# STAP approach for DOA estimation using microphone arrays

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2 in contrast to the conventional method of beamforming the MVDR gives accurate estimates of the DOA of all sound signals generated by sensors of a surveillance system. After some modifications this approach can be also usefully applied to implementation of STAP algorithms in satellite navigation receivers.. SIGNAL MODEL The signal model is based on the scenario, according to which one or several (L) desired signals combined with some sound noise arrive at the microphone array input. The output signal of each microphone is a sum of sound-sourcegenerated signals and thermal noise. The vector of complex samples of the output signal of a microphone array at time instant k can be mathematically described as: L x( k) = bl sl ( k) + l= n( k) where x(k) is the (M x ) complex data vector, s l (k) is the complex signal generated by the lth sound source, b l is the (Mx) microphone array response vector of the signals generated by the lth sound source sound sources and n(k) is the (Mx) complex noise vector and L is the number of sound sources. The signal received from the sound source is given by: sl ( k) = Pl Al ( k)cos(π f 0t + ϕ) () where P l is the received signal power, A l (k) is the modulating baseband signal, separate for each sound source and f 0 is the sound carrier frequency. The microphone noise n(k) occupies the entire frequency bandwidth of an array microphone and can be represented mathematically as bandlimited white additive Gaussian noise (AWGN). 3. SIGNAL PROCESSING Let s assume that a set of sensors and one microphone array are installed for the object protection in the observation area. In such a surveillance system, a video camera can be located above a microphone array (Fig.). Other sound source Sensor A R B R C Sensor B Sensor C () R A α B α A α C Microphone array (video camera) Figure. The observation area. The direction of-arrival of signals is referred to a Cartesian coordinate system, the origin of which coincides with the first element of a microphone array. In our case, the signal processing for DOA estimation consists of three main steps (Fig.). Firstly, the beamforming is performed in order to calculate the beam pattern of a microphone array as: P ( β, θ ) = y( β, θ ) (3) where P is the output signal power of a microphone array steered in the (β,θ)-direction (β - azimuth and θ - elevation). At the second stage the beam pattern thresholding is performed and, finally, the DOA estimates are found as directions where the local maximum exceeds a fixed threshold.

3 x ilbert Transform Beamforming BF STAP Power Estimation Beam pattern Thresholding x M ilbert Transform D-Beam pattern calculation Angular coordinates estimation Figure. The flow-chart of signal processing 4. METODS OF BEAMFORMING The object of beamforming technique is to increase the gain of the microphone array in the right direction and decrease the gain in the other directions. The output of a microphone array with M elements is formed as: y( k) = W x( k) (4) where k is the time instant, and x(k) is the complex vector of array observations, W=[w,w, w M ] T is the complex vector of the beamformer weights, T and denote transpose and conjugate transpose, respectively. Conventional method (BF): In a conventional beamformer, the complex vector of weights W is equal to the array response vector a c, which is determined by an array configuration: W conv = a (5) c MVDR Beamforming method: The optimal weight vector W can be chosen to maximize the signal-to-interferenceplus-noise ratio (SINR) [3]: σ S W ac SINR = W K W n where K n is the interference + noise covariance matrix of size (M x M), and σ S is the signal power. The easy solution can be found by linear constrained optimization. The criterion of optimization is formulated as: minw K W subject to a = W m+ n The solution of (7) is the minimum variance distortionless response beamformer (MVDR): K a W n c MVDR ac K nac c (6) W (7) = (8) In practical applications, K n, is unavailable. For that reason the sample covariance matrix is used instead of it. The sample covariance matrix is estimated as: N K = x( n) x ( n) (9) N n= Many practical applications of MVDR-beamformers require online calculation of the weights according to (8), and it means that the covariance matrix (9) should be estimated and inverted online. owever, this operation is very computationally expensive and it may be difficult to estimate the sample covariance matrix in real time if the number of samples MN is large. Furthermore, the numerical calculation of the weights W MVDR using the expression (8) may be very unstable if the sample covariance matrix is ill-conditioned. A numerical stable and computationally efficient algorithm can be obtained by using QR decomposition of the incoming signal matrix. This matrix is decomposed as X=QR, where

4 Q is the unitary matrix and R is the upper triangular matrix. ence the QR-based algorithm for calculation of beamformer weights includes the following three stages [3]: The linear equation system R z = a is solved for z c, and the solution is * The linear equation system Rz = z is solved for z, and the solution is The weight vector W * * is obtained as W = z /( a ). c z z * ( R ) z = a. * * R z =. c 5. SIMULATION RESULTS In this section the computer simulation is performed in order to demonstrate the capability of the two beamforming techniques, conventional and MVDR, to separate the signals incoming from different azimuth directions. The scenario of simulation includes three sensors (A, B and C) located respectively at a distance of 50m, 60m and 70m from the microphone array (Fig.). In case of alarms these sensors generate a sound power in range from 96dB to 03 db. The parameters of sensors produced by three world-known companies are given in Table. Table. Sensor parameters. Company Sensor LW [db] Sensor frequency [z] SONITRON ES SYSTEM SENSOR Depending on the situation the sensors emit different signals (continuous, intermittent) with parameters given in Table. Table. Signal parameters. Continuous (warning) f_int=0 z T_sig=0s Sensor signals Intermittent-I (alarm) f_int=5 z T_sig=30s Intermittent-II (emergency) f_int= z T_sig=60s It is assumed that in the perpendicular direction relative to the microphone array is a car whose horn generates a signal power of 0dB (Fig.). The distance to the car is 90m. Two types of microphone arrays, uniform linear array (ULA) and uniform rectangular array (URA), are simulated for each sensor type. The microphone array parameters correspond to a flexible microphone array WA0807 produced by the company Brüel & Kjær. It is assumed that all simulated microphone arrays are the same overall dimension of 0.5m. The interelement spacing of each microphone array and as a consequence the corresponding number of elements are determined according to the carrier frequency of a signal generated by the sound source. Table 3. Fine and estimated azimuth of sound sources. Company SONITRON ES SYSTEM SENSOR Acoustic array Source azimuth [ ] Estimated source azimuth [ ] BF filter STAP filter ULA (x) -6; 0; 6; 0; 4-6; 0; 6; URA (x4) -6; 0; 6; -44; 0; 4-6; 0; 6; ; 4 ULA (4x) -6; 0; 6 0-6; 0; 6 URA (4x4) -6; 0; 6; -40; 0; 40-8;-4;-6; 0; 6; ULA (8x) -6; 0; 6; - -6; 0; 6; URA- (8x4) -6; 0; 6; 0-6; 0; 6;

5 Both real and estimated values of the DOA obtained using the two beamforming methods, conventional and MVDR, are presented in Table for each type of a microphone array. Figure 3. Beam patterns for ULA-(for SONITRON) Figure 6. Beam patterns for URA -4x4 ( ES) Figure 4. Beam patterns for URA-x4 (for SONITRON) Figure 7. Beam patterns for URA-x4 ( SYSTEM SENSOR) Figure 5. Beam patterns for ULA-4 (ES) Figure 8. Beam patterns for URA-8x4 ( SYSTEM SENSOR)

6 For comparison, the calculated beam patterns of the all microphone arrays are presented in Fig.3 and Fig.4 - for microphone arrays for detection of signals from sound generators produced by SONITRON, in Fig.5 and Fig 6 - for microphone arrays for detection of signals from sound generators produced by ES, in Fig.7 and Fig.8 - for microphone arrays for detection of signals from sound generators produced by SYSTEM SENSOR. The MVDR beam pattern in Fig. 5 shows that the maximal number of separated signals equals (M-), where M is the number of array elements. The simulation results show that the MVDR method of beamforming allows estimating the DOA of all signals generated by sensors (-6 ; 6 and ) and a signal generated by a car horn (0 -direction) in the observation area. owever, the conventional method of beamforming gives the DOA estimate only of a signal generated by a car horn (0 -direction). 6. CONCLUSIONS The results obtained show that the accurate DOA estimates can be obtained using microphone arrays if the MVDRalgorithm is used for beamforming. It is also shown that the maximal number of separated signals depends on the number of array elements. After some modifications this approach can be useful also for other applications for realization of STAP algorithms for GPS signal acquisition. 7. ACKNOWLEDGEMENTS This work is supported by the ESF&BME Grant BG05PO /40. REFERENCES [] L.Godara," Application of antenna arrays to mobile communications, part II: beam-forming and direction-ofarrival considerations", Proc. of the IEEE, vol.85,no 8, pp.95-45, (997). [] Ioannides, P. and Balanis, C.A., "Uniform circular and rectangular arrays for adaptive beam forming applications", IEEE Trans. Antenn. Wireless Propagat. Lett., vol.4., pp , (005). [3] L. Tummonery, I. Proudler, A. Farina, J. McWhirter, "QRD-based MVDR algorithm for adaptive multi-pulse antenna array signal processing", in Proc. Radar, Sonar, Navigation, vol.4, No, pp. 93-0, (994).

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