A Simple Angle of Arrival Estimation Scheme

Ahmed Badawy∗†, Tamer Khattab†, Daniele Trinchero∗, Tarek ElFouly‡, and Amr Mohamed‡, ∗Politecnico di Torino, DET - iXem Lab. (ahmed.badawy,[email protected]) †Qatar University, Electrical Engineering Dept. ([email protected]) ‡Qatar University, Computer Engineering Dept. (tarekfouly,[email protected])

Abstract—We propose an intuitive, simple and hardware array elements. AAS requires M receivers to estimate friendly, yet surprisingly novel and efficient, received signal’s the AoA, where M is the number of antenna elements in angle of arrival (AoA) estimation scheme. Our intuitive, two- the array. The AoA estimation techniques that use AAS phases cross-correlation based scheme relies on a switched beam antenna array, which is used to collect an omni-directional signal can operate at lower SNRs than the SBS technique but using few elements of the antenna array in the first phase. has higher hardware and computational complexities. The In the second phase, the scheme switches the main beam of AoA estimation techniques that use AAS can be divided the antenna array to scan the angular region of interest. The into two main groups: collected signal from each beam (direction or angle) is cross correlated with the omni-directional signal. The cross-correlation a) Classical AoA techniques which include two main coefficient will be the highest at the correct AoA and relatively techniques which are Delay and Sum, also known negligible elsewhere. The proposed scheme simplicity stems from as Bartlett [6] and Minimum Variance Distortionless its low computational complexity (only cross-correlation and (MVDR), also known as Capon [7]. By steering the comparison operations are required) and its independence of the beams electronically and estimating the power spec- transmitted signal structure (does not require information about the transmitted signal). The proposed scheme requires a receiver trum of the received signal, the AoAs are estimated with switched beam antenna array, which can be attached to a as being the peaks in the spatial power spectrum. The single radio frequency chain through phase shifters, hence, its main drawback of the Bartlett technique is that signal hardware friendliness. The high efficiency of our system can be impinging with angular separation less than 2π/M can observed by comparing its performance with the literature’s best not be resolved. The Capon technique relatively solves performing MUSIC algorithm. The comparison demonstrates that our scheme outperforms the MUSIC algorithm, specially the angular resolution drawback of the Bartlett method at low SNR levels. Moreover, the number of sources that can be on the cost of more baseband processing needed for detected using our scheme is bound by the number of switched matrix inversion. beams, rather than the number of antenna elements in the case b) Subspace techniques which are based on the idea that of the MUSIC algorithm. the signal subspace is orthogonal to the noise subspace. Index Terms—angle of arrival Estimation, AoA, Switched Beam, direction of arrival estimation, DoA. The most widely used technique in this group is the MUltiple SIgnal Classification (MUSIC) [8]. The MU- I.INTRODUCTION SIC technique provides the highest angular resolution and can operate at low SNR levels. This comes on AoA estimation is a process that determines the direction of the cost that it requires a full a priori knowledge of arrival of a received signal by processing the signal impinging number of sources and the array response, whether it on an antenna array. Applications of estimating the AoA is measured and stored or computed analytically. The include , tracking and localization. The subject signal and noise subspaces are distinguished through of AoA has been extensively studied in the literature [1]– an eigen decomposition operation applied at the co- arXiv:1409.5744v1 [cs.SY] 19 Sep 2014 [5]. Referring to the aforementioned books; from a system variance matrix of the received signal. This operation perspective, one can categorize AoA estimation systems into requires a substantial computational complexity. two main categories: An example of integrating SBS with other theories to 1) Switched beam system (SBS) which uses a fixed number estimate the AoA is presented in [9]. Their methodology is of beams to scan the azimuth plane. The AoA is the angle based on neural network, in which they transform the AoA of the beam with the highest received power or signal problem into a mapping problem. This mapping process is a strength (RSS). The SBS is easy to implement since it re- burden to the processor as well as the memory of the system. quires a single receiver and no baseband signal processing Another drawback of their system is that they require a prior technique is needed to estimate the AoA. In other words, knowledge of the number of sources as well as the multiple the hardware and computational complexities of SBSs are access scheme adopted between them. They also assumed low. On the contrary, if the power of the received signal that a power control scheme is implemented such that the is lower than the receiver sensitivity, i.e., at low signal to source powers are equal. Such requirements and assumptions noise ratio (SNR), SBS will fail to estimate the AoA. limits the deployment of their system to very few scenarios. 2) Adaptive array system (AAS) can steer the beam in any Exploiting the power ratio between the adjacent beams to desired direction by setting the weights across the antenna estimate the AoA is presented in [10]. Another table driven SBS system is presented in [11]. Both of these techniques do not tackle the drawbacks of the conventional SBS, rather they make its implementation easier. The concept of using the cross-correlation function to ex- tract features of the signal can be found in many applications; one of which is the passive radar systems. Passive radar sys- tems exploit the transmitters of opportunity such as television ….. d d d=0.5λ signals to detect an airborne target. In passive radar systems, M 4 3 2 1 a cross correlation between a reference signal from the first w w w w w receiver and a directional signal from the second is applied to M 4 3 2 1 estimate bistatic range and doppler shift of the target. The AoA … .. has to be estimated before that at the second receiver to place ….. a null in the direction of the reference signal [12], [13] such Weights Unit that the received directional signal is the reflection from the  airborne target. Another application is localization, in which a cross correlation between two signals received from two antennas is applied to estimate the time difference of arrival tv )( Receiver [14]–[16]. Our contributions in this work as compared to available literature are as follows: We propose a new AoA estimation system that is based on beam switching. Our system cross correlates an omni-directional signal with narrow beam signals nx )( to estimate the AoA. The cross correlation between the omni- Fig. 1: Our SBS for M antenna elements. directional signal and the signals received from the switched beams is the highest at the true AoA and relatively negligible otherwise. We compare the proposed mechanism with the weights are updated to change the direction of the beam, i.e. MUSIC algorithm and show the at our proposed solution φk, to scan the the angular space of interest, where k ∈ [1 : K], outperforms it, particularly for low SNRs. We also compare, where K is the total number of generated beams. Based on qualitatively, the complexity of our approach with the existing the antenna array formation, whether it is a linear, circular or one and conclude that our approach again has lower hardware planar, a(φ) changes accordingly. and computational complexity. To the best of the authors’ 1 knowledge using the cross correlation coefficient between an w = a(φ) (2) M omni-directional signal and directed beam signal to estimate the AoA has not been presented in the literature before. The steering vector for the linear, circular and planar array can The rest of this paper is organized as follows: In Section II be estimated analytically. It’s worth noting that our proposed our system model is presented. An overview of the existing system is independent of the antenna array formation. For AoA estimation techniques is presented in section III. We then a uniform linear array with uniform excitation, a(φ) can be propose our cross correlation based AoA estimation system in given by: Section IV. The paper is then concluded in section VII. h i a(φ) = 1, eβdcos(φ), eβ2dcos(φ), ..., eβ(M−1)dcos(φ) , (3) II.SYSTEM MODEL In our system model, we assume that there exists a source 2π where β = λ is the wave number, λ is the wavelength and that transmits signal s(t). Our receiver is equipped with an φ ranges between [0 : π]. For a uniform circular array (UCA), SBS presented in Figure 1 consisting of M antenna elements, a(φ), can be given by [17]: separated by a fixed separation d and operating at frequency f . Our antenna array has an array response vector also known βr cos(φ−φ ) βr cos(φ−φ ) M a(φ) = [e 1 , e 2 , (4) as steering vector a(φ) ∈ C , where φ is the azimuth angle. The received signal x(t) is then: ..., eβr cos(φ−φM )], (5) X xk(t) = wks(t) + v(t) (1) where M 2πm φm = , m = 1, 2, .., M (6) where v(t) is the additive white Gaussian noise (AWGN), M wk is the vector with dimensions M × 1, which is the weight and φ ranges between [0 : 2π] and r is the radius of the antenna set applied across the antenna array elements such that the array. The elevation angle is assumed to be 90 degrees in the steering vector a(φ) is pointing to an azimuth angle φk. The 1-D angle of arrival estimation techniques. For linear array with uniform excitation, the total number of orthogonal beam (a) (b) 0 0 that can be generated is M. Using the non-uniform excitation such as Dolph-Chebyshev or Taylor [18], [19], it is possible −5 −5 to generate more orthogonal beams for the same number of antenna elements M, as we will show later. The digitized −10 −10 version of the received signal is then x(n) for n = 1 : N, ) (dB) ) (dB) where N is the total number of samples, also known as the φ −15 φ −15 snapshots. −20 −20

III.EXISTING AOAESTIMATION TECHNIQUES Bartlett Bartlett Capon Normalized P( −25 Normalized P( −25 Capon As explained in the Introduction, the AAS requires M MUSIC MUSIC receivers to down convert the received signals from the M antenna elements to the baseband in order to estimate the −30 −30 AoA. The most popular AAS AoA techniques are the Bartlett, −35 −35 Capon and MUSIC. In the Bartlett technique, the beam is 0 100 200 300 0 100 200 300 φ (degrees) φ (degrees) formed across the angular region of interest by applying the weights that correspond to that direction and whichever angle Fig. 2: Comparison of existing AoA estimation techniques that provides the highest power is the estimated AoA. using a uniform circular array for a single source at φ = 180 The spatial power spectrum P (φ) for the Bartlett technique with M = 16 and N = 1000 samples: (a) at SNR = 0 dB and is given by [6]: (b) at SNR = -15 dB H PBartlett(φ) = a (φ)Rxxa(φ), (7) where H denotes the Hermitian matrix operation. , Rxx is the Figure 2 shows the simulation results for the three algo- received signal autocovariance matrix with dimension M ×M. rithms for M = 16, N = 1000 for a UCA : at (a) SNR = Rxx is estimated as: 0 dB and (b) SNR = -15 dB. It is shown that the MUSIC N technique outperforms the two other techniques; achieving a 1 X R = x(n)xH (n) (8) high peak to floor ratio (PFR) of the normalized spatial power xx N n=1 of almost 28 dB for the MUSIC, -13 for the Capon and -10 for the Bartlett at SNR = 0 dB. At low SNR, the Capon and The Bartlett technique suffers from a low resolution. Capon’s Bartlett algorithms almost fail to estimate the AoA achieving technique attempts to overcome the Bartlett low resolution PFR of 2 dB while the MUSIC is achieving 12 dB. In other drawback by setting a constraint on the beam former gain to words, the MUSIC can operate at low SNR levels while the unity in that direction and minimizing the output power from Bartlett and Capon will fail to do so. signals coming from all other directions. In Figure 3, the resolution of the three techniques is inves- The spatial power spectrum for the Capon technique is given tigated. We plot the normalized spatial power spectrum for by [7]: two sources (a) with 20 degrees separation and (b) for 10 1 degrees separation. Again, the MUSIC technique outperforms P (φ) = (9) Capon H −1 a (φ)Rxx a(φ) the two other techniques achieving a resolution of almost 10 degrees with PFR = 5 dB where Capon achieved 20 degrees On the other hand, the MUSIC algorithm exploits the with PFR = 3 dB and Bartlett failed to resolve the two sources orthogonality of the signal and noise subspaces. After an for a separation of less than 30 degrees. The superiority of eigenvalue decomposition (EVD) on R , it can be written xx the MUSIC comes on the cost that it requires an extensive as: computational complexity and that the number of sources must H 2 Rxx = aRssa + σ I (10) be known a priori or estimated. The estimation can be done H H using techniques such as Akaike information criterion (AIC) = UsΛsUs + UvΛvUv , (11) and minimum description length (MDL) [21], which adds extra 2 where σ is the noise variance, I is the unitary matrix, Us computation complexity burden to the system. Also, MUSIC and Uv are the signal and noise subspaces unitary matrices requires that the sources must be uncorrelated. and Λs and Λv are diagonal matrices of the eigenvalues of the signal and noise. IV. PROPOSED CROSS-CORRELATION SWITCHED BEAM The spatial power spectrum for the MUSIC technique is SYSTEM (XSBS) given by [8], [20]: The existing AoA estimation techniques either have a 1 low resolution problem or require extensive computational PMUSIC (φ) = , (12) complexity to estimate the AoA. Moreover, they require M aH (φ)P a(φ) v receivers to implement the AoA estimation technique which H where Pv = UvUv . increases the hardware complexity tremendously. Although the (a) • Phase II: In this phase the omni-directional signal col- 0 lected in the first phase, i.e., xo, becomes our reference ) (dB)

φ −10 signal. The Weights Unit sends the sets of weights wk,

Bartlett for k ∈ [1 : K]. The set wk steers the main beam of −20 Capon the antenna array to the direction φk. The XSBS then MUSIC −30 acquires N samples to collect the signal xk. Normalized P(

0 50 100 150 200 250 300 350 The next step is the core step in our XSBS. A cross φ (degrees) correlation operation between our reference signal xo and (b) th 0 the k beam signal,xk is applied. The cross correlation operation is a simple operation as we will show later on. ) (dB) φ −10 Therefore, the computational complexity of our XSBS is Bartlett −20 still low. Capon MUSIC As we stated earlier, our XSBS is not exclusive to a −30 Normalized P( particular antenna array formation. Rather, it can operate 0 50 100 150 200 250 300 350 φ (degrees) with any formation, linear, circular, planar or any antenna array formation where the steering vector of the antenna Fig. 3: Comparison of existing AoA estimation techniques for can be estimated either analytically or experimentally. An two sources with M = 16, N = 1000 samples and SNR = 0 adequate separation between the antenna elements is needed to dB: (a) φ1 = 180 and φ2 = 200 (b) φ1 = 180 and φ2 = 190 minimize the spatial correlation between the signal collected from each of them. Since the antenna elements are already placed 0.5λ apart, a limited number of antenna elements can be conventional SBSs have both low hardware and computational used as omni-directional diversity antennas. As Mo increases, complexity, they fail to operate at medium and low level SNRs. the XSBS can estimate signal with lower SNR values. This is mainly because the estimated AoA is the angle of the Additionally, the total number of antenna elements in the beam with the highest RSS. array is a key factor in determining the resolution of our We propose a novel cross-correlation based SBS (XSBS) XSBS. The higher the number of antenna elements, the smaller AoA estimation technique. Our XSBS benefits from the low the half power beam width (HPBW) of the antenna array hardware complexity of the conventional SBS, which requires beam. A smaller HPBW leads to a better resolution. On the a single receiver, yet does not sacrifice the resolution or contrary, a higher number of antenna elements will increase performance at medium and low level SNR. Moreover, our the hardware complexity of the XSBS since they will require XSBS requires minimal computational complexity to estimate more components to apply the weights. the AoA since it is based on estimating the cross correlation Using a non-uniform excitation such as Dolph-Chebyshev between two collected one dimensional vector of samples. excitation, it is possible to generate more orthogonal beams With such low hardware and computational complexity, our for the same M. The weights generated based on the Dolph- XSBS will consume less power which will be very beneficial, Chebyshev polynomials are given by [18]: particularly, if implemented on a portable device. Furthermore, w (φ) = W (y) (13) our XSBS does not require neither any prior information on k M−1 the number of the sources nor that the sources be uncorrelated. where y = yo cos(0.5φ). yo is estimated as: acosh(R) A. XSBS Design y = cosh (14) o M − 1 Our XSBS goes through two phases to estimate the AoA: where R is the mainl obe to side lobe ratio. • Phase I: in this phase the Weights Unit depicted in W (y) = cos ((M − 1)acos(y)) (15) Figure 1 sends the first set of weights wo. The set wo is M−1 applied on the antenna elements such that no phase shift To study the resolution of our XSBS, we plot the steered or attenuation is applied at selected antenna elements, antenna array beam for M = 17, separation d = 0.5λ, R = 15 hence these selected antenna elements operate as omni- dB, with Dolph-Chebyshev non-uniform excitation in Fig. 4. directional antennas or stand alone antennas. At the same The achieved HPBW is approximately 6 degrees with a total time the weights are applied at the antenna elements in of K = 32 orthogonal beams scanning the 180 degrees1. As between the selected antenna elements to minimize their M increases, the resolution of the XSBS improves since the contribution to the summed signal to zero. The number HPBW decreases. For a linear array or a planar array, as M of diversity antennas, Mo, as well as the separation increases, Mo increases. For our M = 17 linear antenna array, between them depends on the antenna array formation. Mo = 5 with a separation of 2λ. For a circular array, the The objective is to include as many diversity antennas maximum achievable separation between the antenna elements as possible, yet not collecting a correlated signals. The 1 XSBS then acquires N samples to collect the signal xo. Fig. 4 is plotted using the MATLAB toolbox of [18]. is the diameter of the circle, which is likely = λ. Therefore, 90o Mo should not be > 2. 120o 60o B. Cross Correlation Estimation o o After the completion of the first phase of our XSBS is 150 30 completed by collecting an omni-directional signal, our XSBS φ moves to the second phase of estimating the AoA. In this −30 −20 −10 180o 0o phase, the omni-directional signal, xo, collected earlier now dB becomes our XSBS reference signal. Our XSBS then starts to scan the angular region of interest and collect the the signals x k ∈ [1 : K] o k, for : −150o −30 X xk(n) = wks(n) + v(n) (16) o −60o M −120 −90o The Weights Unit sends the precalculated weight sets, wk, to the antenna array such that the main beam is directed towards th the k angle. The cross correlation coefficient between our Fig. 4: Beam switching antenna array for N = 17 with Dolph- th reference signal and the k signal can be given by: Chebychev excitation and R = 15 dB and d = 0.5λ with a N total of 32 orthogonal beams with HBPW = 6 degrees 1 X R = x (n)xH (n) (17) ko N k o n=1 It is worth noting that Eq. (17) is applied on two vectors each 0 SNR = 15 dB SNR = 0 dB has a dimension of 1 × N, while the autocovariance function −5 in Eq. (8) is applied on a matrix with a dimension M × N. SNR = −15 dB For the MUSIC algorithm, an eigen-decomposition operation −10 is then applied on this autocovariance function along with −15 the other steps explained in the earlier section to estimate the AoA. For our XSBS, Eq. (17) is all the computation −20 needed to estimate the AoA, which tremendously reduces the −25 computational complexity. −30 C. Performance Evaluation

Normalized Cross Correlation Coefficient (dB) −35 We evaluate the performance of our XSBS under different −40 SNR levels, number of samples and for different antenna array 0 20 40 60 80 100 120 140 160 180 formation. We compare the performance of our XSBS to the φ (degrees) MUSIC algorithm, which we showed earlier to outperform the Fig. 5: Normalized cross correlation coefficient for different conventional techniques. SNR for M = 17, M = 5 and N = 1000 samples at different In Fig. 5, we simulate our XSBS with linear antenna array o SNR levels. with Dolph-Chebyshev excitation with M = 17, Mo = 5 and ◦ N = 1000 for a signal arriving φk = 90 at different SNR levels. We plot the normalized cross correlation coefficient Eq. (17), which is now our spatial power, versus the azimuth the MUSIC algorithm is limited by the number of antenna angle φ. It is shown that our XSBS has a superb performance elements M. In other words the MUSIC algorithm can not achieving a PFR = 33 dB at SNR = 27 dB , PFR = 27 dB at estimate the AoA if the number of sources is > M. In addition SNR = 0 dB and PFR = 17 at SNR = -15 dB. to that, the MUSIC algorithm requires that the signals from We then study the effect of changing the number of collected different sources must be uncorrelated. Our XSBS is limited samples N on the performance of our XSBS. In Fig. 6 we by the total number of beams K which is much larger than simulate our XSBS with linear antenna array with Dolph- M. Also, our XSBS does not require any prior information Chebshev excitation with M = 17, Mo = 5 and SNR = 0 about the number of sources. Moreover, our XSBS does not dB for a signal arriving φk = 90 for N = 10, 100 and 1000 require that the signals from different sources be uncorrelated. samples. As expected, as the number of samples increases, We compare the performance of our XSBS to the MUSIC the performance of our XSBS improves. From figures 5 and algorithm in Fig. 7 for the same number of samples of 6, it also can be inferred that at higher SNR values, a lower N = 1000 at very low SNR levels: (a) SNR=-20 dB, (b) number of samples is required to achieve an adequate PFR. SNR = -25 dB and (c) SNR = -30 dB. The MUSIC algorithm Ths MUISC algorithm requires that the number of sources in this figure used a uniform linear array with M = 16, be known a priori. The maximum number of sources for while our XSBS uses an M = 17 linear array with Dolphy- (a) (b) (c) 0 0 0 0 N=1000 N=100 −2 −2 −2 −5 N=10 −4 −4 −4 −10 −6 −6 −6

−15 −8 −8 −8

−20 −10 −10 −10

−12 −12 −12 −25

−14 −14 −14 −30 −16 −16 −16 Normalized spatial power spectrum (dB) Normalized spatial power spectrum (dB) Normalized spatial power spectrum (dB)

Normalized Cross Correlation Coefficient (dB) −35 −18 XSBS −18 XSBS −18 XSBS MUSIC MUSIC MUSIC −40 −20 −20 −20 0 20 40 60 80 100 120 140 160 180 0 100 0 100 0 100 φ (degrees) φ (degrees) φ (degrees) φ (degrees)

Fig. 6: Normalized cross correlation coefficient for different Fig. 7: Spatial power spectrum for our XSBS vs. the MUSIC number of samples for SNR=0 dB for M = 17, Mo = 5 for algorithm at: (a) SNR=-20 dB, (b) SNR = -25 dB and (c) SNR N = 10, 100 and 1000 samples. = -30 dB

(a) Chebyshev excitation. It is shown that the MUSIC algorithm 0 XSBS MUSIC fails to estimate the AoA at SNR levels < 20 dB with PFR −10 = 3dB, while our XSBS can operate at SNR levels as low as -25 dB with PFR = 5 dB. −20 In Fig. 8, we compare the resolution of our XSBS to −30

the resolution of the MUSIC algorithm. We use a uniform Normalized spatial power (dB) 0 50 100 150 200 250 300 350 φ (degrees) circular array for the two techniques. We plot the spatial power (b) 0 spectrum for two sources arriving at angles φ1 and φ2. The two sources for the MUSIC are uncorrelated while we use −10 the same signal for the two sources for our XSBS. We plot ◦ −20 the spatial power spectrum for two sources at φ1 = 180 and XSBS ◦ MUSIC φ2 = 192 at: (a) SNR = 0 dB and (b) SNR = -15 dB. It is −30

shown that the resolution of the MUSIC highly depends on the Normalized spatial power (dB) 0 50 100 150 200 250 300 350 φ received SNR, while for our XSBS, it depends on the HPBW (degrees) of the main lobe. The resolution of the MUSIC algorithm is Fig. 8: Cross correlation coefficient for different number of ◦ ◦ about 8 with PFR = 3dB at SNR = 0 dB and 20 at SNR = samples for SNR=-20 dB for M= 17 and 5 omni directional -15 dB. Our XSBS has a consistent resolution of the HPBW, beams which in this case is 6◦.

V. CONCLUSION

In this paper, we proposed a hardware friendly AoA estima- tion system. Our system first collects an omni-directional sig- nal to be used as a reference signal. Our system then switches the main beam to scan the angular region of interest. The collected signals from the switched beams are cross correlated with the reference signal. The cross correlation coefficient is the highest at the true AoA and relatively negligible otherwise. Our algorithm can operate with any antenna array formation with known steering vector. We showed that our algorithm can operate at very low SNR level, i.e., as low as - 25 dB. As the SNR increases, a fewer samples can be used to achieve an adequate PFR. The number of sources that can be detected using our system is limited by the number of switched beams, which is higher than the number of antenna elements. We compared our algorithm to the MUSIC algorithm and we showed that our algorithm has a superior performance [15] H. Yan and W. Liu, “Design of time difference of arrival estimation over it. Not only because our algorithm does not require any system based on fast cross correlation,” in Future Computer and Communication (ICFCC), 2010 2nd International Conference on, vol. 2, prior information or constraints on the received signal, but May 2010, pp. V2–464–V2–466. also it has a better resolution. The resolution of our system [16] P. Peng, H. Luo, Z. Liu, and X. Ren, “A cooperative target location mainly depends on the HPBW of the main beam rather than algorithm based on time difference of arrival in senor networks,” in Mechatronics and Automation, 2009. ICMA 2009. International the SNR such as MUSIC. Unlike the MUSIC algorithm, our Conference on, Aug 2009, pp. 696–701. system requires a single receiver, which reduces the hardware [17] P. Ioannides and C. Balanis, “Uniform circular arrays for smart anten- complexity tremendously. Moreover, our system is based on nas,” Antennas and Propagation Magazine, IEEE, vol. 47, no. 4, pp. 192–206, Aug 2005. estimating the cross correlation coefficient between one dimen- [18] S. J. Orfanidis, Electromagnetic Waves and Antennas, 2010. sional vector, which has a negligible computational complexity [19] C. Balanis, Antenna Theory: Analysis and Design. John Wiley & Sons, when compared to estimating the eigenvalue decomposition of 2012. [20] A. Khallaayoun, “A High Resolution Direction of Arrival Estimation an autocovariance matrix. Analysis and Implementation in a System,” Ph.D. dissertation, Montana State University. [21] P. Djuric, “A model selection rule for sinusoids in white gaussian noise,” ACKNOWLEDGMENT Signal Processing, IEEE Transactions on, vol. 44, no. 7, pp. 1744–1751, Jul 1996. This research was made possible by NPRP 5-559-2-227 grant from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.

REFERENCES

[1] T. E. Tuncer and B. Friedlander, Classical and Modern Direction-of- Arrival Estimation. Academic Press, 2009. [2] C. A. Balanis and P. I. Ioannides, “Introduction to smart antennas,” Synthesis Lectures on Antennas, vol. 2, no. 1, pp. 1–175, 2007. [3] Z. Chen, G. Gokeda, and Y. Yu, Introduction to Direction-of-Arrival Estimation. Artech House, 2010. [4] S. Chandran, Advances in Direction-of-Arrival Estimation. Artech House, 2006. [5] J. Foutz, A. Spanias, and M. K. Banavar, Narrowband Direction of Arrival Estimation for Antenna Arrays. Morgan & Claypool Publishers, 2006. [6] M. S. BARTLETT, “Periodogram analysis and continuous spectra,” Biometrika, vol. 37, no. 1-2, pp. 1–16, 1950. [Online]. Available: http://biomet.oxfordjournals.org/content/37/1-2/1.short [7] J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proceedings of the IEEE, vol. 57, no. 8, pp. 1408–1418, 1969. [8] R. O. Schmidt, “A signal subspace approach to multiple emitter location and spectral estimation,” Ph.D. dissertation, Stanford University. [9] K. Gotsis, K. Siakavara, and J. Sahalos, “On the direction of arrival (doa) estimation for a switched-beam antenna system using neural networks,” Antennas and Propagation, IEEE Transactions on, vol. 57, no. 5, pp. 1399–1411, May 2009. [10] Y. Ozaki, J. Ozawa, E. Taillefer, J. Cheng, and Y. Watanabe, “Direction- of-arrival estimation using adjacent pattern power ratio with switched beam antenna,” in Communications, Computers and Signal Processing, 2009. PacRim 2009. IEEE Pacific Rim Conference on, Aug 2009, pp. 453–458. [11] J. Lee, D. Kim, C. K. Toh, T. Kwon, and Y. Choi, “A table-driven aoa estimation algorithm for switched-beam antennas in wireless networks,” in Wireless Conference 2005 - Next Generation Wireless and Mobile Communications and Services (European Wireless), 11th European, April 2005, pp. 1–6. [12] M. Ringer and G. J. Frazer, “Waveform analysis of transmissions of opportunity for passive radar,” in Signal Processing and Its Applications, 1999. ISSPA ’99. Proceedings of the Fifth International Symposium on, vol. 2, 1999, pp. 511–514 vol.2. [13] C. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, “Signal processing for passive radar using ofdm waveforms,” Selected Topics in Signal Processing, IEEE Journal of, vol. 4, no. 1, pp. 226–238, Feb 2010. [14] C.-K. Chen and W. Gardner, “Signal-selective time-difference of arrival estimation for passive location of man-made signal sources in highly corruptive environments. ii. algorithms and performance,” Signal Pro- cessing, IEEE Transactions on, vol. 40, no. 5, pp. 1185–1197, May 1992.