Introduction Into Theory of Direction Finding

Home , Adcock antenna, Directional antenna, Radio direction finder, Wullenweber

Direction Finders Introduction into Theory of Direction Finding Introduction into Introduction Applications of direction finding While direction finding for navigation purposes (referred to Theory of Direction as cooperative direction finding) is becoming less important due to the availability of satellite navigation systems, there is a growing requirement for determining the loca- Finding tion of emitters as the mobility of communications equip- ment increases: JJ In radiomonitoring in line with ITU guidelines

WW Searching for sources of interference

WW Localization of non-authorized transmitters JJ In security services

WW Reconnaissance of radiocommunications of criminal organizations JJ In military intelligence [1]

WW Detecting activities of potential enemies

WW Gaining information on enemy‘s communications order of battle JJ In intelligent communications systems

WW Space division multiple access (SDMA) requiring knowledge of the direction of incident waves [2] JJ In research

WW Radioastronomy

WW Earth remote sensing

Another reason for the importance of direction finding lies in the fact that spread-spectrum techniques are increasingly used for wireless communications. This means that the spectral components can only be allocated to a specific emitter if the direction is known. Direction finding is therefore an indispensable first step in radiodetection, par- ticularly since reading the contents of such emissions is usually impossible.

The localization of emitters is often a multistage process. Direction finders distributed across a country allow an emitter to be located to within a few kilometers (typ. 1 % to 3 % of the DF distances) by means of triangulation. The emitter location can more precisely be determined with the aid of direction finders installed in vehicles. Portable direction finders moreover allow searching within the last 100 m, for instance in buildings.

Historical development The DF technique has existed for as long as electromagnetic waves have been known. It was Heinrich Hertz who in 1888 found out about the directivity of antennas when conducting experiments in the decimetric wave range. A specific application of this discovery for determining the direction of incidence of electromagnetic waves was pro- posed in 1906 in a patent obtained by Scheller on a hom- ing DF method.

72 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

The initial DF units were polarization direction finders. The first shortwave direction finder operating on the They consisted of a rotatable electric or magnetic dipole Doppler principle was built in 1941. The rapid progress 1 whose axis was brought to coincidence with the direc- in the development of radar in Great Britain made it tion of the electric or magnetic field. From the direction of necessary to cover higher frequency ranges: In 1943, the polarization, the direction of incidence was then deduced. first direction finders for “radar observation” at around The rotating-loop direction finder is one of the best known 3000 MHz were delivered [1]. 2 direction finders of this type. In 1907, Bellini and Tosi discovered the DF principle that was named after them: a As from 1943, wide-aperture circular-array direction find- combination of two crossed directional antennas (e.g. loop ers (Wullenweber) were built for use as remote direction antennas) with a moving-coil goniometer for determining finders. Since the 1950s, airports all over the world have 3 the direction [1]. Despite this invention, rotating-loop been equipped with VHF/UHF Doppler direction finding direction finders were often used in the First World War systems for air traffic control. (Fig. 1). In the early 1970s, digital technology made its way into 4 The invention made by Adcock meant a great leap forward direction finding and radiolocation; digital bearing genera- in the improvement of the DF accuracy with respect to sky tion and digital remote control are major outcomes of this waves in the shortwave range. The pharmacist by profes- development. sion realized in 1917 that with the aid of vertical linear an- 5 tennas (rod antennas or dipoles) directional patterns can Since 1980, digital signal processing has been increasingly be generated that correspond to those of loop antennas used in direction finding. It permits the implementation of but do not pick up any interfering horizontally polarized the interferometer direction finder and initial approaches field components (G. Eckard proved in 1972 that this is not toward the implementation of multiwave direction finders 6 true in all cases [3]). It was not until 1931 that Adcock an- (super-resolution). The first theoretical considerations were tennas were first employed in Great Britain and Germany. made much earlier, e.g. in [4].

In 1925/26, Sir Watson-Watt took the step from the me- Another important impetus for development came from 7 chanically moved goniometer direction finder to the elec- the requirement for the direction finding of frequency-agile tronic visual direction finder. As from 1943, British naval emissions such as frequency-hopping and spread- vessels were equipped with crossed loops and three- spectrum signals. The main result of this was the broad- channel Watson-Watt direction finders for the shortwave band direction finder, which is able to simultaneously 8 range (“huff-duff” for detecting German submarines). perform searching and direction finding based on digital filter banks (usually with the aid of fast Fourier transform As from 1931, camouflaged direction finders were avail- (FFT)) [5]. able for use in vehicles and as portable direction finders 9 for detecting spies.

Fig. 1: Mobile rotating-loop direction finder for military use (about 1918) [1].

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 73 Direction Finders Introduction into Theory of Direction Finding

Tasks of direction finding The first assumption is based on the undisturbed propaga- The task of a radio direction finder is to estimate the direction of a harmonic wave of wavelength λ. At a sufficiently tion of an emitter by measuring and evaluating electro- large distance, the radial field components are largely magnetic field parameters. decayed so that, limited to a small area, the wave can be considered to be plane: Electric and magnetic field com- Usually, the azimuth α is sufficient to determine the di- ponents are orthogonal to and in phase with one another rection; the measurement of elevation ε is of interest for and are perpendicular to the direction of propagation, emitters installed on flying platforms and especially for the which is defined by the radiation density vector (Poynting direction finding of shortwave signals (Fig. 2). vector) S      E 2 Only in the case of undisturbed wave propagation is the S=×= EH e 0 Z direction of the emitter identical with the direction of inci- 0 dence of the radio waves. Usually, there is a large number where E = RMS value of electric field strength of partial waves arriving from different directions and mak- Z0 = characteristic impedance of free space; ing up a more or less scattered field. The direction finder Z0 ≅ 120 ⋅ πΩ takes spatial and temporal samples from this wavefront  and, in the ideal case, delivers the estimated values αˆ and or by the wave number vector k (Fig. 4). εˆ as the most probable direction of the emitter observed.   2π ke= 0 Bearings can be taken using the following reference direc- λ tions (Fig. 3) (see also EN 3312 [6]): JJ Geographic north (true north) ▷ true radio bearing Overview of main DF principles JJ Magnetic north Direction finding relies on the basic characteristics of elec- JJ Vehicle axis ▷ relative or direct radio bearing tromagnetic waves, which are: JJ Transversality, i.e. field vectors are perpendicular to the direction of propagation DF principles JJ Orthogonality of phase surfaces and direction of propagation Generation and characterization of electromagnetic waves Every DF process essentially employs one of the following Electromagnetic waves are caused by charging and dis- methods (Table 1, on next page): charging processes on electrical conductors that can be JJ Method A: measures the direction of electric and/or represented in the form of alternating currents [7], [8]. magnetic field vectors ▷ polarization direction finders JJ Method B: measures the orientation of surfaces of equal phase (or lines of equal phase if the elevation is not of interest) ▷ phase direction finder

Fig. 2: Deﬁnition of emitter direction Fig. 3: Reference directions

North

Emitter Reference direction True radio bearing Emitter

Dead ahead ε α

Line of bearing (LOB)

DF DF antenna vehicle

Relative radio bearing

74 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

Polarization direction finders are implemented by means of Phase direction finders obtain the direction information dipole and loop antennas. The classic rotating-loop direc- (bearing information) from the spatial orientation of lines 1 tion finder also belongs to this category (rotation of loop to or surfaces of equal phase. There are two basic methods: minimum of received signal ▷ direction of incident wave JJ Direction finding based on directional patterns: perpendicular to loop). Today, polarization direction finders With this method, partial waves are coupled out at vari- are used in applications where there is sufficient space ous points of the antenna system and combined at one 2 only for small antennas, e.g. in vehicles and on board point to form a sum signal. The maximum of the sum ships for direction finding in the HF band. Evaluation is signal occurs at the antenna angle at which the phase usually based on the Watson-Watt method (see section differences between the partial waves are at a minimum. “Classic DF methods”). To obtain unambiguous DF results, The sum signal is thus always orthogonal to the phase 3 however, the phase information must be evaluated in ad- surfaces of the incident wave (maximum-signal direction dition. finding). For minimum-signal direction finding, the partial waves are combined so that the phase differences in the direction of the incident wave become maximal and there 4 is a distinct minimum of the received signal JJ Direction finding by aperture sampling: With this method, samples are taken at various points of the field and applied to evaluation circuits sequentially 5 or in parallel. These circuits determine the bearing by linking the samples, which is today mostly done by mathematical operations 6 Typical examples are interferometers and Doppler direction finders.

The DF methods mentioned so far are suitable only to a 7 Fig. 4: Propagation of space waves limited extent for determining the directions of incidence of several waves that overlap in the frequency domain.

i(r,t)ej(ωt+φ0) With the progress made in digital signal processing, the 8 methods known from the theory of spectral estimation have been applied to the analysis of wavefront and devel- oped. The term “sensor array processing” describes the 9

2π H k0D = –– D = const λ S 10

Table 1: DF principles. 11 Wave characteristic Transversality Phase surfaces I Direction of propagation

DF principle Polarization direction Phase direction finder finder Examples Direction finding with directional Aperture sampling 12 patterns Conversion phase ▷ amplitude Direct evaluation Sensor array processing JJ Rotating loop JJ Directional antenna JJ Interferometer JJ Correlation direction Maximum-signal direction finder finder Minimum-signal direction finder 13 JJ Dipole JJ Adcock with Watson-Watt JJ Rotating-field direction JJ Adaptive beam former evaluation finder JJ Loaded loop JJ Doppler direction JJ MUSIC finder JJ Crossed loop with JJ ESPRIT Watson-Watt evaluation

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 75 Direction Finders Introduction into Theory of Direction Finding technique of gaining information about the parameters Depending on the configuration, systems for determining of incident waves from the signals derived from the ele- the direction finder‘s own coordinates/orientation (GPS, ments, or sensors, of a sensor array (antenna array in di- compass), remote-control units (LAN, WAN), antenna con- rection finding, hydrophone array for sonar). trol units, etc., can be added.

There are basically three different methods: The achievable DF speed mainly depends on the number JJ Beamforming methods, e.g. correlation direction finder, H of receive sections, as this parameter determines the spatial Fourier analysis, adaptive antenna number of antenna outputs that can be measured in paral- JJ Maximum likelihood method as the most general lel. model-based method JJ Subspace methods, e.g. MUSIC, ESPRIT To achieve maximum speed, it must be possible to gen- erate a bearing in a single time step, i.e. from one set of Main requirements on DF systems samples (monopulse direction finding). For unambiguous JJ High accuracy direction finding over the total azimuth range, at least JJ High sensitivity three antenna outputs are required. If there are also three JJ Sufficient large-signal immunity receive sections, multiplexing of the measurement channel JJ Immunity to field distortion caused by multipath is not necessary. propagation JJ Immunity to polarization errors Typical examples of monopulse DF antennas: JJ Determination of elevation in shortwave range JJ Multimode antenna for amplitude comparison direction JJ Stable response in case of non-coherent co-channel finders, e.g. Adcock antenna interferers JJ Interferometer and rotating-field (phase) direction finder JJ Short minimum required signal duration JJ Scanning direction finders: high scanning speed, and For high DF accuracy (e.g. 1°) and large bandwidth (e.g. high probability of intercept (POI) 1 MHz to 30 MHz or 20 MHz to 1000 MHz), five to nine aperture samples are usually required. Since monopulse Components of a DF system solutions would then be very complex, one fixed and two A DF system (Fig. 5) consists of the following compo- sequentially switched receive sections are frequently used. nents: JJ Antenna system The DF converter converts the carrier-frequency antenna JJ DF converter signals to a fixed IF. Since this conversion must be per- JJ Evaluation unit formed with equal phase and amplitude in all receive sec- JJ Display unit tions, the use of a common synthesizer is indispensable. Moreover, with most multipath direction finders, the receive sections are calibrated in order to ensure equal amplitude and phase. Calibration is performed with the aid of a test generator at defined intervals and prior to the actual Fig. 5: DF system components DF operation.

The evaluation unit determines the bearing from the ampli- 1 … N Antenna system tudes and/or phases of the IF signal. with N elements Network

1 … H DF converter Classic DF methods Test Tuner Tuner for H receive sections gen. Using directional antennas Compass, GPS Evaluating the receive voltage of a mechanically rotated Evaluation unit directional antenna with reference to the direction is the simplest way of direction finding. With this method, the Display of – azimuth bearing is derived from the characteristic of the receive – elevation voltage as a function of the antenna rotation angle: When – level a wave arrives, the receive voltage yields the directional – band occupancy – ... pattern of the antenna. The pattern position relative to the antenna rotation angle is the measured bearing [1].

76 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

This type of direction finder is a phase direction finder The drawbacks of this method result from the restricted since the directivity of the receive antenna is achieved by angular detection range, which is due to the directivity 1 superimposing partial waves whose phase differences of the antenna, and the antenna‘s limited rotating speed, depend on the angle of incidence. In the simplest case, which is mainly due to the use of a mechanical rotator: the antenna is rotated and the bearing determined by the JJ Probability of intercept is reciprocal to directivity operator. The antenna is rotated until the receiver output JJ Method fails in case of short-duration signals, i.e. with 2 voltage assumes an extreme value. The antenna direction signal dwell times that are short compared to a scanning thus found is read from a scale, and the bearing is deter- cycle of the antenna mined from it. If the directional antenna (with maximum or minimum pattern) is permanently rotated with the aid Despite these drawbacks, DF methods using mechanically 3 of a motor, and the receive voltage is displayed graphically rotated directional antennas are still in use today since as a function of the angle of rotation, a rotating direction achieving the described advantages with other methods finder is obtained (Fig. 6). Using suitable automatic evalua- involves in part considerably higher cost and effort. In the tion of the receive voltage characteristic, e.g. by means of microwave range, in particular, the mechanical DF method 4 a maximum detector, a fully automatic direction finder is is often the only justifiable compromise between gain, low obtained. noise and expenditure.

The following benefits are common to all variations of this If, in addition to a directional pattern with a maximum in 5 DF method: the direction of the incident wave, a directional pattern JJ High sensitivity due to the directivity of the antenna with a minimum is used, a monopulse direction finder is JJ Simple and inexpensive implementation (only one obtained that even with a slowly rotating or fixed antenna receiver required (single-channel principle)) delivers bearings as long as waves arrive in the main re- 6 JJ Resolution of multiwavefronts is possible (prerequisite: ceiving direction of the antenna. Fig. 7 shows a typical different angles of incidence and high-directivity antenna implementation using log-periodic dipole antennas that are system) connected by means of a 0/180° hybrid. This results in the JJ Same antenna can be used for direction finding and directional patterns shown below. 7 monitoring The quotient of the difference and the sum signal yields a dimensionless, time-independent function, i.e. the DF function: 8 V ()α PF()α= ∆ VΣ ()α After forming the quotient of the two test voltages, the DF 9 function immediately delivers the bearing α.

Fig. 6: DF using a directional antenna Fig. 7: DF using sum-difference method 10

0°

α 11

270° 90° VΣ

Bearing indicator 12 VΔ

Receiver IF without AGC 13 Σ ∆

Typical implementation on the left, directional patterns for sum (Σ) and difference (∆) outputs on the right.

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 77 Direction Finders Introduction into Theory of Direction Finding

Watson-Watt principle The principal advantage of this method is that the bearing If the amplified and filtered signals of a receiving antenna is indicated without delay, which means that it is capable with outputs for a sine-shaped and a cosine-shaped direc- of monopulse direction finding over the entire azimuth tional pattern are applied to the x and y deflection plates range. of a cathode-ray tube (CRT), a line Lissajous figure is obtained in the ideal case, whose inclination αˆ corresponds Suitable antennas (Fig. 9) with sine-shaped or cosine- to the wave angle but exhibits an ambiguity of 180°. The shaped directional patterns are in particular the following: indicated angle is obtained from the ratio of the two sig- JJ Loop antennas (or ferrite antennas) nals as follows: JJ Adcock antennas (monopole or dipole arrays) V α=ˆ arctan x Crossed-loop antennas with Watson-Watt evaluation are V y mainly suitable for mobile applications due to their com- An unambiguous bearing indication is obtained (Fig. 8) if pact size. They feature the following benefits and draw- a blanking signal is additionally used in this DF method, backs: which was first implemented by Watson-Watt in 1926. The JJ Benefits: blanking signal is derived from an omnidirectional receiv- WW Extremely short signal duration is sufficient ing antenna with an unambiguous phase relationship. WW Implementation is simple

WW Minimum space is required If there is a phase difference δ between the two voltages JJ Drawbacks:

WW Vx and Vy , which may be due to ambient interference (e.g. Small-aperture system (D/λ < 0.2) causing errors reflections), the displayed figure is an ellipse. The position in case of multipath propagation of the main axis yields the bearing αˆ , which is calculated WW Large DF errors when receiving sky waves with steep from the two voltages by means of the equation below [9]. elevation angles

V 1 2 Vxy V cosδ α=ˆ Re arctanx = arctan V2 2 2 y VVyx−

Fig. 8: Watson-Watt direction ﬁnder with crossed-loop antenna

Crossed loop α

Omnidirectional receiving antenna

V sense V Brightness y

Vx Vx DF converter CRT Vsense

Blanking

78 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

Adcock antennas feature the following advantages over A number of disadvantages of analog direction finders are crossed-loop antennas: avoided, yielding the following effects: 1 JJ Improved error tolerance for sky wave reception JJ Synchronous operation of channels also on filter edges JJ Wider apertures can be implemented to reduce errors JJ Simple procedure of taking into account correction in case of multipath reception (e.g. D/λ < 1 for 8-fold values for antenna networks, cables, etc. Adcock) JJ No temperature drift in digital section 2 JJ Bearings available as numeric values for evaluation, Modern direction finders no longer display the IF voltages especially for easy transmission to remote evaluation of antenna signals on a CRT but digitally process the sig- stations nals after converting them into a relatively wide IF band 3 (Fig. 10). Doppler direction finder If an antenna element rotates on a circle with radius R, the

Selection is mainly effected by means of digital filters; received signal with frequency ω0 is frequency-modulated bearings are calculated numerically, e.g. using the last with the rotational frequency ωr of the antenna due to the 4 equation above, and displayed on a computer (worksta- Doppler effect. If the antenna element moves toward the tion, PC) with a graphical user interface (GUI). radiation source, the receive frequency increases; if the antenna element moves away from the radiation source, the receive frequency decreases. 5

From the instantaneous amplitude Fig. 10: Conﬁguration 2Rπ u()() t= acos() φ t = acos ω0r t + cos() ω t −α +ϕ 6 λ0 the instantaneous frequency is derived by differentiation of V3 V2 the phase dtφ() 2Rπ 7 ω()t = =ω − ωsin() ω t −α dt 0λ rr V1 V4 0

After filtering out the DC component ω0, the demodulated Doppler signal is obtained as 8 V = ΣV ref 2Rπ V = V3 – V4 – Filtering cos SD= ω rr sin() ω t −α – Bearing λ V = V1 – V2 0 sin calculation 9 DF A/D converter converter

Configuration of a modern direction finder operating on the Watson-Watt principle. 10

Fig. 9: Various antenna conﬁgurations 11

For generating sine-shaped or cosine-shaped directional patterns: crossed-loop antenna, ferrite antenna, H Adcock, U Adcock (from left).

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 79 Direction Finders Introduction into Theory of Direction Finding

The phase of the demodulated signal is compared with a The ambiguous interference pattern is weighted with the reference voltage of equal center frequency derived from directional pattern of the antenna element, which yields an the antenna rotation unambiguous bearing (see Fig.12, diagrams on the right).

Srr=− sin ω t Using the minimum of three omnidirectional receiving elements, unambiguous determination of the azimuth and which yields the bearing α [1]. elevation is possible only if the spacing a between the an-

tennas is no greater than half the wavelength. With Φ1, Φ2,

Since rotating an antenna element mechanically is nei- Φ3 as the phases measured at the outputs of the antenna ther practically possible nor desirable, several elements elements, the azimuth is calculated as (dipoles, monopoles, crossed loops) are arranged on a cir- Φ −Φ cle (Fig. 11) and electronically sampled by means of diode α=ˆ arctan 21 Φ −Φ switches (cyclic scanning). 31 The elevation angle is obtained as To obtain unambiguous DF results, the spacing between the individual antenna elements must be less than half the 22 ()()Φ21 −Φ + Φ 31 −Φ operating wavelength; in practice, a spacing of about one ε=ˆ arccos 2aπλ third of the minimum operating wavelength is selected. In practice, the three-antenna configuration (Fig. 13) is If this rule is adhered to, Doppler DF antennas of any size enhanced by additional antenna elements so that the are possible, i.e. wide-aperture systems with the following spacings between the antennas can be optimally adapted features can easily be implemented: to the operating frequency range, and antenna spacings JJ High immunity to multipath reception of a > λ/2 can be used to increase the accuracy of small- JJ High sensitivity aperture DF systems [1]. Frequently used antenna arrange- ments include the isosceles right triangle and the circular A drawback of the Doppler method is the amount of time array (Fig. 14). it requires. At least one antenna scanning cycle is required in order to obtain a bearing. At a typical rotational fre- Triangular configurations are usually restricted to frequen- quency of 170 Hz in the VHF/UHF range, one cycle takes cies below 30 MHz. At higher frequencies, circular arrays approx. 6 ms. are preferred for the following reasons: JJ They ensure equal radiation coupling between the Interferometer antenna elements The interferometer direction finder was first used in radio JJ They ensure minimum coupling with the antenna mast astronomy [10]. The objective was to increase the resolu- JJ They favor direction-independent characteristics at tion power and the sensitivity of the DF system by super- different positions due to the symmetry around the imposing the signals of only a few antenna elements that center point were however spaced many wavelengths apart (Fig. 12).

Fig. 11: Principle of Doppler direction ﬁnder Fig. 12: Classic two-element interferometer

Element pattern 1 α 0.5 τ 0 Δf –5 –4 –3 –2 –1 0 1 2 3 4 5 1 Interference pattern 1 fscan 0.5 1 2 3 4 1 Delay 0 4 2 –5 –4 –3 –2 –1 0 1 2 3 4 5 Output pattern 1 0.5 Averaging 0 3 –5 –4 –3 –2 –1 0 1 2 3 4 5 Output α in °

Used in radio astronomy; block diagram (left) and antenna patterns (right).

80 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

It is essential to avoid ambiguities, which result from the This is demonstrated by the example of a five-element an- fact that unambiguous measurement of the phase is possi- tenna as shown in Fig. 15. Each column of the lower data 1 ble only in the range of ±180°. As already mentioned, this matrix corresponds to a wave angle a and forms a refer- condition is met in the case of the three-element (small- ence vector. The elements of the reference vectors repre- aperture) interferometer by limiting the spacing between sent the expected phase differences between the antenna the elements to half the minimum operating wavelength. elements for that wave angle. The upper 5 × 1 data matrix 2 With multi-element interferometers, there are the follow- contains the actual measured phase differences (mea- ing possibilities: sured vector). JJ Use of “filled” antenna arrays: Phase differences between neighboring elements are always < 180°; ambiguities are To determine the unknown wave angle (direction of inci- 3 avoided. dence), each column of the reference matrix is correlated JJ Use of “thinned” antenna arrays: There is a phase differ- with the measured vector by multiplying and adding the ence of > 180° between at least one pair of neighboring vectors element by element. This process results in the elements. Such ambiguities in antenna subarrays are correlation function K(a) , which reaches its maximum at 4 today usually eliminated by subjecting the signals from the point of optimum coincidence of reference vector and all elements simultaneously to a pattern comparison by measured vector. The angle represented by that specific way of correlation ▷ correlative interferometer. reference vector is the wanted bearing. 5 The basic principle of the correlative interferometer con- This method constitutes a special form of a beamforming sists in comparing the measured phase differences with algorithm [11], which will be discussed in greater detail in the phase differences obtained for a DF antenna system of the following section. known configuration at a known wave angle. The compari- 6 son is performed by calculating the quadratic error or the correlation coefficient of the two data sets. If the comparison is made for different azimuth values of the reference data set, the bearing is obtained from the data for which 7 the correlation coefficient is at a maximum.

Fig. 13: Three-element interferometer 8

Antenna 3 9

Wave Fig. 15: Principle of correlative interferometer a

12 10 α 56 Antenna 1 87 Measured a 22 phase differences Antenna 2 05 11 12 56 Calculated phase differences for different 87 directions of incidence Fig. 14: Multi-element interferometer 22 of a plane wave 12 05

α K(α) 13

α Three-antenna configuration enhanced to form a multi-element interferometer.

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 81 Direction Finders Introduction into Theory of Direction Finding

Direction finding using sensor array processing Basic design Fig. 16 shows a typical hardware configuration of a DSP- General based direction finder [12]. The development of the classic DF methods was aimed at designing antenna configurations that allowed bearings to The outputs of the individual antenna elements are usually be determined using a circuit design as simple as possible. first taken to a network that contains the following, for It was important to establish a simple mathematical rela- instance: tionship between the antenna signals and the direction of JJ Test signal inputs the incident wave largely independent of frequency, polar- JJ Multiplexers if the number N of antenna outputs to ization and environment. be measured is higher than the number H of receive sections (tuners and A/D converters) in the direction With the development of digital signal processing, new ap- finder proaches have become possible: JJ With high-speed signal-processing chips now available, The signals are then converted to an intermediate frequen- the requirement for a simple and frequency-independent cy that is appropriate for the selected sampling rate of the relationship between the antenna signals and the bearing A/D converters and digitized. To reduce the data volume, no longer applies. Even highly complex mathematical the data is digitally downconverted into the baseband. The

relationships can be evaluated in a reasonably short complex samples xi(t) (i = 1, 2, to N) of the baseband sig- period of time for determining the bearing, or handled nals are filtered for the desired evaluation bandwidth and quickly and economically by means of search routines applied to the bearing calculation section. JJ Numeric methods allow the separation of several waves arriving from different directions even with limited Fig. 17 shows a typical implementation including a nine- antenna apertures (high-resolution methods, super- element circular array antenna and a three-path receiver. resolution, multiwave resolution) The signals of the antenna elements are measured sequentially based on three-element subarrays.

Fig. 16: Typical conﬁguration

... Analog signal processing

Antenna network

... Test Tuner Tuner Tuner generator IF IF IF Synthesizer

A/D A/D ... A/D converter converter converter

Down- Down- ... Digital converter converter signal processing

Filtering and bearing calculation Fig. 17: DSP-based R&S®DDF06A broadband direction finder for the frequency range from 0.3 MHz to 3000 MHz and circular array antenna Typical configuration of a DSP-based direction finder. (R&S®ADD153SR, without cover) for the 20 MHz to 1300 MHz range.

82 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

General DF task For the model discussed here, it is assumed that a signal is

For an antenna array of N elements positioned in an radiated by an emitter with a carrier frequency of f0 (wave- 1

unknown wave field, the general DF task (Fig. 18) is to length λ0) and modulated with the function s(t). The wave

estimate – from the measured data x1(t), x2(t), to xN(t) – the is considered to be plane in the far field of the emitter and parameters listed below: to arrive at an angle α0 (Fig. 19). JJ Number M of waves 2 JJ Directions of incidence of the waves For signal bandwidths that are small in comparison with JJ Amplitudes of the waves the reciprocal of the signal delay between the elements spaced at the maximum distance (narrowband approxima- Procedure tion), the baseband signal at the output of the i-th sensor 3 The task is performed in two steps: can be modeled in accordance with the following equa- JJ Determine the relationships between the measured data tion: x (t) to x (t) and the number, directions and amplitudes of 2π 1 N j ri cos()αβ 0i λ0 the waves involved xi()()() t=α stci0 e + nt() 4 JJ Develop methods for determining the number, directions, = s()()() t ai0 α+ n i t and amplitudes of the main waves involved based on the relationships determined in the first step The term st()()= rtejp() t describes the waveform and the 5 Relationship between the measured data and the amplitude of the signal in the form of the complex enve- parameters of the incoming waves lope.

Data model for a single wave The term nti () describes the inherent noise of the sensor 6 For the sake of simplicity, it is assumed that the emitter channel. and the receiving antennas are located in the same plane, i.e. the elevation angle of the waves can be ignored. It is The term ci0()α describes the characteristic of the an- also assumed that the waves and the antenna elements tenna element. 7 are vertically polarized. 2π j ri cos()α 0i −β The term e λ0 describes the phase displacement due to the delay between the reference point O and the

position ri of the i-th antenna element. The phase dis- 8 placement solely depends on the position of the element

(normalized to the wavelength λ0) and the direction of incidence of the wave. 9

10 Fig. 18: General DF task Fig. 19: Characterization of incoming wave ﬁeld

Wave 1: s1(t), α1 Wave M: sM(t), αM y 11 Antenna array 1 2 3 N

Wave 12

k A 0 Filter 1

AN r x (t) x (t) x (t) x (t) α i Ai Measured data 1 2 3 N 0 13

– Number of waves Algorithm – Amplitudes

– Directions βi

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 83 Direction Finders Introduction into Theory of Direction Finding

The antenna- and direction-dependent quantities are then Characterization of antenna array combined in the direction component: If the wave angle α is continuously varied across the range

2π of interest, the tip of the antenna vector a(α) describes a j ri cos()α 0i −β λ0 ai0()()α= ce i0 α curve in the N-dimensional space (Fig. 20). The curve is referred to as an array manifold and fully characterizes the In the interest of simplified notation and straightforward antenna for the parameter α, except for any loss or gain geometrical interpretation, the signals xi(t) at the element factors [13]. outputs are assumed to be components of a vector x(t) in the observation space: It is obtained by measurement or by calculation.

x()()()()t= st an α+0 t Example: For an ideal crossed-loop antenna (N = 2), it is assumed that one element has a sine-shaped and the

xt11() nt() other a cosine-shaped directional pattern. The array mani-   fold is expressed by the equation xt22() nt() xn()t== ,t()  ...... sinα   a()α= and describes a circle (Fig. 21).   cosα xtNN() nt()

2π j r1 cos()α 01 −β e λ0 2π j r cos()α −β λ 2 02 e 0 a()α=0  ... 2π j r cos()α −β λ N 0N e 0 a(α) designates a specific direction α and is referred to as direction vector. The set of all direction vectors forms the array manifold, a parameter that plays a vital role in every aspect of array processing [13].

Fig. 20: Array manifold Fig. 21: Array manifold

Element 3

a1 = const sinα α = 90° A N = 3 a(α) α

a(α)

α = 180° α = 0° a2 = const cosα α

Element 2

α = 270°

Element 1

Array manifold characterizing an antenna array. Array manifold of a crossed-loop antenna.

84 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

Solution for single-wave model Assuming a measured vector with noise superimposed on

Assuming there is no noise, i.e. n(t) = 0, the measured it, which is the case in practice, x and a(α0) are no longer 1

vector x(t) differs from the direction vector a(α0) only with located on a straight line. The bearing can only be estimat- respect to length. To solve the DF task, the direction vector ed as the best approximation between x and a(α0): has to be found that is parallel to the measured vector. The H degree of parallelism can be determined from the direction α=ˆ0 argmax xa() α 2 cosine between the two vectors, which is proportional to α the scalar product (Fig. 22). This approach by estimation corresponds to the beamforming method. Like in conventional antenna arrays, the H x⋅ a()() α= xa α element signals xi are multiplied by complex weighting 3 * factors waii=α() and added together (Fig. 23). This xH is the vector whose conjugate has been taken and that yields a sum signal which, corresponding to the resulting has been transposed relative to x. directional pattern, depends on the direction of incidence

α0 of the wave and the look direction α. The asterisk (*) in 4 the term above means conjugate complex. Fig. 22: Determining the bearing α0

The response of the output signal y to the variation of the weighting factors w is used for direction finding same as 5 Signal from i antenna element 2 with a classic rotating or goniometer direction finder. The α 0 only difference is that – with numeric generation of the antenna pattern – the DF speed is limited only by the com- puting power. α 6

a(α) 7 x

x∙a(α) 8 Signal from antenna element 1

Determining the bearing α0 from the direction vector a, which is parallel to the measured vector x. 9

Fig. 23: Beamforming by weighting the outputs of an antenna array 10 Antenna element 1 1 … N 0.9

0.8 11 0.7

x x 0.6

1 … N pattern Directional 0.5 12 W1 WN 0.4

Σ 0.3 y 0.2 13 0.1 Output 0 0 50 100 150 200 250 300 350 400 α in °

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 85 Direction Finders Introduction into Theory of Direction Finding

If antenna arrays with largely the same elements and an By optimizing the weighting factors, the level of the array geometry that can be described by analytical means secondary maxima can be lowered, but the width of the are used, the weighting factors can in most cases directly main maximum is increased at the same time. be calculated from the array geometry. If multiport antennas are used (Fig. 24), the variation of the port voltages Vi The super-resolution (SR) DF methods are to solve this as a function of the wave angle is as a rule determined by problem. measurements. Minimum-signal direction finders are considered the Since beamforming using general multiport antennas grandfathers of the SR direction finders. In the early days often does not yield a distinct directivity of the (synthetic) of direction finding, bearings of co-channel signals were antenna pattern, the following terms are used in this case taken by alternately suppressing the waves by means of as well: a rotating loop [1]. It is worth mentioning that signals can JJ Correlation method only be separated by audiomonitoring of the modulation, JJ Vector matching i.e. that correlation with acoustic patterns is required in order to determine the loop null. Multiwave direction finding and super-resolution DF methods Beamforming methods If unwanted waves are received in addition to the wanted Adaptive antennas are antenna arrays with beamformers wave in the frequency channel of interest, the conven- that allow the automatic spatial suppression of unwanted tional beamforming method will lead to bearing errors waves [13], [14], [15]. In communications systems, this is as a function of the antenna geometry. There are two ap- done in order to optimize the signal-to-noise ratio; in direc- proaches to solve this problem: tion finding, the weighting applied in order to suppress JJ If the power of the unwanted wave component is lower signals is used to determine the directions of incidence of than that of the wanted wave component, the direction the incoming waves. finder can be dimensioned to minimize bearing errors, in particular by choosing a sufficiently wide antenna aper- The weighting of the beamformer is selected such that ture (see [1], chapter on multiwave direction finding) the output power is minimized under certain secondary JJ If the unwanted wave component is greater than or equal conditions. In the case of the Capon beamformer [16], the to the wanted wave component, the unwanted waves secondary condition for setting the weighting is defined must also be determined in order to eliminate them. such that the antenna gain remains constant for a given

When using conventional beamforming algorithms, this direction αr. means that the secondary maxima of the DF function must also be evaluated. The limits are reached if either of the following occurs:

WW The ratio between the primary maximum and the secondary maxima of the directional pattern becomes too small

WW The angle difference between the wanted and the unwanted wave is less than the width of the main lobe

Fig. 24: General multiport antenna with typical application

Port i Port 2 V Port 1 Port 3 i Port 0

Port 0

V1 Port 2 Port 1

86 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

If the incoming waves are uncorrelated, the beamformer is Subspace methods adjusted for nulls to occur in all signal directions except for Subspace methods are intended as a means of eliminat- 1 direction αr (Fig. 25). ing the effect of noise. The N-dimensional space opened up by the element outputs is split up into subspaces. The If the direction of an incident wave coincides with the giv- common MUSIC (multiple signal classification) algorithm en direction αr , there is a distinct maximum in the output makes use of the fact that signals lie perpendicular to 2 power. Fig. 26 shows an example of the angular spectrum the noise subspace. If the direction vectors are projected of a Capon beamformer with a nine-element circular array to the noise subspace, nulls that are independent of the (D/λ = 1.4) and five uncorrelated waves. noise level are obtained if signals are present [13], [17]. The reciprocal value is normally used as the DF function, 3 As with a minimum-signal direction finder, the resolution so that distinct peaks occur at the directions of incidence highly depends on the signal-to-noise ratio. of the signals (Fig. 28 on next page).

Fig. 27 shows the same receiving scenario with noise in- 4 creased by a factor of 10. The resolution of waves arriving at angles of 5° and 10° is no longer possible.

Fig. 25: Super-resolution direction ﬁnding through nulling

Antenna element 90 6 1 … N 120 1 60

0.8

150 0.6 30 0.4 7 0.2 180 0 x1 … xN

W1 WN 210 330 8

Σ 240 300 y 270 9 Output

10 Fig. 26: DF function of Capon beamformer Fig. 27: DF function of Capon beamformer

Capon beamformer Capon beamformer 10 5 11 0 0 ) ) –5 conv conv –10 –10 –20 12

), 10 × log(P –15 ), 10 × log(P ac ac –30 –20 10 × log(P 10 × log(P –40 –25 13 –50 –30 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 α in ° α in °

Comparision with conventional beamformer (S/N = 100); Comparision with conventional beamformer wave angles: 5/15/40/60/220°. (S/N = 10).

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 87 Direction Finders Introduction into Theory of Direction Finding

Display of bearings In addition to the usual receiver settings such as frequency Operators of direction finders rely heavily on the display and bandwidth, the following parameters are set and dis- of DF results, which can generally be divided into two played on direction finders: categories: JJ Averaging mode (If the signal level drops below the JJ Results from a direction finder operating at a single preset threshold, averaging is stopped and either frequency channel continued or restarted the next time the threshold is JJ Results from a multichannel direction finder exceeded, depending on the averaging mode.) JJ Averaging time Single-channel direction finders JJ Output mode

If a bearing is to be taken of a single frequency channel, WW Refresh rate of display the following parameters are usually displayed: WW Output of results as a function of the signal threshold JJ Bearing as a numeric value being exceeded JJ Azimuth as a polar diagram JJ Elevation as a bargraph or a polar diagram Fig. 28: DF function (combined with azimuth display) JJ DF quality MUSIC 350 JJ Level 300 JJ Bearing histogram JJ Bearings versus time (waterfall) 250 )/dB

conv 200 Fig. 29 shows a choice of possible displays. 150 100 ), 10 × log(P mu 50 0 10 × log(P –50 0 50 100 150 200 250 300 350 400 α in °

With MUSIC algorithm (S/N = 10).

Fig. 29: Bearing display with single-channel direction finding

DF quality Averaging Output Averaging mode mode time

Azimuth IF spectrum

Level Elevation

88 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

Multichannel direction finders With multichannel direction finders, it is essential that the Multichannel direction finders are implemented by means individual events can be quickly recognized and activities 1 of digital filter banks (FFT and polyphase filters). Depend- taking place on different channels correctly assigned. ing on the configuration level, this enables quasi-parallel Therefore, the following display modes are usually direction finding in a frequency range from a few 100 kHz provided: up to a few 10 MHz. Larger frequency ranges can be cov- JJ Bearings versus frequency 2 ered by direction finding in the scan mode (Fig. 30). JJ Bearings versus frequency and time (e.g. by displaying the bearings in different colors) JJ Level versus frequency (power spectrum) JJ Level versus time and frequency (e.g. by displaying the 3 level values in different colors) JJ Histograms

Fig. 30: Multichannel direction ﬁnder 4

Filter bank DF processing Level 1 f 01 Azimuth 1 B = 25 kHz 5 Elevation 1 Level 2 f 02 Azimuth 2 B = 25 kHz IF bandwidth Elevation 2 10 MHz DF converter 6

Level 400 f 08 Azimuth 400 f B = 25 kHz 0 Elevation 400 7

Frequency 8

Fig. 31: Multichannel (wideband) display

Bearings of a Azimuth versus 10 frequency hopper frequency

Histogram Bearing of a selected 12 signal Spectrum

Level versus 13 time and f requency

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 89 Direction Finders Introduction into Theory of Direction Finding

Processing of bearings tive to the DF platform and must be active long enough to fix its position. Position finding Bearings can be used in various ways to estimate the po- Emitters operating in the shortwave range can be located sition of an emitter of interest, depending on the degree by means of a single direction finder under certain condi- of sophistication of the DF system and the achievable ac- tions. The direction finder must be able to measure azi- curacy. Maximum accuracy is attained if several direction muth and elevation, and the virtual height of the reflecting finders are employed to determine the emitter position ionosphere layer must be known (Fig. 34). by way of triangulation [1]. If more than two bearings are used for position finding, an ambiguous result is usually Emitter preclassification obtained (Fig. 32). Bearings are vital characteristics of a detected signal. They facilitate quick segmentation, i.e. the assignment of sub- The most probable position can be calculated in a variety spectra to the overall spectrum of an emitter. This makes it of ways. For example, the position can be determined by possible to determine the center frequency and the band- minimizing the error squares or by maximum likelihood width of an emission, which allows its automatic transfer estimation. to a hand-off receiver for analysis. Cluster analysis of bearings makes it possible to separate the signals of emitters If a moving direction finder takes several bearings of an operating in overlapping spectra, especially those of fre- emitter, the emitter position can be determined by a run- quency hoppers. ning fix (Fig. 33). The emitter may move only slightly rela-

Fig. 32: Position ﬁnding Fig. 34: Single station location

Direction ﬁnder 3 α3 Emitter Position 3 Ionosphere Line of position 3

α Line of 1 position 2 Line of position 1

α2 ε Direction ﬁnder 1 Direction ﬁnder 2 Position 1 Position 2

Triangulation.

Fig. 33: Position ﬁnding Fig. 35: Processing of bearings

DF position 2 DF position 1 Variation of envelopes of signals from different

α2 α1 emitters

Accumulation of bearings in azimuth versus frequency

subrange Bi (cluster analysis)

Center frequency Bandwidth Bearing ...

– Transfer to receiver for analysis – Database – Position calculation Running fix.

90 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

DF accuracy Sensitivity is understood to be the field strength at which DF accuracy is affected by a number of factors: the bearing fluctuation remains below a certain standard 1 JJ Wave propagation is usually disturbed by obstacles deviation. JJ Signals radiated by emitters

WW are modulated Noise may occur in the following form: WW are limited in time JJ External noise (atmospheric, galactic, industrial noise) 2 WW frequently operate at unknown carrier frequencies JJ System-inherent noise (antenna amplifiers, JJ The following are superimposed on the reception field: DF converters, A/D converters)

WW noise WW co-channel interferers The following basic considerations apply to system- 3 JJ Noise and tolerances in the DF system inherent noise.

Noise Uncorrelated noise in the receive sections (Fig. 36) causes In addition to intermodulation distortion, interference statistically independent variations of the measured signals 4 caused by noise has a limiting effect on the sensitivity of a as a function of the S/N ratio. The variations become no- DF system. ticeable as bearing fluctuations.

The bearing fluctuation of general antenna arrays can be 5 determined by comparing the variation of the measured vector x with the corresponding variation of α on the curve a(α). Fig. 37 shows this relationship for a two-element ar- Fig. 36: Model describing signal and noise ray. The “faster” the antenna vector “moves”, the smaller 6 the effect of the variation of the measured vector on the variation of α [17].

α0 The relationship between the minimum bearing fluctuation 7 and the signal-to-noise ratio for a given antenna geometry (expressed by a(α)) is determined by the Cramer-Rao Signal Signal … bound (CRB) [13]. s(t)a (α ) s(t)a (α ) 1 0 N 0 8 For a general antenna array at whose outputs K samples are taken, the variance σ2 of the bearing fluctuation is Noise n1(t) Noise nN(t) therefore defined by the following equation:

x1(t) xN(t) −1 1 1+∂ 2SNRaHH a aH  aa ∂ a 9 σ22 ≥σ = 1− Bearing estimation from K samples CRB 2HH 2KSNR aa ∂αaa ∂α Bearing The equation simplifies if omnidirectional receiving ele- 10 ments are used and the antenna array is of conjugate sym- Fig. 37: Relationship metrical design: −2 2 1 ∂a x2 σ=CRB 2 ()1 + NS N R . 11 2KNS N R ∂α α n(t) 0 For the important case of a circular array with diameter D

α and N omnidirectional receiving elements, the following 12 x(t) applies at a constant elevation angle ε: s(t)a(α ) λ2 11 0 σ=2 + a(α) CRB_UCA 22 22 2 . πεKD cos NS N R N SNR 13

Fig. 38 shows the typical effect of the antenna diameter, the wavelength and the number of elements of a circular x 1 array on the S/N ratio that is required for a specific bearing Relationship between bearing fluctuation and signal-to-noise ratio. fluctuation.

Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 91 Direction Finders Introduction into Theory of Direction Finding

2 If direction finding is based solely on amplitude evaluation, For N = 2, this corresponds to the equation for σCRB_UCA as is the case with the Watson-Watt method, the Cramer- mentioned above, if the term Rao bound is determined by: 1 11 1 22 2 N SNR σ=CRB_ WW  +2 2K S N R 2SNR The effect of the S/N ratio on the bearing fluctuation is par- which can be ignored for large S/N ratios, is removed and ticularly obvious in the case of a narrowband two-element ε is set equal to 0. interferometer. In narrowband systems, the noise voltage becomes approximately sine-shaped with slowly varying The above relationship clearly shows how important it is amplitude and phase so that, assuming large S/N ratios, that the relative antenna basis D/λ is as large as possible. the following applies to the phase variation [19]: Limitation of upper operating frequency because of 2 1 σ=ϕ ambiguity 2SNR The required S/N ratio decreases as the frequency in- Given a sufficiently long observation time, the phase varia- creases, because the length of the array manifold a(α) also tion can be reduced by way of averaging. If the data used increases. With a constant number N of antenna elements for averaging is uncorrelated, averaging over K samples (= dimension of the observation space), however, various improves the phase variation as follows: sections of the curve a(α) approach each other (Fig. 40 on

2 next page). At the same time, the probability of measured 2 σϕ σ=ϕav vectors being positioned on such curve sections increases. K This leads to large bearing errors [17]. By mapping the phase variation to virtual variations of the positions of the DF antennas (Fig. 39), the bearing stan- The problem can be solved by increasing the number of dard deviation is as follows: elements N: The increase in dimension of the observation space will accommodate the extended length of the array λ σ≅ manifold. πD 2SNRK

Fig. 38: Minimum required S/N ratio

SNR in line with the CRB 40 N = 5 N = 9 30

20 Fig. 39: Effect of phase noise on bearing error

10 Incident wave K=1

0 2σα K=100 Bearing ﬂuctuation –10

–20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2σφ D/λ Required SNR in dB at output of antenna element for σ = 2° output of antenna element for SNR in dB at Required

φ = const. Minimum SNR for a bearing fluctuation (standard deviation) of 2° as Physical positions of antenna elements a function of the antenna diameter as referenced to the wavelength Virtual positions of antenna elements in case of noise and the number K of samples taken.

92 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

Measurement errors Multiwave-related problems Different gain and phase responses in the receive sections As already mentioned, the simple case of a plane wave 1 cause bearing errors that increase as the antenna aperture hardly ever occurs in practice. In a real environment, other decreases relative to the wavelength. Fig. 41 shows this waves usually have to be taken into account: effect for a two-element interferometer. JJ Waves from other emitters operating on the same frequency channel ▷ incoherent interference 2 Prior to the DF operation, the receive sections of most JJ Secondary waves (caused by reflection,refraction, multipath direction finders are calibrated for synchroni- diffraction – see Fig. 42) ▷ coherent co-channel zation by means of a test generator. The magnitude and interference (prerequisite: detours are small relative to phase responses are measured, and the level and phase the coherence lengths determined by bandwidth B) 3 differences are stored. In DF operation, the measured values are corrected by the stored difference values before In practice, a large number of waves is involved [20]. the bearing is calculated. Fig. 43 shows a typical azimuth distribution of waves generated by a mobile emitter in a built-up area. The direct 4 As regards the frequency response of the filters, synchro- wave component with amplitude 1 arrives at an angle of nization must be ensured not only in the middle of the fil- 90°. ter passband but also at the band limits. Digital filters have the decisive advantage that they can be implemented with 5 absolutely identical transmission characteristics. Fig. 42: Coherent secondary waves

Emitter 6 Fig. 40: Ambiguities

x2 α0 n(t) Sudden variation of bearing 7

Scatter object α

s(t)a(α0) 8

x(t) a(α) DF antenna 9 Secondary waves caused by reflection.

x1 Fig. 43: Azimuth distribution of waves As D/λ increases, various sections of the curve a(α) approach each 1 10 other. This causes large, sudden variations of the bearing if the S/N ratio and the number of elements remain constant. 0.8 11 Fig. 41: Effects 0.6

Incident wave

Amplitude of incident waves 0.4 12

D/λ = 1 0.2 Phase error Phase error D/λ = 1 13

0 φ = const. 0 50 100 150 200 250 300 350 Azimuth Impact of phase synchronization tolerances on bearing error for different antenna apertures. Waves radiated by an emitter in a built-up area.

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Fig. 44 shows the resulting wavefront as a contour plot for The effect of the number of antenna elements is obvious the amplitude and phase [12]. when looking at the density of the isophase curves. To avoid 180° ambiguities in areas of high density, the spac- If the majority of waves arrives from the direction of the ing between the antenna elements should be smaller in emitter, the bearing error can be sufficiently reduced these areas than with interference-free reception. This re- by increasing the aperture of the antenna system. This quires a higher number of antenna elements. effect is shown by Fig. 45 for an interferometer direction finder. The pattern of the isophase curves in Fig. 44 shows Fig. 46 shows the effect of the antenna size and the num- that two measures are required in order to increase the ber of antenna elements on the bearing error for two cir- DF accuracy: cular antennas in a two-wave field with an amplitude ratio JJ The antenna aperture should be as wide as possible of 0.3 of the reflected wave to the direct wave. The nine- JJ The number of antenna elements should be significantly element antenna delivers increasingly more accurate bear- higher than with interference-free reception ings up to a diameter of five wavelengths, whereas the bearings obtained with the five-element antenna become Fig. 46 shows the positive effect of a wide antenna aper- instable already from a diameter of 1.6 wavelengths. ture on the DF accuracy for a two-element interferometer. Arranging the antenna elements at a spacing that is large relative to the operating wavelength will prevent bearings from being obtained at points where the isophase curves strongly bend.

Fig. 44: Resulting ﬁeld

2 3.5 Amplitude

1.5 3 1

y/λ 2.5 0.5 2 0 1.5 –0.5 1 –1 –1.5 0.5 Isophases with –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 π/4 spacing x/λ

Field within a range of 4 × 4 wavelengths (the amplitudes are color- Fig. 46: Bearing errors

coded; the lines represent isophases with π/4 spacing). 20 Five-element 18 circular array Nine-element 16 circular array 14 Fig. 45: Reducing bearing error 12

Incident wave in ° Bearing error 10

Reﬂection 8 6 4 D/λ = 1 2

D/λ = 1 0 φ = const. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Diameter in λ

Error of interferometer direction finder reduced by increasing antenna Errors of a five- and a nine-element circular array antenna as a func- aperture. tion of the antenna diameter expressed in operating wavelengths in a two-wave field.

94 Rohde & Schwarz Radiomonitoring & Radiolocation | Catalog 2011/2012 Direction Finders Introduction into Theory of Direction Finding

References Reference No. Description 1 [1] Grabau, R., Pfaff, K.: Funkpeiltechnik. Franckh’sche Verlagshandlung, Stuttgart 1989. [2] Godara, L. C.: Application of Antenna Arrays to Mobile Communication, Part I, Proceedings of the IEEE, Vol. 85, No. 7, July 1997. Part II, No. 8, Aug. 1997. [3] Eckart, G.: Über den Rahmeneffekt eines aus vertikalen Linearantennen bestehenden Adcock-Peilers. Sonderdruck 9 aus den Berichten der Bayerischen Akademie der Wissenschaften 1972. 2 [4] Baur, K.: Der Wellenanalysator. Frequenz, Bd. 14, 1960, Nr. 2, S. 41-46. [5] Jondral, F.: Funksignalanalyse. Teubner, Stuttgart 1991. [6] DIN 13312 Navigation, Begriffe. [7] Harrington, R. F.: Time-Harmonic Electromagnetic Fields. McGraw-Hill Book, New York, 1961. 3 [8] Balanis, C.A.: Antenna Theory. Harper & Row, New York, 1982. [9] Mönich, G.: Antennenspannungen und Peilanzeige bei Sichtpeilern nach dem Watson-Watt-Prinzip. Frequenz 35 (1981) Nr. 12. [10] Burke, B.F., Graham-Smith, F.: Introduction to Radio Astronomy. Cambridge University Press, Second Edition 2002. [11] Demmel, F.: Einsatz von Kreisgruppen zur echtzeitfähigen Richtungsschätzung im Mobilfunkkanal. ITG Fachbericht 149, 4 VDE-Verlag 1998. [12] Demmel, F.: Practical Aspects of Design and Application of Direction-Finding Systems. In: Tuncer, T. E., Friedlander, B. (Ed.): Classical and Modern Direction-of-Arrival Estimation. Elsevier Inc. 2009. [13] Van Trees, H.L.: Optimum Array Processing. John Wiley & Sons, 2002. [14] Hudson, J.E.: Adaptive Array Principles. Peter Peregrinus, New York, 1981. 5 [15] Griffith, J.W.R.: Adaptive Array Processing. IEEE Proc., Vol. 130, Part H, No. 1, 1983. [16] Capon: High-resolution frequency-wave number spectrum analysis. IEEE Proc., Vol. 57, pp. 1408-1418, 1969. [17] Schmidt, R.O.: A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation. Dissertation, Dep. of Electr. Eng., Stanford University, Nov. 1981. 6 [18] Gething, P.J.D.: Radio Direction Finding and Superresolution. Peter Peregrinus Ltd., London, 1990. [19] Höring, H.C.: Zur Empfindlichkeitssteigerung automatischer Großbasis-Doppler-Peiler durch Einsatz eines Summationsverfahrens vor der Demodulation. Dissertation, TU München 1970. [20] Saunders, R.S.: Antennas and Propagation for Wireless Communication Systems. John Wiley & Sons, 1999. 7 [21] Schlitt, H.: Systemtheorie für stochastische Prozesse. Springer Verlag, 1992.

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