STAP approach for DOA estimation using microphone arrays

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1 STAP approach for DOA estimation using microphone arrays Vera Behar a, Christo Kabakchiev b, Vladimir Kyovtorov c a Institute for Parallel Processing (IPP) Bulgarian Academy of Sciences (BAS), b Faculty of Mathematics & Informatics Sofia University, c Institute of Information Technologies Sofia, Bulgaria ABSTRACT In this paper, the Space-Time Array Processing (STAP) approach is applied to sound source localization using adaptive microphone arrays. Two beamforming methods, conventional and MVDR are used for estimating the direction-of arrival (DOA) of sound signals arrived at the microphone array from different sensors in the observation area. The simulation scenario describes a situation where three sensors generating three different sound signals (warning, alarm and emergency) and one source of natural noise (car) are located at various points in the observation area. The results obtained demonstrate that in contrast to the conventional method of beamforming the MVDR gives accurate estimates of The DOA of all sound signals generated by sensors in the observation area. Keywords: STAP, source localization, microphone array; DOA estimation, acoustic signal processing. INTRODUCTION In modern security and surveillance systems, the operational control of protective and warning means is based on the analysis of alarms received from different sensors installed in the observation area. In this paper we consider a situation where the operational control of a video camera is based on an assessment of the direction of arrival (DOA) of sound signals from sensors of a video alarm system. It is well-known that the angle of arrival of sound signals can be estimated by a set of directional microphones. In such a system, each directional microphone is used for estimation of the DOA of signals received from a certain specific sensor. Therefore, the number of directional microphones must be equal at least to the number of sensors installed in the surveillance coverage of a system. In this paper, a two-dimensional microphone array is proposed to be used for DOA estimation instead of a set of directional microphones. Simply stated, a microphone array is two or more microphones used at the same time to capture sound. The advantage of using more than one microphone to capture sound is that it allows the software that is processing the microphone signals to determine the position of the sound in the observation area. In addition, the higher directivity of the microphone array reduces the amount of captured ambient noises and reverberated sound. We consider the case, where the signal source is in the array s far-field, and sound sources in space generate the sound waveforms that propagate through the air. The DOA estimate is the direction, in which the local maximum of the beam pattern formed by the microphone array exceeds a fixed threshold. The video cameras are steered in such direction, from which have been arrived the signals having the most important priority (emergency, alarm and warning). Different methods of beamforming can be used for DOA estimation. The conventional non-adaptive method of beamforming is the simplest, according to which the array weights with equal magnitudes and the different phases are selected for steering the beam in the desired direction []. This beamformer provides maximum SNR but it is not effective in the presence of multiple signals arrived from different directions. The other method of beamforming such as an adaptive Minimum Variance Distortionless Response (MVDR) method overcomes this problem by suppressing all signals from off-axis directions [,3]. The MVDR-beamformer adaptively calculates the array weights that provide the maximum gain in the desired direction while minimizing the power in the other directions. In this paper, two beamforming methods, conventional and MVDR are used for DOA estimation using a rectangular flexible microphone array. The simulation scenario includes three sensors, which generate three types of signals (warning, alarm and emergency), and one source of natural noise (car). The parameters of three sound generators produced by three well-known companies (SoniTron, Es and Sensor Systems) and also the parameters of a flexible microphone array produced by the company Brüel & Kjær are used in simulations. The results obtained demonstrate that

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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