FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT . Estimating the Frequency Response of a Receiver Blind Identification Yu Deyue September 2012 Master’s Thesis in Electronics Master’s Program in Electronics/Telecommunications Examiner: Niclas1 Björsell Supervisor: Efrain Zenteno 2 Yu Deyue Estimating the Frequency Response of a Receiver Abstract Consider a receiver that has an unknown impulse response in the form of linear time-invariant system, which is driven by an input signal and random noise with an unknown distribution. If the unknown impulse response of the receiver could be identified, then its equivalent frequency response can be used for calibration, using deconvolution aiming to regain the original signal under measurement. Hence, the estimation of the transfer function of the receiver is of great importance from both theoretical and practical applications. This thesis is devoted to the identification of the receiver’s unknown finite impulse response (FIR form), by observing only the output signal through it. More specifically, not only the amplitude and phase but also the orders of the finite impulse response of the receiver are unknown. A blind algorithm is tested for the identification of the unknown communication channel of the receiver in simulation. Further, in a practical implementation performed in this thesis such blind algorithm is combined with a technique to compute the receiver’s transfer functions. The word blind indicates that there is no restriction in the input signal set, it is allowed to be non-stationary with unknown statistical model, and hence this algorithm is particularly suitable for de- reverberation technology. The implementation of the blind algorithm is demonstrated through the Matlab simulation, and verified through experimental measurements, where several of the impairments of hardware will be considered in the analysis. i Yu Deyue Estimating the Frequency Response of a Receiver Acknowledgment I would like to thank the supervisor, Ph.D. Mr Efrain Zenteno for his constructive comments, careful reviews and scientific supervision. My thanks also give to all the people in ITB/Electronics at the University of Gävle, for their contributions of making a pleasant working environment. ii Yu Deyue Estimating the Frequency Response of a Receiver Table of contents Abstract .................................................................................................................................................... i Acknowledgment .................................................................................................................................... ii Table of contents .................................................................................................................................... iii 1 Introduction ..................................................................................................................................... 1 1.1 Problem statement .................................................................................................................... 1 1.2 Thesis goal ............................................................................................................................... 4 2 Theory ............................................................................................................................................. 5 2.1 Modulation ............................................................................................................................... 5 2.1.1 Digital carrier modulation ................................................................................................ 5 2.2 Blind channel identification ..................................................................................................... 6 2.2.1 SIMO (two-output) ........................................................................................................... 6 2.2.2 SIMO (more than two-output) .......................................................................................... 8 2.2.3 SISO to SIMO equivalence .............................................................................................. 9 2.3 System identification .............................................................................................................. 10 3 Simulation ..................................................................................................................................... 11 3.1 Channel order known ............................................................................................................. 12 3.1.1 Noiseless channel ........................................................................................................... 13 3.1.2 Noisy channel ................................................................................................................. 18 3.1.3 Consider the different feature input ................................................................................ 24 3.2 Channel order unknown ......................................................................................................... 25 4 Measurements ................................................................................................................................ 29 4.1 Hardware device introduction ................................................................................................ 29 4.2 Measurement set-up ............................................................................................................... 29 4.3 Noise reduction ...................................................................................................................... 30 4.4 Receiver identification ........................................................................................................... 31 4.4.1 Received data.................................................................................................................. 32 4.4.2 Existing channel ............................................................................................................. 33 iii Yu Deyue Estimating the Frequency Response of a Receiver 4.4.3 Order selection................................................................................................................ 35 4.4.4 Identified receiver models .............................................................................................. 37 4.4.5 Validation of the identified receiver models .................................................................. 39 5 Discussion ..................................................................................................................................... 42 6 Conclusions ................................................................................................................................... 43 7 Future work ................................................................................................................................... 44 References ............................................................................................................................................. 45 iv Yu Deyue Estimating the Frequency Response of a Receiver v Yu Deyue Estimating the Frequency Response of a Receiver 1 Introduction In digital signal processing applications, when a signal is measured through a receiver, the measured signal becomes shaped by the frequency response of the receiver (or its time equivalent impulse response). Such frequency response can be represented by a linear system, that is, a figure conveying both amplitude and phase distortions, so any signal will suffer when it is applied to such a system. The estimated frequency response of the receiver can be used for calibration, deconvolving signal that is observed to regain the original signal under measurement, so the estimation of frequency response of receiver compensate for the effect introduced in the receiver at measurement. The problem of deconvolving any signal that observed through one or more unknown multichannel arises in data communication applications. It is more often, the unknown input signals change rapidly and become more unrealistic. In this thesis, an algorithm is tested for the blind identification of multichannel outputs FIR systems of the receiver using the measured data and without requiring any knowledge of the input signals statistics. But this blind algorithm requires some assumptions on the input. However, the statistical model of the input could be unknown or there may not be enough data samples to do a reasonably and accurate estimation. The oversampling is certainly necessary in the output. The algorithm that tested in this thesis (blind identification of frequency response of receiver) is based on the eigenvalue decomposition of a correlation matrix [1]. The input signal could be obtained by deconvolution of the identified receiver’s FIR with the received signal. 1.1 Problem statement The output is observed from an unknown linear time-invariant system with unknown input . See the Figure.1.1 below. The problem is to identify the or inverse or, equivalently, so it could recover the input . unknown Figure 1.1 An input passes through an unknown linear time-invariant system to the output. In the measurement, we use the discrete output data to identify the unknown linear system. The output data may have some possible small perturbations, which may affect the blind identification [2]. 1 Yu Deyue Estimating the Frequency Response of a Receiver The output is observed from an