acquisition notebook (c).

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Figure 6.3: Virtual element relative positions of the MIMO array board.

independent and contribute to the angular resolution of the overall system. The redundant elements can obviously still be used in order to improve the SNR level.

6.1.1 Antenna and PCB design

The coherent MIMO approach, aimed at the synthesis of digital beams, requires a uniform λ/4 spacing between the elements of the virtual array, as it acts like an active phased array with colocated antennas. From the physical elements point of view, this condition is achieved by placing the transmitter array at a λ/4 distance from the first element of the receiver array. In order to facilitate the integration of the antennas with the front-end electronics, a microstrip folded dipole (quasi-Yagi) antenna has been designed. The isolation between the λ/2 spaced elements in digitally steered array systems is a central issue and the requirement becomes more stringent when the antenna elements are closer. Recent studies [85–88] referring to similar layouts have shown average isolation levels in the order of 20dB for closely packed and strongly coupled antennas. Here, the 9dBm transmitted power should not cause compression and thus de-sensitization of the receiver. This condition requires an effective 15dB isolation. Since a straightforward printed dipole antenna on a Rogers RO4350 [89] substrate already measures 10mm in width, the effective required spacing of 8mm (λ/4 at the reference frequency of 9.4GHz) together with the 15dB isolation cannot be achieved easily. The basic antenna design uses an open dipole radiator in combination with a single director. The reflector is formed by the truncated ground plane of the microstrip. This

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6.1 RADOCA MIMO radar description 79

Figure 6.4: Layout of λ/4 (8mm) spaced microstrip fed quasi-Yagi antenna.

basic design was already described in [90]. In order to realise the λ/4 spacing, the open ends of the dipole have been bent over 90o to reduce the width of the dipole from 10mm to 7.2mm. The reduction in effective width supports an increase of the azimuth beamwidth as required. The actual structure resulted in a 0.8mm spacing between the TX and RX antennas which would normally result in a very low isolation of much less than 10dB, leading to an un-usable receiving channel. However, the problem is solved by the balanced nature of the antenna. The overall coupling between two neighboring antennas is from center to center and can be seen as an “inphase” signal. The ending sections of the dipoles of the two antennas that are λ/4 apart introduces an out-of-phase signal to be coupled. As a result, an effective suppression of the λ/4 spaced transmitter-receiver couples is obtained. The basic straightforward design is shown in Fig.6.4. The balun for the antenna, effectively connecting the 50 Ohms front-end electronics to the radiating antenna is formed by a simple λ/2 microstrip line, meandered to fit

Figure 6.5: Scattering parameter measurements of the λ/4 spaced elements.

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the narrow spacing requirement. The measured result of the λ/4 spaced antenna pair shows an isolation of better than 15dB and a better than -10dB input reﬂection over an 8GHz to 12GHz frequency range as it is shown in Fig.6.5. The λ/2 spaced antennas exhibit more than 25dB of isolation over the same frequency range. The estimated antenna gain is around 4dBi. The front-end electronics and the antenna require only a single board of 0.254mm thickness for all interconnections. For mechanical stability reasons, the ﬁnal design consists of a 4-layer board with a total thickness of 1.4mm.

6.2 Board calibration

The importance of the calibration procedure, and the related implications on the performance of an array based radar system, has already been analysed in Ch.2 and Ch.3. Calibration techniques aimed at compensating for the errors that derive from the MC effect are based on the evaluation of the MC matrix. Those techniques require antenna pattern measurements for each element of the array [91]- [92]. As it has been shown in Ch.4, a reference transmitter from different and known angular positions can also be used to perform the matrix estimation. Here a technique, which exploits the design characteristics of the coherent MIMO system described in Sec.6.1, is illustrated. By referring to (5.2) and (5.4), the angular response of a far field point scatterer can be represented by the vector:

x = αaR(θ) ⊗ aT(θ) + n, (6.1) where α is the complex amplitude of the target located at the angular position θ and n is the vector of the white gaussian noise components. In order to highlight the eﬀects of the calibration errors, (6.1) can be rewritten as:

jφT jψ1 jψ2 jkd sin θ jψ3 jk2d sin θ x = AT e ξ1e ξ2e e ξ3e e i jψNM jk(NM−1)d sin θ ··· ξNM e e + n, (6.2)

jφT jψ1 jψNM where α = AT e , ξ1 . . . ξNM and e . . . e represent the amplitude and phase 2π channel errors respectively, k = λ and d is the spacing of virtual MIMO elements. By considering that the evaluation of the calibration error components is meaningful in terms of the mutual dependance between the diﬀerent channels, it is possible to normalise (6.2) for a given complex value without loosing any information. If the normalisation is performed with respect to the ﬁrst channel value, we have:

ξ ejψ2 ξ ejψ3 ˜ 2 jkd sin θ 3 jk2d sin θ x = 1 jψ e jψ e ξ1e 1 ξ1e 1 ξ ejψNM NM jk(NM−1)d sin θ ˜ ··· jψ e + n, (6.3) ξ1e 1

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6.2 Board calibration 81

that can be written in an equivalent way as:

jφ2 jkd sin θ jφ3 jk2d sin θ x˜ = 1 a2e e a3e e i jφNM jk(NM−1)d sin θ ··· aNM e e + n˜, (6.4)

ξi jφi j(ψi−ψ1) being ai = and e = e . ξ1 According to (6.4), the phase errors can be seen as oﬀsets from the linear behavior of the steering vector phase; the amplitude errors are the fractional values which deviate from the unit. As already seen in Sec.3.2.1, those errors are the eﬀect of a complex weighted sum of the interferences coming from all the channels of the real array. Thus, the m-th element of (6.4) is represented by:

N i X i jφm jk(m−1)d sin θ x˜m = cmmxm + cmnxn = ame e +n ˜m. (6.5) n,n6=m

With respect to a MIMO system, we know that the spacing between similar elements, for instance the receivers, is proportional to the number and the spacing of the other elements [24]; an example of this positioning is depicted in Fig.6.6. The choice is made in order to avoid the overlapping of the virtual elements. When the distance between the elements becomes larger with respect to the wavelength, it is reasonable to consider the mutual coupling interaction negligible. Thus, we can write from (6.5):

i jφm jk(m−1)d sin θ cmmxm ≈ ame e (6.6) and then:

jφm cmm ≈ ame , (6.7) that can be directly measured from the observations. Considerations drawn to retrieve (6.7) are equivalent to say that for MIMO array composed by many transmitter/receiver elements, the mutual coupling matrix which characterises the real structure reduces to a diagonal matrix.

Figure 6.6: Required spacings of the receiver elements for increasing number of the transmitters.

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Figure 6.7: Measured and expected phase behavior of the reference scatterers.

6.2.1 Experimental results

Design choices of the MIMO radar, related to the integration of all the RF components on a single layer board, do not allow to perform data acquisitions in receiving mode only, i.e. without switching on the transmitters. The array transmitters have then been used for the experiment and the reflection from three different scatterer points have been considered as references. The choice of multiple reference points was meant to compensate for the signal fluctuations caused by the presence of noise. Average values have then been exploited for the compensation. As described in Sec.6.1, the spacing between the receiver elements of the board is equal to λ/2, which produces

(a) (b)

Figure 6.8: Measured and average (a) phase oﬀset and (b) fractional amplitude values for the reference scatterers.

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6.2 Board calibration 83

(a) (b)

Figure 6.9: Eﬀect of the calibration on the pattern synthesis (a) ﬁrst scatterer (b) second scatterer.

an overlapping of the MIMO virtual elements. A secondary eﬀect, introduced by this spacing value, is that the linear correspondence in (6.7) is not completely satisﬁed and a partial degradation of the compensation algorithm is introduced. For the purpose of the experiment this degradation is tolerated. The radar was set to transmit the maximum bandwidth of 1.6GHz with a sweep duration of 2.6ms and the responses of the 18 independent MIMO elements were considered. In Fig.6.7 the phase behaviors of the measured scatterer points are depicted and compared with the expected linear behavior; the expected values are computed

(a) (b)

Figure 6.10: Eﬀect of the tapering on the calibrated and un-calibrated patterns (a) ﬁrst scatterer (b) second scatterer.

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as linear ﬁtting out of the measurements. By following this procedure, the knowledge of the target locations in the angular domain is not required. According to the esti-

mated linear fitting, the cmm coefficients, which are used for the compensation, are evaluated and presented in Fig.6.8.(a) and Fig.6.8.(b) for the phase and amplitude quantities respectively. The values have then been used to restore the ideal shape of the antenna pattern for the considered MIMO array structure; results of the calibration are illustrated in Fig.6.9 for two out of the three scatterers under analysis; similar results also characterise the third reflector. The quality of the calibration method can be observed and an overall improvement greater than 2dB can be distinguished in all the plots. It is also interesting to observe the effect of the compensation method when a side lobe reduction window is applied to the array. Fig.6.10 confirms the improvement in the pattern shaping that is provided by the proposed calibration. The effect is particularly clear in the Fig.6.10.(b) where the achieved sidelobes level is equal to -20dB and it is 6dB lower than the un-calibrated case.

6.3 Moving target detection in TDM MIMO radars

This section investigates the eﬀect that a TDM based waveform orthogonality produces on the moving target detection capabilities. With respect to the system presented in Sec.6.1, the reference waveform which is considered for the analysis is the FMCW. Exhaustive descriptions of the FMCW theory and some applications to modern radar systems can be found in the literature [69, 77, 93, 94]; a summary is also presented in Appendix C. Here the beat signal:

1 2 j2π[fcτ+ατt− ατ ] sb(t) = e 2 , (6.8)

as a result of the mixing operation between the transmitted and the received signals, B is considered. In (6.8), fc represents the carrier frequency, α = T being B the transmitted bandwidth and T the pulse duration and τ is the round trip time delay associated to the target position. The beat signal is a sinusoidal signal with a range

(R) - beat frequency (fb) dependence given by:

2R f = ατ = α , (6.9) b c

the maximum unambiguous range is then related to the sampling scheme which is

applied at reception. If a real sampling fs is considered, the maximum unambiguous range results to be: c R = f . (6.10) max 4α s

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6.3 Moving target detection in TDM MIMO radars 85

Figure 6.11: Example of a FMCW transmission scheme for a TDM MIMO array.

When a moving target with radial velocity vD is taken into account, the time delay associated to its position becomes: 2 2 τ = (R + v t) = τ + v t, (6.11) c D 0 c D and by substituting (6.11) into (6.8), the beat frequency becomes: 2v f ≈ ατ + D f = ατ + f . (6.12) b 0 c c 0 D Now, the measured beat frequency corresponds to the sum of two diﬀerent components that depend on both the range and the speed information of the target. This dependency introduces ambiguities in the range Doppler response of the target; the main peak response is indeed shifted with respect to the true position. Diﬀerent waveform techniques, based on non-linear frequency modulations [95], can resolve the issue. However, in the case of moderate velocities (or equivalently for short pulse du- rations) the shift introduced by the additional Doppler component can be tolerated. Under the aforementioned assumption, the range information can be associated to the

frequency shift in the fast time (fs) dimension, whereas the Doppler velocity can be retrieved by means of a phase comparison on the slow time (T ) dimension. The phase variation of the scatterer response, which is experienced in two consecutive sweeps, is equal to:

∆φ = 2πfDT, (6.13) and by considering that the unambiguous phase interval is [−π π], the maximum unambiguous Doppler frequency and speed result to be: 1 λ f = ± v = ± . (6.14) D 2T D 4T By referring to the MIMO case with a TDM approach and to Fig.6.11, the synthesis

of an entire MIMO baseline requires NT eﬀective sweeps that are then equivalent to a single transmission for the virtual array. As a consequence, the maximum unambigu-

ous Doppler estimations in (6.14) are degraded by a factor of NT which depends on

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(a) (b)

Figure 6.12: FMCW Range/Doppler processing (a) FMCW Range/Doppler processing with a 3 stages MTI canceler (b).

the number of the active transmitters. This condition represents a severe limitation on the performance of MIMO radar systems based on the mentioned transmission scheme. A visual example is provided in Fig.6.12, where the radar demonstrator has

been set to transmit at fc = 9.25GHz a waveform with pulse length T = 363µs and bandwidth B = 500MHz. In Fig.6.12.(b) a 3 points Moving Target Indicator (MTI) [69,77] is also applied to highlight the Doppler components belonging to target while the suppression of the static clutter is performed. Since the 4 transmitters are used and sequentially switched on according to the approach in Fig.6.11, it can be seen that the unambiguous Doppler interval is equal

to vD = ±4.9m/s. For the proposed case, the moving target of interest, consisting of a slow manoeuvring car, could still be detected. Yet the degradation with respect to a conventional FMCW radar, that would ensure a Doppler speed interval in the range [−19.6 19.6]m/s, is considerable. In Sec.6.3.1 and Sec.6.3.2 more details about the eﬀect of the Doppler component on the mentioned system are provided and in Sec.6.3.3 a transmission scheme to overcome the mentioned limitation is proposed.

6.3.1 Doppler speed impact

The sketch in Fig.6.11 has helped in deﬁning the diﬀerence between a conventional

and a TDM MIMO basic pulse. The latter has been noticed to be constituted by NT eﬀective pulses, each of them allows synthesising a part of the overall MIMO array. By referring to the FMCW modulation principle, the beat signal belonging to the

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6.3 Moving target detection in TDM MIMO radars 87

m-th sub-array can be written as:

1 2 j2π[f0τm+ατmt− ατm ] xm(t) = e 2 , (6.15)

where τm is now the round trip delay associated to the target for the MIMO sub-array under analysis. If we consider the status vector v = [R0, θ, vD], which characterises the distance, the azimuth position and the radial velocity of the target respectively, the time delay takes the form (under far-ﬁeld point scatterer assumption): 2 md + nd τ = R + T R sin θ + v t0 , (6.16) m c 0 2 D

being mdT the relative position of the m-th transmitter and ndR the relative position of the n-th receiver; t0 represents the time of the performed measurement and it can be expressed as: 0 t = T (m + kNT − 1), (6.17)

with k = [0,...,NMIMO −1], where NMIMO is the number of MIMO sweeps that are considered for the processing. According to (6.17) and by neglecting the contribution

due to R0, equation (6.16) can be rewritten in the following way: 2 d τ = T sin θ + v T m m c 2 D nd + R sin θ + v T (kN − 1) . (6.18) 2 D T

It must be noticed from (6.18) that the target speed vD is multiplied by both T and NT T and this dependance affects the processing steps that are performed after the matched filtering. Furthermore, the variable m is related to both the angular information and the radial velocity; that effectively results in a de-pointing of the array pattern associated to transmitting array2.

6.3.2 Multi domain signal analysis A conventional mean to analyse the performance of a radar system, in terms of achievable resolutions, ambiguities location and sidelobes shape, is based on the evaluation

2If we consider the m dependency in (6.18), we can relate it to the generic array factor:

N−1 X j 2π n[ d sin θ+v T ] F (θ) = ane λ 2 D . (6.19) n=0

By performing the array steering towards the direction θ0, without accounting for the speed component, the eﬀective pointing direction results to be: 0 −1 2vDT θ = sin sin θ0 − . (6.20) 0 d

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Figure 6.13: TDM MIMO 3D matrix data structure.

of the waveform ambiguity function. With respect to the time domain division, the virtual baseline synthesis requires the information from all the transmitters and it implies that multiple basic pulses must be received. This leads to the deﬁnition of the reference waveform:

T s(t) = [s1(t), s2(t), . . . , sNT (t)] . (6.21) By referring to the expressions (5.23)-(5.28) retrieved in Sec.5.2, we can write in a matrix form that: Z +∞ 2 H j2πfD t χ¯(v) = xR(t)s (t + τ)e dt . (6.22) −∞ The analysis which is performed hereinafter is aimed at describing the behavior of (6.22) in both the range/Doppler and azimuth/Doppler domain; the second analysis depends on the fact that we are considering a TDM MIMO array, thus we can have different information according to different steering angles. With respect to these premises and by referring to (6.16)-(6.22) we can then define:

+∞ 2 Z 2vD ∗ j2π λ t χ(v)|τ(R=R0) = s(t)s (t + τ)e dt (6.23) −∞

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6.3 Moving target detection in TDM MIMO radars 89

and: +∞ 2 Z 2vD ∗ j2π λ t χ(v)|τ(θ=θ0) = s(t)s (t + τ)e dt , (6.24) −∞ that are the ambiguity functions when the variation in the time delay τ is considered in both the range and the angular domains. The data structure of a TDM MIMO array can be represented by means of a 3D matrix as illustrated Fig.6.13. The evaluation of the ambiguity functions, thanks to the FMCW transmission, can be performed as it follows:

• (6.23) is computed by ﬁrstly applying a FFT along the fast time dimension and by selecting the 2D matrix corresponding to the range bin of the target. For a given scanning angle θ, the matrix is multiplied by the steering vectors of the transmitter and receiver elements; the sum along the receiver direction is done. Finally, in order to estimate the Doppler contents of the signal, a second FFT is performed along the transmitter channels direction.

• (6.24) evaluation almost follows a reverse approach. At ﬁrst, the steering vectors associated to the target angle of arrival are multiplied by the 3D data matrix; then the summation along the receivers direction is done and the corresponding 2D matrix is retrieved. Finally, the 2D FFT is computed in order to obtain the desired function.

105 −15 100 −15

100 −10 90 −10 95 −5 80 −5 90 0 70 0 85 5 60 5 Doppler speed [m/s] Doppler speed [m/s] 80 10 50 10 75 40 15 15 70 30 0 50 100 150 200 250 −80 −60 −40 −20 0 20 40 60 80 Range [m] Azimuth angle [o]

(a) (b)

o Figure 6.14: Ambiguity functions of a target with status vector v0 = [50m, 20 , 3m/s] in a sequential TDM transmission mode: Range/Doppler (a) and Angle/Doppler (b) maps.

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−15 105

−10 100

95 −5 90 0 85 5 80 Doppler speed [m/s] 10 75

15 70

−80 −60 −40 −20 0 20 40 60 80 Azimuth angle [o]

o Figure 6.15: Angle/Doppler map for a target with status vector v0 = [50m, 20 , 3m/s] in a conventional FMCW radar with transmitted pulse length of NT T .

Let us now consider the case of a MIMO array with NT =NR=4. The transmitted waveform has T =405µs, B=150MHz and, for the beat signal, a sampling frequency

fs=1.4MHz has been chosen. By considering these values, the maximum unambiguous Doppler speeds are vD = ±4.9m/s and the unambiguous range Ru '285m. o For a target status vector v0 = [50m, 20 , 3m/s], the range/Doppler and the azimuth/- Doppler responses are presented in Fig.6.14. With respect to Fig.6.14.(a), it can be noticed that side peaks are present in the Doppler domain and they are related to the

quantity vD(kNT T ) in equation (6.18). The spacing between the effective speed and the side peaks is indeed equal to: λ voff = ± . (6.25) 2NT T However, the amplitude of these spikes is negligible in the considered case3. On the other hand, if we refer to the azimuth/Doppler domain and to the results obtained in Fig.6.14.(b), the effect introduced by the offset (6.25) is highlighted and an effective reduction of the unambiguous Doppler interval can be clearly noticed. This result is not in contrast with the theory as, in order to synthesise the MIMO virtual baseline,

the acquisition time is increased by a factor of NT . On the other hand, the presented example diﬀers from the case of a conventional FMCW radar with a pulse length of

NT T as it is shown in Fig.6.15. In this case, the ambiguities of the real target are eﬀectively located at Doppler speeds that are proportional to λ/(2NT T ).

3We refer to the behavior of the target response. A similar consideration cannot be drawn in presence of strong clutter reﬂections.

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6.3 Moving target detection in TDM MIMO radars 91

6.3.3 Effect of the random selection of the active transmitter In the previous section it has been discussed the effect of the periodic term: 2 τ = v (kN T ), (6.26) NT c D T introduced by the use of multiple transmitters in a TDM MIMO system. It was noticed that the sequential selection of the active emitter effectively produces a reduction of the unambiguous Doppler interval. This limitation, when multiple MIMO sweeps are considered in the processing (which is always the case when accurate estimation of the target speed has to be performed), can partially be overcome by introducing a random selection of the active transmitter. By referring to (6.34) we can write the time delay associated to the i-th transmission as: 2 d + d τ = R + T xi Rxn sin θ + v t , (6.27) i c 0 2 D

where T xi is randomly chosen and: k − 1 t = T (i − 1) + , (6.28) fs

being i = 1 ...NT NMIMO and k = 1 . . . T fs. The random transmitter sequence is realised in order to have the same number of transmissions by each element. In this way, as in the sequential transmission mode, the contributions for the diﬀerent virtual sub-arrays are identically weighted. Results of the randomization on the range/Doppler and the azimuth/Doppler do-

−15 100 −15 105

100 −10 90 −10

95 −5 80 −5

90 0 70 0 85 5 60 5 Doppler speed [m/s] Doppler speed [m/s] 80 10 50 10 75 15 40 15 70 30 0 50 100 150 200 250 −80 −60 −40 −20 0 20 40 60 80 Range [m] Azimuth angle [o]

(a) (b)

o Figure 6.16: Ambiguity functions of a target with status vector v0 = [50m, 20 , 3m/s] in a random TDM transmission mode: range/Doppler (a) and azimuth/Doppler (b) maps.

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105 105 −15 −15 100 100 −10 −10 95 95 −5 −5 90 90 0 0 85 85 5 5 Doppler speed [m/s] 80 Doppler speed [m/s] 80 10 10 75 75 15 15 70 70

−80 −60 −40 −20 0 20 40 60 80 −80 −60 −40 −20 0 20 40 60 80 Azimuth angle [o] Azimuth angle [o]

(a) (b)

o Figure 6.17: Ambiguity functions of two targets with status vectors v0 = [50m, 20 , 3m/s] and o v1 = [50m, 35 , 10m/s] in a sequential (a) and random (b) TDM transmission mode.

mains are presented in Fig.6.16. From the comparison with the sequential approach, two considerations can be drawn: in the range/Doppler case, the low amplitude side peaks are now completely removed; in the azimuth/Doppler one, the introduced randomization produces a spreading of the ambiguous peaks and allow retrieving the position of the target in the larger Doppler interval related to the single FMCW pulse duration. It is of interest to observe the results of the proposed scheme for the multiple targets

102 120 −15 −15 100 −10 −10 X: 20 Y: 3 115 Value: 102.5dB 98 X: −41 Y: 13 −5 −5 Value: 102dB 96 0 0 110

5 94 5 Doppler speed [m/s] Doppler speed [m/s] X: 20 Y:3 105 10 X: −43 Y: 6.5 92 10 Value: 121dB Value: 91.0dB 15 15 90 100

−80 −60 −40 −20 0 20 40 60 80 −80 −60 −40 −20 0 20 40 60 80 Azimuth angle [o] Azimuth angle [o]

(a) (b)

Figure 6.18: Eﬀect of the number of integrated sweeps on the sidelobes level: (a) 16 MIMO sweeps (b) 128 MIMO sweeps.

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6.3 Moving target detection in TDM MIMO radars 93

Table 6.1: Main to Maximum Sidelobe Level MIMO Sweeps MMSL [dB] 8 9.5 16 11.5 64 16 128 19

case that is presented in Fig.6.17. Here the scenario presents an additional target with o status vector v1 = [50m, 35 , 10m/s], which locates itself in the ambiguous Doppler region of the sequential transmission. It is clear from the processing results that, whereas with a conventional approach (Fig.6.17.(a)) a correct positioning of the target is not achievable, with the randomised (Fig.6.17.(b)) method the location in the azimuth/Doppler map can be resolved.

As observed in the azimuth/Doppler results, which are presented in Fig.6.16 and Fig.6.17, the introduced randomization produces a spreading of the ambiguous peaks. The amplitude of the random peaks has been checked for diﬀerent values of the integrated sweeps and it has been noticed that the average level of the unwanted peaks decreases as the number of integrated sweeps increases. Such behavior is illustrated by the comparison in Fig.6.18, where the cases of 16 and 128 integrated sweeps are considered.

The MMSL (Main to Maximum Sidelobe Level) varies according to the same be- 1 havior (∝ N ) and Table 6.1 depicts the values for diﬀerent numbers of integrated sweeps for the simulated cases. It can be seen that the value of the highest sidelobe remains quite high for a number of integrated MIMO sweeps lower than 64, which implies that the proposed method for extending the unambiguous Doppler range can only be used when long integration time is available. On the other hand, the randomization of the transmitters sequence can be used in conjunction with a conventional transmission scheme in a subsequent bursts mode. In this way, whereas the conventional sequential transmission is used to perform the targets detection in the extended Doppler interval, the random burst allows resolving the ambiguities on the identiﬁed objects.

It must also be highlighted that no degradation of the system performance in terms of both angular, Doppler and range resolutions has been measured when the diﬀerent transmitters are equally used during the data acquisition.

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6.4 High resolution techniques applied to coherent MIMO arrays

The previous section has analysed a possible mean to improve the Doppler speed retrieval capability of a coherent MIMO radar based on a TDM transmission scheme. The attention is now given to the other domains that characterise the target status vector: the range and the angular ones. As it has been discussed in Ch.2, the angular resolution of an antenna system is dictated by the working frequency (wavelength) and the antenna aperture [29]. The range resolution depends on the characteristics of the transmitted signal, specifically on the waveform bandwidth [70]. The aforementioned quantities represent the physical resolutions of a radar system. The application of spectral analysis techniques to the angular domain in the one-dimensional (1D) case [96,97] and the two-dimensional (2D) extension (azimuth and elevation) estimation [98, 99] have demonstrated the improvement related to the high resolution processing. Similar approaches have also been used in the range dimension [100]. In Sec.6.4.2, a novel technique that combines both the angular and the range high resolution processing is presented. Since the algorithm is based on the MUltiple SIg- nal Classification (MUSIC) estimator, the related basic theory is briefly illustrated in Sec.6.4.1.

6.4.1 The MUltiple SIgnal Classiﬁcation (MUSIC) method The MUSIC algorithm [101–104] is a parametric estimator for the localization of signals in white Gaussian noise. Since the algorithm performs a decomposition of the received data covariance matrix, in order to evaluate the eigenvalue amplitudes and distribution, it is referred to as a subspaces technique. The data matrix X is collected by an array of sensors. The size of X is [M,N] being M the number of sensors and N the number of acquired snapshots at a given range bin (the application of the algorithm to the angular domain is considered). The covariance matrix results to be: 1 R = XXH = BR BH + σ2 I , (6.29) x N s w M

2 where Rs is the signal sources covariance matrix, σw is the noise power and IM is the identity matrix. The steering vectors related to the target locations are collected into steering matrix:

B = [b(θ1) b(θ2) ... b(θs)] , (6.30) and the structure of the vectors depends on the geometric characteristics of the array as it has been explained in Ch.2.

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6.4 High resolution techniques applied to coherent MIMO arrays 95

The MUSIC algorithm principle is based on the capability of separating the subspaces related to the noise and the signal components. In order to retrieve this information,

an Eigenvalue Decomposition (EVD) of the Rx matrix is performed. The number of eigenvalues belonging to the signal components is then evaluated. Most common techniques to estimate the number of signals in white Gaussian noise environment are: the Minimum Description Length (MDL) and the Akaike Information Criterion (AIC) [105–107]. The performance of both the estimators considerably decreases when the scatterers are correlated, i.e. the signals are coherent with each other. In this case the matrix in (6.29) is rank deﬁcient and the signal eigenvalues can be wrongly associated to the noise subspace. The issue can be solved by applying spatial smoothing techniques [108, 109] to the received data matrix in order to decorrelate the signals while restoring the high resolution capability of the MUSIC processing.

The identiﬁcation of the signal subspace allows isolating the matrix Wn of the noise eigenvectors. These eigenvectors are orthogonal to the signal subspace that is spanned by eigenvectors of the form of b(θ). As a result, the squared Euclidean distance:

2 H H d = b (θ)WnWn b(θ) (6.31)

is minimal for all the values of θ which correspond to the target DOAs. It is then possible to identify the function: 1 PM (θ) = , (6.32) H H b (θ)WnWn b(θ) that presents peak values in the same directions and is normally referred to as the MUSIC pseudo spectrum.

6.4.2 2D-MUSIC algorithm description The 2D (range and azimuth) information retrieval process, by means of high resolution algorithms, can be approached in two different ways. The first solution consists of a “2 times 1D” implementation: the MUSIC processing is applied on the angle and the range dimensions separately and then the two sub-products are combined in an incoherent way. The second solution allows retrieving the 2D information about the object at the same processing step; it can then be defined as a fully coherent 2D processing and the novel algorithm, which has been implemented, belongs to this category. The implementation of the MUSIC algorithm model in the 2D case implies the definition of a new steering vector that includes both the range and the angular information about the target. In order to determine this steering vector, the FMCW model, which has been used in Sec.6.3, has been taken as reference and extended to the case of multiple targets. The beat signal received at the m-th channel, in presence of K targets,

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takes then the form: K 1 2 X j2π[fcτk(m)+ατk(m)t− ατk(m) ] xm(t) = γke 2 + w(t), (6.33) k=1 being w(t) the noise component and where: 2 τ (m) = [R + md sin(θ )] (6.34) k c k k

allows highlighting both the range (Rk) and the bearing (θk) positions of the target. The model refers to a receiver sensor based on a liner array conﬁguration.

The signal in (6.33) is then sampled with a sample frequency fs; for a single sweep we have the digital signal:

K n 1 2 X j2π[fcτk(m)+ατk(m) − ατk(m) ] xm(n) = γke fs 2 + w(n), (6.35) k=1

with n = 0...N −1 and N = T fs. It must be highlighted that, contrary to Sec.6.4, here N represents the number of samples in the fast time (range) dimension. By collecting the contributions from all the M channels, the X spatial/time sampled data matrix, of size M × N and that is associated to a single FMCW sweep is then retrieved. The mentioned matrix is considered for the description of the 2D-MUSIC algorithm. The processing steps can be summarised as it follows:

• X is scanned by a window of dimensions [l1 × l2] as shown in Fig.6.19. In total we have p1 = M − l1 + 1 positions that belong to the spatial domain of the signal and p2 = N −l2 +1 positions associated to the time domain of the signal.

• Each sub-matrix is reshaped into a [l1l2 × 1] vector and collected into the new data matrix X˜ . According to the used notation, the dimensions of X˜ are [l1l2 × p1p2].

Figure 6.19: Data matrix samples and scanning window procedure.

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6.4 High resolution techniques applied to coherent MIMO arrays 97

• The data smoothed covariance matrix can be computed as:

1 h i C = X˜ X˜ H + J(X˜ X˜ H)∗J , (6.36) 2p1p2

being:  0 0 ... 1   .   . 0 1 0  J =   (6.37)  .. .   0 . 0 .  1 0 ... 0

the [l1l2 × l1l2] transition matrix [109]. After EVD operation, the (l1l2 − K) eigenvectors associated to the noise subspace W˜ can be identiﬁed.

• Finally, the 2D-MUSIC spectrum is evaluated as:

1 S(τi) = , (6.38) H H a (τi)W˜ W˜ a(τi)

where the steering function vector a(τi) is equal to:

a(τi) = (6.39)

l −1 h j2π[f τ (0)] j2π[f τ (0)+ατ (0) 2 ], e c i , ..., e c i i fs

l −1 j2π[f τ (1)] j2π[f τ (1)+ατ (1) 2 ,] e c i , ..., e c i i fs

l −1 T j2π[f τ (l −1)] j2π[f τ (l −1)+ατ (l −1) 2 ]i e c i 1 , ..., e c i 1 i 1 fs ,

and the Residual Video Phase (RVP) [110] contribution has been neglected.

The maximum number of signals that can be detected is associated to the number of degrees of freedom, i.e. number of elements, provided by the array. The use of coherent MIMO radars then represents an interesting application, since this number is larger than the physical elements one. The presented processing can straightforwardly be applied to the MIMO systems; in that case the M value represents the number of virtual channels that have been retrieved.

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6.4.3 Simulated and Experimental Results

The validity of the algorithm has been tested on both simulated and real data scenarios. With respect to the ﬁrst case and in order to resemble the system presented in Sec.6.1, the radar parameters selection in Tab.6.2 has been used. The single channel SNR has been set to 20dB and 10 MIMO sweeps have been integrated to compute the covariance matrix in (6.36). The simulated scenario consists of 6 equal RCS point targets that present an angular separation of 5o and a range separation of 0.6m; both values do not allow to discriminate and separate the targets neither in range nor in angle. The speciﬁc target positions (range/angle) are listed in Tab.6.3 and the angular reference is taken perpendicular to the x-axis at the 0m point. In Fig.6.20 the results of the conventional DBF processing and the proposed 2D-MUSIC algorithm

are presented respectively. By referring to the latter one, the values l1 = 10 and l2 = 280 have been used to compute (6.36). It can easily be noticed that, whereas the standard processing does not provide a clear identiﬁcation of the number and the location of the targets, the high resolution method allows discriminating the presence of the 6 diﬀerent objects.

Table 6.2: Radar parameters selection for the simulated scenario Number of transmitters NT =4 Number of receivers NR=4 Carrier frequency fc=9.4GHz Sampling frequency fs=1.4MHz Transmitted bandwidth B=250MHz Sweep duration T =363µs Angular resolution δθ=7.2o Range resolution δR=60cm

22 0 22 0

21.5 −5 21.5 −5

21 −10 21 −10

−15 20.5 20.5 −15

−20 −20 Y[m] 20 Y[m] 20

−25 −25 19.5 19.5 −30 −30 19 19 −35 −35 18.5 18.5 −40 −40 −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 X[m] X[m]

(a) (b)

Figure 6.20: Simulated scenario with 6 targets spaced by 0.6m in range and 5o in angle: DBF processing (a) 2D-MUSIC processing (b).

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6.4 High resolution techniques applied to coherent MIMO arrays 99

Table 6.3: Target positions for the simulated scenario o o o [R1, θ1] = [20.6m, 5 ] [R2, θ2] = [20.6m, 0 ] [R3, θ3] = [20.6m, −5 ] o o o [R4, θ4] = [20m, 5 ] [R5, θ5] = [20m, 0 ] [R6, θ6] = [19.4m, 5 ]

(a) (b)

Figure 6.21: Cut at the 20.6m range bin for the 3 scatterers case (a); cut at the 20m range bin for the 2 scatterers case (b).

More details about the processing results are shown in Fig.6.21 and Fig.6.22, where the angular and range cuts at the peak locations of the MUSIC spectrum are presented. The DBF output curves at the same positions are also plotted. It can be

(a) (b)

Figure 6.22: Cut at the 5o angular bin for the 3 scatterers case (a); cut at the 0o angular bin for the 2 scatterers case (b).

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seen that the exact angular (5o, 0o and −5o) and range (19.4m, 20.0m and 20.6m) values have been identified for all the targets and the reduced sidelobes level introduced by the 2D-MUSIC method can also be appreciated. For the presented scenario, the number of targets has been given as an input to the processing; thus it has not directly been estimated from the simulated data set. However, in the real application, it has been retrieved from the acquired data. Being not the purpose of this work to analyse the behavior of the different signal estimation algorithms, the MDL method proposed in [105] has been chosen. The scenario for the real data test is shown in Fig.6.23 where the main features have been highlighted. The scene is characterised by the presence of two handrails, multiple air pipe unions and a corner reflector that was used as reference scatterer. The MIMO radar test board has been set to transmit the following FMCW waveform: up-sweep duration 363µs, down-sweep duration 37µs and transmitted bandwidth B = 600MHz. The down-sweep of the pulse is not considered during the processing but it is required by the board controller to ensure the correct switching time from one transmitter to the other. Its value for the designed board is normally taken equal to 10% of the up-sweep duration. Results of the DBF and the 2D-MUSIC processing are shown in Fig.6.24. The data

smoothing factors for the second case have been chosen equal to l1 = 16 and l2 = 200; the main reasoning resides on limiting the overall computation time required by the processing. The optimal selection of the two parameters is an issue which has not

Figure 6.23: Scenario for the measured data set collection with highlighted targets.

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6.5 Summary 101

(a) (b)

Figure 6.24: Real data scenario: DBF processing (a) 2D-MUSIC processing (b).

been analysed in this work and it will be taken into account in the follow-on of the research. By referring to the targets that have been considered in Fig.6.23, the improvement provided by the proposed two dimensional high resolution technique, with respect to the DBF one, can be appreciated. Not only the positioning and the separation between the diﬀerent objects is better assessed, but it can be noticed how the handrail on the left side of the image is better highlighted by the 2D-MUSIC processing. It is then possible to state that the validity of the method is also conﬁrmed by its application to the experimental data set.

6.5 Summary

The chapter has introduced the compact and coherent MIMO test board that has been realised at TNO. The design choices, which have led to the definition of the antenna section characteristics, have shown the capability of operating in two different configurations: as a conventional phased array and as a MIMO array. The achieved antenna element isolation, as direct consequence of the proposed layout, has been capable of ensuring the expected working behavior of the radar. The application of the signal processing techniques, which have been described throughout the chapter, has confirmed both the validity of the implemented processing models and the quality of the realised system. Specifically, by exploiting the real array configurations in MIMO radar, which consists of receiving array elements spaced by a distance greater than the wavelength, a simple calibration model has been retrieved. The model is based on the evaluation of the calibration coefficients as offset values from the estimated theoretical phase

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and amplitude behavior of the array. An a-priori knowledge of the target position in the azimuth plane is not necessary. Yet accounting for the calibration performance degradation, due to the redundant spacing of then antenna elements, the results have shown a good compensation of the array non linearities and a good retrieval of the ideal array pattern shape. With respect to a FMCW modulation, the analytical description of the received signal for the virtual MIMO array has been retrieved. By considering the phase behavior of the signal, a double relation between the sweep duration and the target Doppler speed has been observed. As a direct result, an effective reduction of the unambiguous Doppler interval is introduced by the sequential transmissions that are needed to obtain the waveform diversity. A possible way to restore the full extent of the Doppler region has been investigated and the introduction of a random selection of the active transmitter has shown interesting results for this purpose. On the one hand, under the assumption that all the transmitters were uniformly used, no degradation of the system resolution was encountered. On the other hand, for a limited number of integrated sweeps, the level of the produced side lobes in the azimuth/Doppler domain is not sufficiently low to ensure good detection performance. Surveillance systems where relatively slow moving targets need to be detected can be considered suitable applications for the presented technique. The RADOCA system falls into this category since one of its main tasks is the detection of human beings. The last section of the chapter focuses on the topic of high resolution signal processing. An extension of the conventional MUSIC processing to the 2D case for both azimuth and range information retrieval has been presented. By exploiting the characteristics of the array steering vectors in the time and the spatial domains, a fully coherent algorithm has been defined. The model has been presented with respect to the FMCW waveform but it can in principle be generalised to any transmitted waveform. The validity of the proposed method has been assessed by means of both simulations and experiments. In the former case, all the targets have been spaced by angular and range distances lower than the theoretical resolutions; thus not allowing a correct separation between them with conventional processing techniques. In the latter case, a data acquisition was performed in an outdoor environment characterised by the presence of multiple objects without the a-priori knowledge of the exact locations of the different targets. A comparison with the DBF technique has been carried out and the improvements of the proposed method have clearly arisen in both cases. Further developments of the algorithm can be identified. First of all it is known that the spectrum obtained with the high resolution techniques does not refer to the real amplitudes of the received signals, it is indeed commonly referred to pseudo-spectrum. An estimation technique of the effective target reflectivity is then required, above all when high resolution imaging applications are foreseen.

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Chapter 7

Conclusion and outlook

The research that has been described in this thesis was conducted over a period of four years in a cooperation activity between the Delft University of Technology and the radar group of TNO - Defence, Security and Safety in the Hague. The project focussed on the study of novel digital beamforming and signal processing algorithms for array based radar systems.

In the first part of the thesis, the case of a circular array, meant to be used as a Pas- sive Coherent Locator (PCL), has been investigated. The referred structure allows simultaneously retrieving, by means of digital beamforming synthesis, the reference signal coming from the chosen transmitter of opportunity and the signal reflected by a possible target which is present in the region of interest. The synthesis of the digital beams, which is aimed at retrieving the mentioned signals, must meet specific requirements. Sidelobes level, interference suppression and angular resolution are parameters of interest while evaluating the beamforming performance. The research activity has considered all these aspects, developed a novel technique for the array pattern shaping and confirmed the radar performance with a data acquisition cam- paign. Furthermore, since the application of any digital beamforming scheme requires a proper calibration of the array section, an ad-hoc procedure has been implemented.

The second part of the thesis has analysed the application of digital beamforming and signal processing algorithms to the coherent Multiple-Input Multiple-Output (MIMO) radars. This novel class of radar sensors has been the object of several research studies in the last years. The applicability of conventional processing techniques, the limitations arising from the non ideal orthogonality among the transmitted probing signals and the eﬀective performance enhancement provided by the synthesised virtual array

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104 7. Conclusion and outlook

are still under investigation. These concepts have been considered with a speciﬁc focus, on the one hand, on the analytical characterisation of the array pattern synthesis and its degradation due to array non linearities introduced by the illumination errors; on the other hand, novel techniques aimed at calibrating the real array system and improving the related radar performance have been developed.

The technical introduction of the research study is included in Ch.2. Here all the basic notions about antenna and antenna array theories are provided. These concepts have then been used, throughout the thesis, both to analyse the characteristics of the antenna sections of the radar demonstrators and to qualify the performance of the beamforming algorithms. The causes of pattern synthesis degradation, such as antenna coupling and element illumination errors, have also been introduced. These descriptions have then been referred to in the speciﬁc cases of interest for both the circular and the MIMO arrays.

7.1 Conclusions

The research activity concerning the design and the application of array processing and digital beamforming schemes to passive and coherent MIMO radar systems led to the following results and conclusive remarks:

• Internal and external measurements can eﬀectively be used for PCL array digital calibration. A technique for the compensation of the mutual coupling eﬀect in the digital domain has been presented. The proposed method accounts for both the RF and the digital sections of the radar receiver. By combining a set of internal and external measurements with an optimisation approach, the expected shape for the PCL array pattern can be retrieved and made available to the digital beamformer.

• A novel digital beamforming technique for circular arrays has been invented and better performance, with respect to classical UCA beamformer, has been con- ﬁrmed. The analytical expression of the weights for circular array pattern shaping has been retrieved in a closed form. The comparison with the phase modes theory approach has shown the better performance of the proposed method in terms of achieved angular resolution of the synthesised array pattern.

• The potentiality of the UCA PCL system has been conﬁrmed. The entire digital signal processing chain of a PCL radar has been developed. The system validation has been carried out thanks to the comparison of the radar detections with the ground truth data provided by an ADSB receiver. The quality of the

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7.1 Conclusions 105

resulting overlay between the two data streams has conﬁrmed the capabilities of the PCL radar.

• The sidelobes performance of a conventional array is always better than the one achieved by the equivalent MIMO array structure. The impact of the illumination errors on the synthesis of coherent MIMO array patterns, for the linear array case, has been characterised in an analytical and closed form expression. According to the related study, it has been possible to state that: although the angular resolution of a MIMO array depends on the product between the transmitter and receiver number of elements, the sidelobes behavior of the same array, when illumination errors are considered, is inversely proportional to the number of elements of the array with a lower spacing.

• A TDM MIMO array has been designed and the related calibration procedure has been implemented. A coherent TDM MIMO radar has been realised on a PCB. Due to the high level of integration, an extensive characterisation of the antenna section could not be obtained. A technique for the estimation of the calibration coefficients of the virtual elements, which exploits the MIMO configuration and can directly be applied on field measurements, has been proposed. The achieved level of sidelobes reduction has validated the suggested solution.

• The available Doppler interval in TDM MIMO systems can be re-established. The use of a TDM transmission scheme produces a reduction of the unambiguous Doppler interval that is proportional to the number of transmitters. This issue has been solved by introducing a random selection procedure for the active radiator within the transmission sequence. Simulations have conﬁrmed the validity of the approach and the possibility to re-establish the original Doppler interval extension in the case of TDM MIMO radars and for slow moving targets.

• The MUSIC algorithm can be extended to a multidimensional domain in a fully coherent way. An innovative 2D high resolution algorithm, based on the MUSIC processing, has been developed. By combining at the same time the spatial and the fast time sampling capabilities of the array, the angular and range information about the target are retrieved as a result of a fully coherent processing. The validity and increased performance provided by the algorithm have been assessed by means of simulations and real data acquisitions. The experiments and the comparison with conventional signal processing approaches have highlighted the beneﬁts of the proposed method.

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106 7. Conclusion and outlook

7.2 Recommendations and future work

Although being a topic that has largely been analysed since several decades, the subjects of array processing, digital beamforming and the issues related to their application to modern systems continue to be of high interest in the radar community. Array based radar systems, which provide a digitisation capability at a channel level, indeed oﬀer extended signal processing ﬂexibility. However, in order to fully exploit these type of systems, proper design choices are required from both the hardware point of view and the signal processing approach.

The data throughput which is produced by fully digital systems can be a driving factor for the following processing steps. By referring to the PCL system presented in Ch.4, it was indeed necessary to perform a digital decimation, and consequently a single transmitter selection, in order to handle the channel data streams provided by the ADC. The mentioned compromise represents a stringent limitation for the PCL performance, since it prevents the possibility of realising a multilateral/multistatic system by exploiting the diﬀerent radio stations which are available. A considerable gain in terms of coverage and both range and angular resolutions can be achieved by upgrading the data links of the current system. The frequency agility of the system does depend on the radiating characteristic of the array elements. With the aim at preventing any variability of the PCL performance related to the selection of transmitters on the all FM band, wideband radiators would be recommended to improve the EM behavior of the system antenna section. Concerning the digital processing, the array pattern shaping procedure in Ch.3 represents the ﬁrst step for improving the angular resolution of the PCL. As a further development, the application of high resolution techniques for improved angular and range resolution can be considered. The results obtained by the two dimensional approach with the MIMO demonstrator obviously represent a reliable perspective.

The opportunities offered by the MIMO processing applied to the radar field are continuously evolving. The additional degrees of freedom that are offered by the coherent MIMO systems are particularly suitable for the application of digital beamforming schemes. In that sense, the RADOCA demonstrator has confirmed the validity of this combination. One of the main research interests in this field regards the behavior of the sidelobes with respect to the selected orthogonality approach and target characteristics. The analysis conducted in Ch.5 has indeed tackled this problem from an antenna section point of view and a preliminary answer from the mentioned perspective has been provided. By referring to the proposed high resolution technique based on the MU- SIC method, research activities towards different directions can be foreseen. At first,

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7.2 Recommendations and future work 107

it must once again be noticed that the output of the algorithm represents a pseudo amplitude value. It would be of large interest to retrieve, for the detected targets, an estimation of the true reflectivity signature. In that way, high resolution imaging applications by means of a stationary system can be performed. It has then been discussed the importance of applying a data smoothing technique, in presence of coherent targets, to the received slow and fast time data samples in order to avoid a rank deficiency of the related covariance matrix. The optimal dimensioning of the averaging window has to be investigated. On the one hand, it should prevent an ex- cessive reduction of the available degrees of freedom in both domains (angle, range); on the other hand, the target decorrelation should still be ensured. Research activities have started to investigate the potentiality of the MIMO/DBF processing in combination with SAR acquisition geometries. In that sense, the possibility of synthesising the virtual channels would allow reducing the data throughput of the radar system, that is a desirable advantage in airborne as well as in space based configurations. Equivalently, the multiple degrees of freedom offered by the MIMO processing would represent an added value for interferometric, tomographic and GMTI signal processing. Under this perspective, further studies must be conducted in order to ensure the coherency among the multiple acquisitions. Enhanced performance can be achieved by combining the orthogonal transmissions with the spatial selectivity, i.e. by transmitting different waveforms in different directions. This approach, usually referred to as space-time coding or colored transmission, allows overcoming some limitations related to the wide beam illumination (spreading of the clutter spectrum, uniqueness of the transmitted waveform in multi-task systems, degraded multipath rejection capability). At the same time, since a wide area is scanned, there is no reduction of the system coverage at the receiver side. A signif- icant effort is required, at both the system design and the signal processing levels, in order to ensure the electronic steering capability at transmission and the agile synthesis/selection of the colored waveforms. The related research activity, which can be seen as an extension of the MIMO work produced in this thesis, obviously represents a challenging opportunity for future investigations.

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108 7. Conclusion and outlook

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Appendix A

PCL system measurements

The PCL system measurements have concerned with the characterisation of the analog receiver components and the antenna element patterns. By referring to the first ones, that are presented in Sec.A.1 and Sec.A.2, two specific evaluations have been performed: the RF gains and the noise figures for each of the channels of the passive radar subsystem. Specifically, the variations of the channel behaviors, due to the introduction of the attenuator blocks, have been checked. In Sec.A.3, the measurement procedure leading to the estimation of the element patterns in the array set-up are presented.

A.1 Receiver channel gains

A reference signal has directly been injected into the passive radar receiver in order to perform the measurements. To improve the isolation between the signal generator and the receiver itself, an additional attenuator has been included in the chain as

Figure A.1: Set-up of the gain measurements.

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110 A. PCL system measurements

Table A.1: Gain values of the receiver channels Channel Both attenuators Pre-Attenuator Both attenuators number OFF ON ON 1 26.8dB 16.6dB 6.7dB 2 26.8dB 16.6dB 6.7dB 3 27.4dB 17.3dB 7.3dB 4 27.3dB 17.1dB 7.1dB 5 26.6dB 16.4dB 6.5dB 6 27.0dB 16.8dB 6.9dB 7 26.8dB 16.6dB 6.7dB 8 26.9dB 16.7dB 6.7dB

depicted in Fig.A.1. The attenuation provided by the attenuator was equal to 10dB. The behavior of the 8 channels has been checked by simultaneously switching on/oﬀ the pre and post attenuators of the passive receiver. Table A.1 summarises the measurement results in terms of gain provided at the output of the receiver. The external attenuation is not included in the results.

A.2 Channel noise ﬁgures

The noise figures have been measured in order to check the effect of the attenuator series which are present in the receiver rack. The values have been estimated according to the setup in Fig.A.2. An HP346B noise source [111] has been taken as reference and the noise floor has been retrieved by means of an HP8970A noise meter [112], that has been connected to the output of the receiver. The frequency of 100MHz has been considered and, at that frequency, an average gain of 26.8dB has been measured for the channels with the attenuators switched off. This value is in line

Figure A.2: Set-up of the noise ﬁgure measurements.

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A.3 Element patterns 111

Table A.2: Noise ﬁgure values Channel Both attenuators Post-Attenuator number OFF ON 1 4.5dB 7.0dB 2 4.6dB 7.1dB 3 4.6dB 7.0dB 4 4.6dB 6.9dB 5 4.6dB 7.4dB 6 4.5dB 7.1dB 7 4.5dB 7.1dB 8 4.5dB 7.1dB

with the previous measurement set-up in Sec.A.1. Tab.A.2 shows the measured noise figures for all the receiver channels. The pre-attenuator was switched off during these measurements as it is the non-preferred one, due to its placement just before the low noise amplifier; anyway, its effect has been evaluated on one of the channels and taken as representative of all the others. The values are presented in Tab.A.3 As expected, the degradation introduced by the pre-attenuator is equal to the attenuation it provides (10dB) and it leads to a final value for the noise figure, when both the attenuators are considered, of roughly 17dB.

A.3 Element patterns

Due to the size of the array structure, it was not possible to perform the measurements in the anechoic chamber available at TNO. The element pattern of the array elements have been characterised in an open air far ﬁeld measurement setup, by placing the array on a rotating platform and using a bow-tie antenna as reference transmitter. The following procedure has been used:

• A reference transmitter, consisting of a biconical dipole antenna Fig.A.3.(a), was connected to the ﬁrst port of a spectrum analyzer whereas a channel of the PCL array Fig.A.3.(b) was connected to the second one. All the other channels

Table A.3: Noise ﬁgure dependency with the attenuators conﬁguration Channel Both attenuators Pre-Attenuator Both attenuators number OFF ON ON 1 4.5dB 14.5dB 17.0dB

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112 A. PCL system measurements

were characteristically loaded.

• The transmitter and the array were located according to the geometry in Fig.A.3.(c), at a distance of ca. 25m which ensured operation in the far ﬁeld. The array was placed on a rotating platform Fig.A.3.(d).

• While keeping the same position of the transmitter, the array was turned to cover the 360 degrees on the azimuthal plane and the S21 parameter was measured.

• The procedure was repeated for the other channels

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A.3 Element patterns 113

(b) (a)

(d)

(c)

Figure A.3: Element pattern measurement setup: reference transmitter (a), PCL array ARx and reference transmitter AT x (b), measurements geometry (c) and rotating platform with scaled plane (d)

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114 A. PCL system measurements

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Appendix B

Illumination error eﬀects on the synthesis of MIMO array pattern

Proof that:

2 2 h|F (θ)| iNORM ' |F (θ)|iNORM (B.1) M−1 h i N−1 h i |F (θ)|2 P |b |2 σ2 + ∆2 + |F (θ)|2 P |a |2 σ2 + ∆2 T i m δR T R i n δT R + m=0 n=0 N−1 M−1 2 P P |an||bm| n=0 m=0

The four main contributions, related to the diﬀerent combinations of the (m, n) indexes, have been retrieved in Ch.5. For a better understanding of the steps, they are here recalled:

" N−1 M−1 2 −(σ2 +σ2 ) 2 X X 2 2 δT δR h|F (θ)| i (n6=n0) = e |F (θ)|i + |an| |bm| (m6=m0) n=0 m=0 M−1 N−1 # 2 X 2 2 X 2 − |FT (θ)|i |bm| − |FR(θ)|i |an| (B.2) m=0 n=0

N−1 M−1 2 2 2 X X 2 2 h|F (θ)| i (n=n0) = (1 + ∆T )(1 + ∆R) |an| |bm| (B.3) (m=m0) n=0 m=0

M−1 " N−1 # 2 −σ2 X 2 2 X 2 δT 2 h|F (θ)| i (n6=n0) = e (1 + ∆R) |bm| |FT (θ)|i − |an| (B.4) (m=m0) m=0 n=0

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116 B. Illumination error eﬀects on the synthesis of MIMO array pattern

N−1 " M−1 # 2 −σ2 X 2 2 X 2 δR 2 h|F (θ)| i (n=n0) = e (1 + ∆T ) |an| |FR(θ)|i − |bm| (B.5) (m6=m0) n=0 m=0 By combining (B.2) and (B.3):

2 2 2 −(σδ +σδ ) 2 h|F (θ)| i1 = e T R |F (θ)|i N−1 M−1 h 2 2 i X X 2 2 2 2 −(σδ +σδ ) + |an| |bm| (1 + ∆R)(1 + ∆T ) + e T R n=0 m=0 " M−1 N−1 # 2 2 −(σδ +σδ ) 2 X 2 2 X 2 − e T R |FT (θ)|i |bm| + |FR(θ)|i |an| (B.6) m=0 n=0

and by combining (B.4) and (B.5):

M−1 2 2 −(σδ ) 2 X 2 2 h|F (θ)| i2 = e T (1 + ∆T ) |bm| |FT (θ)|i m=0 M−1 N−1 2 −(σδ ) 2 X 2 X 2 − e T (1 + ∆T ) |bm| |an| m=0 n=0 N−1 2 −(σδ ) 2 X 2 2 + e R (1 + ∆R) |an| |FR(θ)|i n=0 M−1 N−1 2 −(σδ ) 2 X 2 X 2 − e R (1 + ∆R) |bm| |an| . (B.7) m=0 n=0

2 2 The terms h|F (θ)| i1 and h|F (θ)| i2 can now be collected and normalised by the quantity: N−1 M−1 !2 2 2 −(σδ +σδ ) X X ρ = e T R |an||bm| . (B.8) n=0 m=0 This normalisation leads to:

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117 2 2 | | n n (B.9) a a | | 1 1 − − =0 =0 P P n n N N 2 2 2 i 2 i | | ) ) | | θ θ m m ( ( b b R R || || F F n n | | a a | | + + 1 1 2 2 − − =0 =0 | | P P m m M M m m 2 b b 2 1 1 2 | | | | | 2 2 − − n 1 1 =0 =0 n n P P a n n a N N − − | =0 =0 a | | | | P P 1 m m m 1 M M 1 m b − b =0 − 2 i 2 i − =0 =0 P | | || P n P || N n ) ) n N N n n θ θ 2 2 a 2 | ( ( a | | | | T T m 1 m 1 m b b F F − b | =0 − | =0 | | | P P 1 1 m M 1 m M − =0 − 1 =0 − =0 1 P P − − P m − M =0 m − M m =0 M P 2 2 P n ) N ) n | | ) N 2 2 T 2 R 2 T m m ) b b ∆ | ) ∆ | | ∆ R 2 2 R m 2 δ | | 2 δ b σ n n σ || + a a + (1 + (1 + | | n (1 + ) T ) T ) a 2 1 1 δ 2 δ T | R T σ 2 δ − − σ =0 =0 2 δ 2 ( δ 1 ( σ σ X X σ ( m m − − M M =0 ( ( − P e − 1 1 e − − m M e e − − e =0 =0 1 X X n n N N − − =0 − − P n i i N 2 i 2 i 2 2 ) ) 2 i 2 | | 2 | ) ) R R ) 2 2 δ δ ) | | θ θ | θ | ( ( σ σ R ( m m m 2 δ m + + T T b b R b σ b T T F F || || || F 2 2 || δ δ | | + | n n n 2 2 σ σ n T 2 | | ( ( a a | 2 δ a a | | | | − − σ n m m 1 1 ( 1 e e 1 b b a | | | − − − =0 =0 − =0 − =0 1 1 P P e 1 P P m m M M m M m M − − =0 =0 − ) + ) + =0 1 1 P P P 1 1 n 2 T 2 T m m N M M − − =0 =0 − − =0 =0 P P ) ) ) P P ∆ ∆ n n N N n n N N 2 R 2 T 2 T ∆ ∆ ∆ ) ) ) ) R R R R 2 2 δ δ 2 δ )(1 + )(1 + 2 δ σ σ σ σ 2 R 2 R (1 + + + (1 + (1 + + + ) ) ) ∆ ∆ T T 2 iNORM 2 iNORM T T 2 2 δ δ | | R T T 2 δ 2 δ 2 2 2 δ δ δ ) ) σ σ σ σ ( ( σ σ σ ( θ θ ( ( ( ( ( ( − − − − (1 + (1 + − − − e e e e F F h e h e e | | = + + = + + + NORM NORM i i 2 2 | | ) ) θ θ ( ( F F h| h|

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118 B. Illumination error eﬀects on the synthesis of MIMO array pattern 2 | n a | (B.11) 1 (B.10) − =0 P n N 2 2 i | ) | θ m ( b R || F n | a i | + 1 1 2 − =0 | − P m M m ) b 1 2 R | − 1 =0 ∆ P 2 n N − | 2 =0 P 2 n m | M 2 2 | a | | | 2 i m n (1 + | m n 1 b ) ) a b | a | − θ | T =0 2 || P 2 δ ( | 1 n 1 N n σ n T − =0 ( − a 2 =0 P a | | P e n F N | n | N h 1 m 1 2 2 | 2 − b =0 | − | =0 | P P m m n M − 1 m m M b b a | 1 − =0 | | 1 2 P 1 − =0 1 2 1 − m M =0 P | − P n =0 | N − − =0 n ) =0 N P 2 P m P m n M m N m 2 R M b 2 b | ) | 2 i ) i 2 ∆ | || 2 T | ) m 2 R | n n b θ ∆ a m ∆ ( a + 1 | || | b 2 ) 1 n R 2 (1 + 1 || ) a R − F =0 n | − =0 2 | | δ | P R (1 + P a 1 m σ (1 + 2 M δ ) | m M m m ) σ + − + 1 =0 b 1 R b ( 1 T P 2 δ T i − || 2 δ =0 m || − =0 M − − 2 δ =0 σ P 1 σ P n P n ( n e N σ 1 n ( m N M ( a e a e | − | − =0 e 1 − P ) 1 n 1 ) N − − i =0 − 2 i P 2 T − =0 | − 2 T =0 n 2 i N 2 i P ) | P | m ) ∆ M m ) M θ ∆ ) + 1 ( θ 1 R 1 θ 2 ) δ ( ( R − − =0 σ =0 R P T P n R F 2 δ n N + N | F (1 + σ F )(1 + | 2 T ) | | 2 δ + 2 2 R 2 | R n σ | T 2 δ ( 2 δ a ∆ m n σ | σ − ( b a ( | 1 e | e e 1 h − 1 =0 ) P − 2 =0 n − N (1 + =0 2 T | P P h n ) m N M m ∆ ) ) 2 R b + | 2 T 2 R ∆ 1 ∆ ∆ − =0 P )(1 + m M 2 R (1 + 2 i | ) (1 + (1 + 2 iNORM 2 iNORM ∆ ) | | R ) ) θ 2 δ ) ) T R ( σ θ θ 2 2 δ δ ( ( ( T σ σ ( − ( (1 + F F F e e | e | | h + + = = + + + NORM NORM i i 2 2 | | ) ) θ θ ( ( F F h| h|

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119 (B.12) i i ) (B.14) (B.13) ) 2 R 2 R ∆ ∆ + i T 2 δ 1 (1 + σ T − 2 δ σ ) e 2 R (1 + − ∆ − ) ) 2 T 2 T ∆ (1 + ) ∆ T 2 δ + σ (1 + ( R e 2 δ R h 2 δ σ σ 2 | e n − a | (1 + 1 − − =0 + 1 P n T N 2 ) 2 2 δ 2 i 2 R | | σ + 1 2 δ | ) | σ m θ 2 T m m b + ( b | b ∆ 1 + T 2 R || 2 || δ | n F σ n + n ' | ( a a a | e ) | | 2 R ) + 1 T 1 1 2 δ ∆ 2 T − i =0 − − =0 =0 σ P 1 P ( P ∆ m M + m m M M e 1 − 1 1 R − 2 δ =0 ) − − =0 =0 P P P n σ N 2 T n n N N )(1 + ∆ R + 2 R 2 δ i T σ ) ∆ 2 δ 2 R 0, then the following approximations hold: σ (1 + ) ∆ 1 + ' R (1 + 2 δ 2 δ 1 + h ' σ h σ ( ) 2 (1 + e 2 2 ) R h | 2 2 δ | | T 2 | σ 2 δ m | ( m m σ b m e b ( | b m b | e 2 b || | 2 | || | n n 1 n a n a | a − =0 ) + | a | | P 1 1 2 T m 1 M 1 − =0 − =0 − 2 i =0 P ∆ − =0 | P P m M P 2 iNORM m ) M m M | 2 iNORM m M 1 θ | 1 ) 1 ( 1 ) − =0 θ − − =0 P =0 θ ( T − (1 + P n =0 P N ( n ) P n N N n F N F | R | F 2 δ σ ( e + + = h + ' | − NORM NORM i i 2 | 2 | ) ) θ θ ( ( F F h| h| and by neglecting the second order terms which derive from (B.13), we obtain: If we consider the presence of small errors, i.e.

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120 B. Illumination error eﬀects on the synthesis of MIMO array pattern (B.15) i 2 R ∆ + T 2 δ σ h 2 | n a | i 1 2 n − =0 P ∆ n N 2 2 i + | ) | T θ 2 δ m ( b σ R || h F n 2 | | a | n + 1 a | i − =0 1 P 2 T m M − =0 P ∆ 1 n N − 2 =0 2 i + P | n N ) | R θ 2 δ ( m σ b R h || F 2 n | | a | m + b 1 | i − =0 1 P 2 m − m =0 M P ∆ 1 m M − =0 2 i + P | n N ) R θ 2 δ ( σ T h F 2 | | m + b | 1 − =0 P m M 2 i 2 iNORM | | ) ) θ θ ( ( T F F | ' | + NORM i 2 | ) θ ( F h| That ﬁnally leads to: Q.E.D.

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Appendix C

Basic theory of FMCW

A frequency modulated continuous wave (FMCW) signal like the one presented in Fig.C.1, also referred to as sawtooth modulated signal, is characterised by the instan- taneous transmitted frequency:

B B f (t) = f − + t = f + αt (C.1) t c 2 T 0

being fc the carrier frequency, B the transmitted bandwidth, T the pulse duration and with 0 < t < T . For simplicity in the description, the expression with the initial

frequency f0 and the sweep rate α is considered. According to (C.1), the transmitted signal is represented by: α 2 j2π[fct+ t ] st(t) = e 2 . (C.2)

Figure C.1: Transmitted and received sawtooth modulated signals

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122 C. Basic theory of FMCW

Under narrow band assumption, the received signal is a time delayed version of the transmitted one: α 2 j2π[fc(t−τ)+ (t−τ) ] sr(t) = e 2 (C.3)

2R0 where, in the case of a stationary target, τ = c being c the speed of light and R0 the range location of the target. In the case of homodyne FMCW radar, the received signal is then mixed with the transmitted one producing the signal:

α 2 j2π[fcτ+ατt− τ ] sb(t) = e 2 (C.4) characterised by the so called beat frequency:

fb = ατ (C.5) which is directly related to the range information. Therefore, unlikely pulse radars where the maximum unambiguous range is dictated by the pulse repetition interval

(time), in FMCW systems it depends on the frequency fs which is used to sample the received signal. According to the Nyquist criterion, the maximum unambiguous range is: c f R = s (C.6) max 2α 2 The range resolution is directly related to the frequency resolution, i.e. to the observation time, and it results: c c 1 c δR = δf = = . (C.7) 2α 2α T 2B

If the case of a moving target characterised by constant velocity vD, the time delay takes the form: 2 2v τ = (R + v t) = τ + D t (C.8) c 0 D 0 c and by replacing (C.8) in (C.4), we obtain:

2 1 2 2vD 2vD 2α vD 2 j2π fcτ0− 2 ατ0 +(ατ0+fc c −ατ0 c )t+ c vD − c t sr(t) = e (C.9)

vD Under the assumption that c 1, the resulting beat frequency component is: 2v f ' ατ + f D = ατ + f (C.10) b 0 c c 0 D

being fD the Doppler frequency shift induced by the target movement. As a result, an ambiguity is introduced in the range estimation of the target since the peak of the signal response is shifted with respect to the true target location. Several modulation techniques have been proposed in the literature to overcome this limitation of the conventional FMCW system [95].

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List of Acronyms and Symbols

Acronyms

ADC Analog to Digital Converter

ADSB Automatic Dependent Surveillance Broadcast

AIC Akaike Information Criterion

CDM Code Division Multiplexing

CFAR Constant False Alarm Rate

DBF Digital Beam Forming

DDC Digital Down Conversion

DPI Direct Path Interference

DR Dynamic Range

ECCM Electronic Counter Counter Measure

ECM Electronic Counter Measure

EVD Eigenvalue Decomposition

FDM Frequency Division Multiplexing

FDTD Finite Diﬀerence Time Domain

FMCW Frequency Modulated Continuous Wave

FNB First Null Beamwidth

GMTI Ground Moving Target Indicator

HPB Half Power Beamwidth

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124 List of Acronyms and Symbols

INR Interference to Noise Ratio

LAN Local Area Network

LMS Least Mean Squared

MC Mutual Coupling

MDL Minimum Description Length

MF Matched Filter

MTI Moving Target Indicator

PCB Printed Circuit Board

PCL Passive Coherent Locator

RADOCA RAdar DOme CAmera

RCS Radar Cross Section

RVP Residual Video Phase

SAR Synthetic Aperture Radar

SIMO Single Input Multiple Output

SLL Side Lobe Level

SLR Side Lobe Reduction

SNR Signal to Noise Ratio

TDM Time Division Multiplexing

UCA Uniform Circular Array

ULA Uniform Linear Array

Symbols

χ(τ, fD) Ambiguity function

η Antenna eﬃciency

ηc Conduction eﬃciency

ηd Dielectric eﬃciency

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List of Acronyms and Symbols 125

ηi Illumination eﬃciency

ηr Reﬂection eﬃciency

λ Wavelength

C Mutual coupling matrix

P Digital section compensation matrix

S Scattering parameters matrix

T Transmission coeﬃcients matrix

V Interference source directions matrix

φ Azimuth angle

2 σI Interference power

2 σn Noise power θ Elevation angle

ξ Speed stretching factor

D(θ, φ) Antenna directivity

E(θ, φ, r) Electric ﬁeld

F (θ, φ) Array factor

fc Carrier frequency

fi(θ, φ) Ideal element pattern

fN Nyquist frequency

fn(θ, φ) Element pattern

fs Sampling frequency

G(θ, φ) Antenna gain

k Free space wave number

P (θ, φ) Array pattern

U(θ, φ) Radiation intensity

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126 List of Acronyms and Symbols

vD Radial (Doppler) speed

xs(t) Surveillance channel signal

xr(t) Reference channel signal

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Summary

Antenna Array Signal Processing for Multistatic Radar Systems

The introductions of Digital Beam Forming (DBF), original signal exploitation and waveform multiplexing techniques have led to the design of novel radar concepts. Pas- sive Coherent Locator (PCL) and Multiple-Input Multiple-Output (MIMO) sensors are two examples of innovative approaches. Beside the inherent benefits of this class of sensors, related to the use of emitters of opportunity and the waveform diversity for the PCL and the MIMO cases respectively, an additional gain is achieved by using ad-hoc array signal processing techniques. The well-known advantages provided by the antenna arrays, or phased arrays, are, among others, the possibility of synthesising arbitrarily steered beams, especially in the case of DBF, the capability of shaping the array pattern sidelobes region and the opportunity of placing nulls towards specific directions. The last feature allows suppressing, or mitigating, the echoes of unwanted signals (clutter, jammer, interferences) that are present inside the radar scenario and that can degrade the detection performance of the system. With DBF, the interferences suppression can adaptively be done in real time. This thesis has focused on the development of novel array processing algorithms, with emphasis on antenna pattern optimisation. Also, attention was paid to resolution enhancement and clutter suppression techniques exploiting the available radar architectures. A PCL and a MIMO array system have been investigated in order to validate the proposed techniques. Specifically, the first part of the thesis deals with the development of the array signal processing chain of a PCL system based on a circular array. The performance of digital beamforming algorithms highly depends on the behavior of the antenna section of the array; indeed, an inaccurate characterisation of the element channels and their mutual influence degrades the shape of the synthesised array pattern. A complete analysis of the circular array is presented in the text and a technique for the mutual

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138 Summary

coupling compensation, based on an optimisation approach, was retrieved. The effec- tiveness of the method was validated. Furthermore, a new pattern shaping technique for the sidelobes reduction was developed. Due to the poor angular resolution of the PCL array, the criteria for estimating the quality of the retrieved algorithm was represented by the achievable sidelobes suppression level for a given angular resolution. A comparison with the phase modes approach has proven the better performance of the proposed method. Concerning the validation of the PCL system, the entire signal processing chain of the sensor was developed and the related behavior was success- fully assessed by the comparison with the ground truth data provided by an ADSB transponder. The second part of the thesis refers to coherent MIMO radars and to the benefits they provide with respect to conventional array-based radars. The linear array configuration was taken as reference and a MIMO test board, the RADOCA system, has been realised and studied. By first recalling the peculiarity of such systems, i.e. the possibility of synthesising virtual array structures, the research activity has investigated the effect that illumination errors produce on the related pattern behavior. The analytical expression of the errors affected pattern was retrieved and the comparison with conventional linear array systems showed the higher degradation they produce on MIMO based arrays. The focus was then moved to the identification of calibration and array processing techniques, capable of exploiting both the MIMO radar principle and the additional degrees of freedom provided by the virtual channels. By referring to the RADOCA demonstrator, a calibration procedure was retrieved and validated thanks to real data acquisitions. Then, with the aim of enhancing the system performance, two objectives were reached: the extension of the maximum unambiguous Doppler interval, by means of a random selection of the radar transmitter sequence, and the identification of a novel 2D high resolution technique based on the MUSIC algorithm. The comparisons with traditional approaches highlighted the benefits of the proposed techniques.

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Samenvatting

Antenna Array Signal Processing for Multistatic Radar Systems

De introductie van Digitale Bundelvorming (‘Digital Beamforming’, DBF), signaalexploitatie en het gebruik van meerdere golfvormen hebben geleid tot nieuwe radar concepten. ‘Passive Coherent Locator’ (PCL) en ‘Multiple-Input Multiple- Output’ (MIMO) sensoren zijn twee voorbeelden van zulke innovatieve methoden. Inherente voordelen van deze sensoren zijn gerelateerd aan toevallig aanwezige zenders voor PCL en golfvormdiversiteit in het geval van MIMO. Daarnaast is met behulp van ad-hoc signaalverwerkingstechnieken nog extra voordeel te behalen. Bekende voordelen van antenne arrays zijn onder andere de mogelijkheid tot bundelsturing in elke richting (DBF), controle over het zijluspatroon en de mogelijkheid tot onderdrukking van signalen in speciﬁeke richtingen. Dit laatste punt maakt het mogelijk om ongewenste signalen die de prestaties van de radar kunnen verlagen, zoals clutter, jamming, en interferentie, te onderdrukken. DBF maakt het mogelijk om interferentie adaptief te onderdrukken in real-time. De focus van deze scriptie is op de ontwikkeling van nieuwe algoritmes voor arrays met nadruk op optimalisering van het antennepatroon. Daarnaast komen technieken voor het verbeteren van de resolutie en het onderdrukken van clutter aan bod, die gebruik maken van de beschikbare, innovatieve radararchitectuur. Om de voorgestelde technieken te valideren zijn een PCL en een MIMO arraysysteem onderzocht. In het eerste deel van dit proefschrift wordt de ontwikkeling van de signaalverwerkingsketen van een PCL systeem behandeld dat gebaseerd is op een circulair array. De prestaties van DBF algoritmes zijn sterk afhankelijk van het gedrag van de antennes in het array. Een onnauwkeurige karakterisering van de signaalkanalen en hun wederzijdse be¨ınvloeding degraderen de vorm van het gecombineerde antennepatroon. De tekst bevat een complete analyse van het circulaire array. Met behulp van optimalisatietechnieken was het mogelijk een nieuwe methode voor de compensatie van de wederzijdse be¨ınvloeding te ontwikkelen.

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140 Samenvatting

Vervolgens is de effectiviteit van deze methode gevalideerd. Daarnaast is een nieuwe techniek ontwikkeld om zijlussen te onderdrukken met behulp van patroonvorming bij een minimale verbreding van de hoofdlus. De reden hiervoor is de beperkte hoekresolutie van het PCL array. In een vergelijking met de zogenaamde ‘phase modes approach’ is de betere prestatie van het voorgestelde algoritme aangetoond. De volledige PCL signaalverwerkingsketen is ontwikkeld en vervolgens gevalideerd met behulp van data van een ADSB transponder. Het tweede deel van dit proefschrift behandelt coherente MIMO radars en de voordelen hiervan ten opzichte van conventionele radars met een antenne-array. Hiervoor is een lineair array als referentie genomen. Een MIMO testboard, het zogenaamde RADOCA systeem, is ontwikkeld en bestudeerd. Vervolgens worden de bijzonderheden van een dergelijk systeem beschreven, namelijk de mogelijkheid om een virtueel array te maken. Het effect dat belichtingsfouten (bijvoorbeeld fase- of positioneringsfouten) hebben op het bundelpatroon is onderzocht en hiervoor is een analytische uitdrukking afgeleid. Het blijkt dat een MIMO array gevoeliger is voor belichtingsfouten dan een conventioneel lineair array. Vervolgens zijn kalibratie- en array-processingtechnieken ge¨ıdentificeerd, die gebruik maken van de extra vrijheden die het MIMO principe biedt. Dankzij het RADOCA demonstratiemodel was het mogelijk om een kalibratieprocedure te ontwikkelen en te valideren gebaseerd op opgenomen data. Met het oog op het vergroten van de prestaties van het systeem zijn de volgende twee verbeteringen gerealiseerd: het verlengen van het maximale niet-ambigue Dopplerinterval, door middel van random selectie van de volgorde van radarzenders; het verhogen van de resolutie door een nieuw 2D-MUSIC algoritme. In een directe vergelijking met de traditionele technieken is de meerwaarde van bovenstaande algoritmes aangetoond.

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Author’s publications

Journal Papers

J1 F. Belﬁori, S. Monni, W. van Rossum and P. Hoogeboom, “Antenna Array Char- acterisation and Signal Processing for an FM Radio-Based Passive Coherent Location Radar System,” Radar, Sonar and Navigation, IET, Vol. 6, Is. 8, pp. 687-696, Oct. 2012.

J2 F. Belﬁori, W. van Rossum and P. Hoogeboom, “Coherent MIMO Array Design with Periodical Physical Element Structures,” Antennas and Wireless Propaga- tion Letters, IEEE, Vol. 10, pp. 1341-1344, 2011.

J3 F. Belﬁori, W. van Rossum and P. Hoogeboom, “A Coherent MUSIC Tech- nique for Range/Angle Information Retrieval: Application to an FMCW MIMO Radar,” Invited paper - to appear in Radar, Sonar and Navigation, IET, Special Issue on Bistatic and MIMO Radars and their Applications in Surveillance and Remote Sensing.

Conference Papers

C1 F. Belﬁori, W. van Rossum and P. Hoogeboom, “Application of 2D MUSIC Algo- rithm to Range-Azimuth FMCW Radar Data,” in Radar Conference (EuRAD), 2012 European, Oct. 2012, pp. 242-245, Amsterdam, Netherlands.

C2 F. Belﬁori, W. van Rossum and P. Hoogeboom, “2D-MUSIC Technique Applied to a Coherent FMCW MIMO Radar,” in Radar Systems (Radar 2012), IET In- ternational Conference on, Oct. 2012, pp. 1-6, Glasgow, Scotland. (Awarded with the best student paper prize).

C3 F. Belﬁori, W. van Rossum and P. Hoogeboom, “Array Calibration Technique for a Coherent MIMO Radar,” in Radar Symposium (IRS), 2012 13th International, May 2012, pp. 122-125, Warsaw, Poland.

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142 Author’s publications

C4 F. Belﬁori, W. van Rossum and P. Hoogeboom, “Random Transmission Scheme Approach for a FMCW TDMA Coherent MIMO Radar,” in Radar Conference (RADAR), 2012 IEEE, May 2012, pp. 178-183, Atlanta, USA.

C5 F. Belﬁori, L. Anitori, W. van Rossum, M. Otten and P. Hoogeboom, “Digital Beam Forming and Compressive Sensing Based DOA Estimation in MIMO Ar- rays,” in Radar Conference (EuRAD), 2010 European, Oct. 2011, pp.285-288, Manchester, UK.

C6 F. Belﬁori, N. Maas, P. Hoogeboom and W. van Rossum, “DMA X-Band FMCW Radar for Short Range Surveillance Applications,” in Antennas and Propagation (EUCAP), Proceedings of the 5th European Conference on, Apr. 2011, pp. 483- 487, Rome, Italy.

C7 F. Belﬁori, P. Hoogeboom, “Analysis of a Novel MIMO System for Security Ap- plications,” in Phased Array Systems and Technology (ARRAY), 2010 IEEE International Symposium on, Oct. 2010, pp. 338-343, Waltham, USA.

C8 F. Belﬁori, S. Monni, W. van Rossum and P. Hoogeboom, “Side-Lobe Suppression Techniques for a Uniform Circular Array,” in Radar Conference (EuRAD), 2010 European, Sep. 2010, pp. 113-116, Paris, France.

C9 F. Belﬁori, S. Monni, W. van Rossum and P. Hoogeboom, “Mutual Coupling Compensation Applied to a Uniform Circular Array,” in Radar Symposium (IRS), 2010 11th International, Jun. 2010, pp. 1-4, Vilnius, Lithuania.

Patent

P1 P. Hoogeboom and F. Belﬁori, “Antenna System, Radar Device and Radar Method with 360 Degree Coverage,” European Patent Application No. 10155992.0, Sep. 2011.

Technical Report

R1 F. Belﬁori, S. Monni, W. van Rossum and D. Deurloo, “Passive Radar Advantages and Threats”, Technical Report, TNO, The Hague, Netherlands, Dec. 2010.

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About the author

Francesco Belfiori was born in Roma, Italy, on September 6, 1982. In September 2001 he started his Telecommunication Engineering studies at the “Universitàdegli studi di Roma - La Sapienza”. He received the Bachelor degree and the Master degree from the same university, both summa cum laude, in 2004 and 2007 respectively. He graduated with a thesis entitled “SHARAD radar sounder simulation: efficient scattering approximation from a coherent surface”. The activity was carried on at the SHARAD Operation Centre (SHOC) located at the Thales Alenia Space facilities in Roma. From June 2007 to January 2008 he worked as a software engineer at ElsagDatamat S.p.a.; he cooperated at the development of the mission planning tool for the NH-90 helicopter in force of the Italian Army. In 2008 he joined the Electronics Division of D’Appolonia S.p.A. as an R&D engineer. During this period he conducted applied research activities in the fields of electronics, radar and remote sensing, signal and image processing. In February 2009 he started working on his PhD degree in a joint cooperation between the Delft University of Technology and TNO Defence, Security and Safety, in the Netherlands. The subject of the research was about the application of digital beamforming and signal processing techniques to passive and MIMO radar systems. During his PhD work, in 2012, he spent three months at the Institut d’ Electronique´ et de Télécommunications de Rennes (IETR) at the “Universitéde Rennes 1”, France, where he worked in cooperation with Prof. L. Ferro-Famil. He is a student member of IEEE and serves as a reviewer for IEEE, IET, Elsevier and Springer journals.

Award

Best student paper prize at the 2012 IET - International Conference on Radar Sys- tems (RADAR2012), Glasgow, UK. Awarded for the article entitled: “2D-MUSIC Technique Applied to a Coherent FMCW MIMO Radar”.

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144 About the author

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Acknowledgements

Although a very high weight is on your own shoulders, on the PhD way you meet many people that help you in carrying it on. The achievements you reach at the end are then always the result of combined efforts and, even if they bring your name, you know you would not have done much without that support. First of all, I would like to thank my supervisor Prof. Peter Hoogeboom, who gave me the possibility to challenge myself with the research activity on array signal processing. He secured founding for this research and he introduced me to the radar groups of TNO and of the Delft University of Technology. I am especially thankful to Dr. Wim van Rossum, my daily supervisor at TNO. He has been a mentor in these four years and he has always been capable of providing critical feedbacks and keen remarks during our discussions. It has been a pleasure to work with you and I hope to keep the same passion and dedication for research you have shown to me. At the Delft University of Technology, many thanks go to Prof. Fran¸coisLe Chevalier for the several advices and suggestions about my research. One of them also brought me to the lovely city of Rennes, where I was glad to work at the IETR laboratory of the “University of Rennes 1” in cooperation with Prof. Laurent Ferro-Famil. He has been truly inspiring to me and I really look forward to finalising the activity we have started together. Felt gratitude goes to the TNO radar group and especially to its Italian creek: Daniela, Stefania, Bernadetta, Lorenzo, Giampiero and Daniele. You have been as a new family for me and, after knowing you, I finally realised what the “brain drain” means. Same feeling I share with all the other great scientists and very good friends I had the fortune to meet at TU Delft. It is a long list and definitely worth of being written. Dana, Tobias, Diego, Alexey, Dima, Teun, Karolina, Ricardo, Guendalina and Igor: the time spent together simply had no price. Among others, I want to express my deep heart gratitude to my paranymphs: my sorellina italiana Laura and frère fran¸caisYann. Thanks for being so close to me in these years, for sharing the many doubts, concerns and pains about our PhD tracks.

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146 Acknowledgements

It has been a long way for the all of us but at the end we all managed. The city of Delft is truly an agglomerate of multiple cultures and the time I spent here, learning about the diﬀerent habits and traditions, was just great. Though, it would have not been so without the presence of the many dutch and international friends I met. Special thanks then go to Jitske, Leen, Renske, Illy, the “thai” couple Anne and Martijn and the bundes one Christian and Kati. A list like that cannot obviously be complete without an italian component: Elena, Riccardo and the meta- crew: Alex, Simone, Adriano and Christian; thanks for the enjoyable time we have spent together in front of a well arranged table, drinking beer and all complaining about our politically devastated country. Living abroad could result in breaking down the connections with the people you left behind. I feel really lucky by not having faced anything of that, thanks to the presence of all my friends in Rome. Every time I come back, you just behave as I had never left, regardless the last occasion we have met or talked to each other. I could never thank you enough for that.

Finally, I would like to thank those who share the most important part of my heart: my father Pietro, my brother Stefano and my sister in love Cristiana with their little Matteo. The choice to leave you was one of the most though I had ever taken and it often led to rethinking. If I am here today is only because of your constant support and encouragement: I will forever be in debt with you. The very last thought is for my mother, Anna, to whom this thesis is dedicated: I know you have followed me along the way and I hope that today you are proud of me. Infine vorrei ringraziare coloro che occupano il posto piùimportante nel mio cuore: mio padre Pietro, mio fratello Stefano e mia cognata Cristiana con il loro piccolo Matteo. La scelta di lasciarvi èstata una delle piùdifficili che io abbia mai preso ed èspesso stata motivo di ripensamento. Se sono qui oggi èsolamente grazie al vostro supporto e incoraggiamento costanti: saròsempre in debito con voi. L’ ultimo pensiero èper mia madre, Anna, a cui questa tesi èdedicata: so che mi hai seguito lungo la strada e spero che oggi tu sia orgogliosa di me.

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