... Anatoly Yakovlev', H. K. Hwang', Zekeriya Aliyazicioglu', Anne Lee2. 'California State Polytechnic University, Pomona,. Electrical and Computer Engineering,.
Direction of Arrival Estimation using Advanced Signal Processing Marshall Grice', Jeff Rodenkirch', Anatoly Yakovlev', H. K. Hwang', Zekeriya Aliyazicioglu', Anne Lee2 'California State Polytechnic University, Pomona, Electrical and Computer Engineering,
gricegdcsupomona.edu, ji rodenkirchdgcsupomona.edu, aayakov1ecvgdcsupomona.edu, h1,dihwang csuipomona.ed., zaliy_zicigcsupomona .edu Pomona, California 91768, USA 2Raytheon Company, Ann L_Lee n.com El Segundo, CA, USA
Abstract- Accurate estimation of signal direction of arrival (DOA) has many applications in communication and radar systems. For example, in defense application, it is important to identify the direction of possible threat. One example of commercial application is to identify the direction of emergency cell phone call such that the rescue team can be dispatched to the proper location. DOA estimation using a fixed antenna has many limitations. Its resolution is limited by the mainlobe beamwidth of the antenna. Antenna mainlobe beamwidth is inversely proportional to its physical size. Improving the accuracy of angle measurement by increasing the physical aperture of the receiving antenna is not always a good option. Certain systems such as a missile seeker or aircraft antenna have physical size limitations; therefore, they have relatively wide mainlobe beamwidth. Consequently, the resolution is quite poor. Also, if there are multiple signals falling in the antenna mainlobe, it will be difficult to distinguish them.
Instead of using a filxed antenna, an array antenna system with innovative signal processing would enhance the signal~~~. DO. It also alohsteailt oietf DOA.It has resolution of signal multiple targets. Two types of signal processing methods, model based and eigen-analysis estimation techniques, are presented in this paper. The model based approach models the observed data as the output of a linear shift invariant system driven by zero mean white noise. The signal's DOA can be estimated by evaluating the model parameters. This approach has properties similar to the maximum entropy spectrum estimationestimtion Some of the problems robles in the he maximum maimum [111. Sme 1]. ofthe entropy method, such as the line splitting effect, are also
The eigen-analysis method based on temporal averaging has been investigated by many authors in the past [2]. However, temporal averaging requires average over multiple time samples to estimate the covariance matrix. Sometimes, the radar system prefers to have an estimated covariance in a single snapshot. We propose eigen-analysis based on spatial smoothing so that we can have estimated covariance in a single snapshot. Performances based on several different spatial averages are discussed in this paper. Extensive computer simulations are used to verify the processing algorithms. For narrowband signals, both processing algorithms provide enhanced resolution and have ability to resolve multiple targets as long as the number of targets is less than the system's degree of freedom. SMI provides better performance than the LMS method due to the fact that this method is relatively immune to excessive mean square error. However, for multiple wideband waveforms, sometimes the array antenna has difficulty to resolve them, especially if signals arimignthateawtharospilsprto. are ipingin tanb tennitna stial atin. This problem can be solved by extending the array antenna a space time adaptive processor (STAP) [3]. STAP is basically replacing the sngle weilght at the output of each array element by an adaptive filter. Statistical analysis of the performance of the processing algorithms and processing resource requirements are discussed in this paper.
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An array sensor system has multiple sensors distributed in space. This array configuration provides spatial samplings of the received waveform. A sensor array has better performance
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parameter estimation. Its superior spatial resolution provides a means to estimate the direction of arrival (DOA) of multiple signals. A sensor array also has applications in interference rejection [4],
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electronic steering [5], multi-beam forming [6], etc. This technology is now widely used in communications, radar, sonar, seismology, radio astronomy and so on. In this paper, we concentrate the discussion on application in estimating the DOA of multiple signals. Two processing techniques discussed in this paper are (a) Spatial Smoothing method and (b) Model Based approach [7].
III. SPATIAL SMOOTHING METHOD Narrowband signal is defined as when the signal bandwidth is a small fraction of c/D, where c is the speed of light and D is the diameter of antenna. If the signal impinging on nth antenna element is u1(t), its relation with the reference signal of the element at the origin uo(t) is:
u,1(t) uo(t-c1) m(t-c1)expU27rfo(t-c1)] (1) =
=
II. ARRAY SENSOR SYSTEMS
where t11 is the relative delay of the signal reach to nth element and element at the origin and
Three different array antennas with 7, 19 and 25 antenna elements are discussed in this paper and their configurations are shown in Fig. 1. y
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and 3n =(a)
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=(:nYnwhere rn( Yn) is the coordinate vector ofthe nth element, k is the unit vector of the impinging signal. For narrowband
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(c) Fig. 1. Array Antenna with (a) 7 elements (b) 19 elements and (c) 25 elements
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the nth element. *Assume that the number of signals impinging on the antenna is L, and that the array antenna has M elements. Usually, M > L. For finite number of data sequence, sequence of received data can be considered as a vector in the sample space. If the noise is assumed to be white, it spans over the whole sample space. Signals having sufficient narrowband span over L dimensional subspace. For example, radar signal of moving target is a sinusoid with frequency equal to the Doppler frequency shift. If there are L targets, the received waveform at the reference sensor at the origin uo(n) can be expressed as
L
Antenna elements are uniformly placed on the x-y plane. (4) ct-e2E;fl + vo(n) uo(n) _ 1 To avoid the grating lobe effect, the inter-element spacing is d is set to be d = X/2, where X is the wavelength of the center where cc, fi, and i 1, 2,.. , L are the complex amplitude and frequency. frequency of the ith sinusoid, vo(n) is the additive white noise Assuming that the antenna elements are placed on the x-y with variance &2. Since the signal at the other sensors has a plane, and the signal impinging the antenna is from an relative phase shift, the waveforms of the other sensors are elevation angle 0 and azimuth angle 4. The geometry L 2fin + vk(n), k 1,2,.. ,M-l Uk() (5) relationship of array antenna and signal's DOA is shown in i4 Fig. 2. Define the signal matrix S as
lo ',/'
S =
e j2Xfi e2 27f2
2L(6)
= 0~~~~~~ Ds+c2
The correlation matrix of received data sequence R is Fig. 2. Geometrical Relation of Array Element and Signal's DOA
516
(6)
where S= [sI, S2, , SL], D diag[P1, P2, ,P, Pi=, Pi'1,, L are the power of the sinusoid, I is the identity matrix. The eigenvectors of matrix R are q1, q2, .q,q with the associated eigenvalues Xk, X2,.., XM, where X1 > X2> . XM. All the signals are confined by the space spanned by eigenvector ql, q2, , qL. Define the matrix VN as VN = [qL+1, qL+2, , qM]. (8) Since the signal vectors belongs to space spanned by eigenvectors q1, q2, , qL, they are orthogonal to the space defined by VN. Thus the signals DOA can be defined as the peaks of the spectrum defined by the following equation: 1 SH (0, (P)V VNHS(0, (P) =
r1=[xlxl ± X2X2 ± X3X3 ± X4X4 ± X5X5 ± X6X6 ± X7X7 ± X8 X8 ± x9 X9 ]/9 r22 r33 r44 rll r12 = [X1 X2 + X2 X3 + X4 X5 + X5 X6 + X7 X8 + X8 x ]/6 r34 e e e e r13 = [xl X4 + X2 X5 + X3 X6 + X4 X7 + X5 X8 + X6 X9 ]/6 r24 r14= [X X5 + X2 X6 + X4 X8 + X5 X9 ]/4 r23 = [X2 X4 + X3 X5 + X5 X7 + X6 X8 ]/4 * rij= ril Fig. 4. shows an example of creating an array with 4 elements from the origin array with 19 elements. 2
where s(0, X) is the scan vector scans over all possible azimuth + and elevation 0 angles. Equation (9) is the famous MUSIC (Multiple Signal Classification) algorithm. One of the key computations of the MUSIC algorithm is to estimate the correlation matrix R. If there are multiple snapshots u(n) = [uo(n), u1(n), . ., (n)]T, n 1, 2, u. .K available, then the estimated correlation matrix R is
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UUH (10) Fig. 4. 4 Element Subset (Red Dots) From 19 Element Array where U= [u(1), u(2),. , u(K)]. Fig. 5 shows the MUSIC spectrum with spatial smoothing method This technique is referred to as the time averaging method. of using 4 elements subset from array of 19 elements. Assume that Performance of the time averaging method is thoroughly there is only one signal, SNR =20 dB and signal's DOA is (650, 150). evaluated in our previous work. However for certain radar system applications, it is desired to have a reasonable GG Thela(1X=15 Phi[l :65 | R
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estimation of the correlation matrix from a single snapshot./ This can be achieved by using the technique of spatial smoothing method. If the array has a large number of sensor elements, we can use a smaller subset provided the number of elements in the subset is larger than L to compute the spatial correlation matrix. The correlation of ith and jth sensors in the subset is computed by averaging all the correlation with the same geometry relation in the whole sensor array. Using this method, the correlation matrix can be estimated by data from a single snapshot. For example, if the sensor array consists of 9 elements as shown in Fig. 3, we can compute the correlation matrix of 4 element subset by only using elements 1, 2, 4, 5 of the original array. The elements 1, 2, 3, 4 of the subset are elements 1, 2, 4, 5 of the original array.
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Fig. 5 shows that spatial smoothing provides a very accurate estimation of the DOA of signal. Fig. 6 shows the
peak of the MUSIC spectrum from multiple independent simulations. The mean values of the azimuth and elevation angles are Vt = 65. 110 and to = 15.030, which are very close to the true DOA. The variance of the angle error is a = .0026. 19Sensors SNR=20dBSubsetelernent: [1 2 4 5]
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Fig. 3. Construct a 4 Element Subset from 9 Element Array
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The corresponding correlation element of 4 x 4 correlation matrix arecompted by the follwing
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The spatial smoothing method also provides multiple signal detection capability. For example, if there are two signals from DOA of (650, 15°) and (650, 250), using subset with elements 1, 2, 4, 5 of 19 element array, the MUSIC spectrum is shown in Fig. 7. The SNR of this simulation is 20 dB.
IV. MODEL BASED APPROACH
The model based approach iS to assume that the observed data u(n) is the output of a linear shift invariant system driven by zero mean white noise. Fig. 10 shows the block diagram of the model based approach. a 2
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Fig. 7. MUSIC Spectrum with Two Signals from (650, 150) and (650, 250)
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Arbitrarily increasing the number of elements in the subset does not necessarily improve the performance. Fig. 8 shows another possible subset with elements[I 2 4 5 6 89 1011 13 14 15 17 18] from 19 element array. 3
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