Design and analysis of compressive antenna arrays for direction of arrival estimation

Abstract

In this paper we investigate the design of compressive antenna arrays for direction of arrival (DOA) estimation that aim to provide a larger aperture with a reduced hardware complexity by a linear combination of the antenna outputs to a lower number of receiver channels. We present a basic receiver architecture of such a compressive array and introduce a generic system model that includes different options for the hardware implementation. We then discuss the design of the analog combining network that performs the receiver channel reduction, and propose two design approaches. The first approach is based on the spatial correlation function which is a low-complexity scheme that in certain cases admits a closed-form solution. The second approach is based on minimizing the Cramer-Rao Bound (CRB) with the ´ constraint to limit the probability of false detection of paths to a pre-specified level. Our numerical simulations demonstrate the superiority of the proposed optimized compressive arrays compared to the sparse arrays of the same complexity and to compressive arrays with randomly chosen combining kernels.

Description

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Keywords

University of Compressive Sensing, DOA Estimation, Measurement Design

Citation

[1] H. Krim and M. Viberg. Two decades of array signal processing research: the parametric approach. IEEE Signal Processing Magazine, 13(4):67–94, Jul 1996. [2] H. L. Van Trees. Detection, estimation, and modulation theory. Part IV., Optimum array processing. Wiley-Interscience, New York, 2002. [3] S. Valaee, B. Champagne, and P. Kabal. Parametric localization of distributed sources. IEEE Transactions on Signal Processing , 43(9):2144– 2153, Sep 199 13 [4] J. C. Chen, K. Yao, and R. E. Hudson. Source localization and beamforming. IEEE Signal Processing Magazine, 19(2):30–39, Mar 2002. [5] A. Richter, D. Hampicke, G. Sommerkorn, and R. S. Thom¨a. Joint estimation of dod, time-delay, and doa for high-resolution channel sounding. In IEE Vehicular Technology Conference, volume 2, pages 1045–1049 vol.2, 2000. [6] R. S. Thom¨a, M. Landmann, and A. Richter. Rimax-a maximum likelihood framework channel parameter estimation in multidimensional channel sounding. International Symposium on Antennas and Propagation, pages 53–56, 2004. [7] W. D. Blair and M. B. Pearce. Monopulse doa estimation of two unresolved rayleigh targets. IEEE Transactions on Aerospace and Electronic Systems, 37(2):452–469, Apr 2001. [8] M. Landmann and R. S. Thom¨a. Common pitfalls in multidimensional high resolution channel parameter estimation. In IEEE Digital Signal Processing Workshop and 5th IEEE Signal Processing Educati on Workshop, pages 314–319, Jan 2009. [9] R. Roy and T. Kailath. Esprit-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(7):984–995, Jul 1989. [10] R. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation , 34(3):276–280, Mar 1986. [11] P. Stoica, B. Ottersten, M. Viberg, and R. L. Moses. Maximum likelihood array processing for stochastic coherent sources. IEEE Transactions on Signal Processing , 44(1):96–105, Jan 1996. [12] Y. Lo. A mathematical theory of antenna arrays with randomly spaced elements. IEEE Transactions on Antennas and Propagation , 12(3):257– 268, May 1964. [13] A. Moffet. Minimum-redundancy linear arrays. IEEE Transactions on Antennas and Propagation , 16(2):172–175, Mar 1968. [14] W. K. Ma, T. H. Hsieh, and C. Y. Chi. Doa estimation of quasistationary signals via khatri-rao subspace. In International Conference on Acoustics, Speech and Signal Processing, pages 2165–2168, April 2009. [15] R. L. Haupt. Thinned arrays using genetic algorithms. IEEE Transactions on Antennas and Propagation , 42(7):993–999, July 1994. [16] A. Trucco and V. Murino. Stochastic optimization of linear sparse arrays. IEEE Journal of Oceanic Engineering , 24(3):291–299, Jul 1999. [17] H. Gazzah and K. Abed-Meraim. Optimum ambiguity-free directional and omnidirectional planar antenna arrays for doa estimation. IEEE Transactions on Signal Processing , 57(10):3942–3953, Oct 2009. [18] P. P. Vaidyanathan and P. Pal. Sparse sensing with co-prime samplers and arrays. IEEE Transactions on Signal Processing , 59(2):573–586, Feb 2011. [19] P. Pal and P. P. Vaidyanathan. Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8):4167–4181, Aug 2010. [20] E. J. Cand´es and T. Tao. Near optimal signal recovery from random projections: universal encoding strategies. IEEE Transactions on Information Theory, 52:5406–5425, 2006. [21] E. J. Cand´es, J. Romberg, and T. Tao. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2):489–509, Feb 2006. [22] D. L. Donoho. Compressed sensing. IEEE Transactions on Information Theory, 52(4):1289–1306, 2006. [23] V. Cevher, A. C. Gurbuz, J. H. McClellan, and R. Chellappa. Compressive wireless arrays for bearing estimation. In International Conference on Acoustics, Speech and Signal Processing, pages 2497–2500, March 2008. [24] C. Feng, S. Valaee, and Z. Tan. Multiple target localization using compressive sensing. In Global Telecommunications Conference, pages 1–6, Nov 2009. [25] J. H. G. Ender. On compressive sensing applied to radar. Signal Processing, 90(5):1402 – 1414, 2010. Special Section on Statistical Signal Array Processing. [26] D. Malioutov, M. Cetin, and A. S. Willsky. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Transactions on Signal Processing , 53(8):3010–3022, Aug 2005. [27] A. C. Gurbuz, V. Cevher, and J. H. Mcclellan. Bearing estimation via spatial sparsity using compressive sensing. IEEE Transactions on Aerospace and Electronic Systems, 48(2):1358–1369, APRIL 2012. [28] A. Gretsistas and M. D. Plumbley. A Multichannel Spatial Compressed Sensing Approach for Direction of Arrival Estimation, pages 458–465. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010. [29] P. Stoica, P. Babu, and J. Li. Spice: A sparse covariance-based estimation method for array processing. IEEE Transactions on Signal Processing , 59(2):629–638, Feb 2011. [30] D. Model and M. Zibulevsky. Signal reconstruction in sensor arrays using sparse representations. Signal Processing, 86(3):624 – 638, 2006. Sparse Approximations in Signal and Image ProcessingSparse Approximations in Signal and Image Processing. [31] K. Han, Y. Wang, B. Kou, and W. Hong. Parameters estimation using a random linear array and compressed sensing. In International Congress on Image and Signal Processing (CISP), volume 8, pages 3950–3954, Oct 2010. [32] M. Rossi, A. M. Haimovich, and Y. C. Eldar. Spatial compressive sensing in mimo radar with random arrays. In Annual Conference on Information Sciences and Systems (CISS), pages 1–6, March 2012. [33] S. Shakeri, D. D. Ariananda, and G. Leus. Direction of arrival estimation using sparse ruler array design. In International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), pages 525– 529, June 2012. [34] M. B. Hawes and W. Liu. Compressive sensing-based approach to the design of linear robust sparse antenna arrays with physical size constraint. IET Microwaves, Antennas Propagation, 8(10):736–746, July 2014. [35] Y. Wang, G. Leus, and A. Pandharipande. Direction estimation using compressive sampling array processing. In 2009 IEEE/SP 15th Workshop on Statistical Signal Processing , pages 626–629. IEEE, 2009. [36] J. F. Gu, W. P. Zhu, and M. N. S. Swamy. Compressed sensing for doa estimation with fewer receivers than sensors. In IEEE International Symposium of Circuits and Systems (ISCAS), pages 1752–1755, May 2011. [37] R. Baraniuk, M. Davenport, R DeVore, and M Wakin. A simple proof of the restricted isometry property for random matrices. Constructive Approximation, 28(3):253–263, 2008. [38] T T. Cai, T. Jiang, et al. Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices. The Annals of Statistics, 39(3):1496–1525, 2011. [39] Y. C Eldar and G. Kutyniok. Compressed sensing: theory and applications. Cambridge University Press, 2012. [40] M. Ibrahim, F. Roemer, and G. Del Galdo. On the design of the measurement matrix for compressed sensing based doa estimation. In International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 3631–3635, April 2015. [41] TriQuint Semiconductor. Phase shifters, August 2016. http://www.triquint.com/products/all/control-products/phase-shifters. [42] H. B. Lee and M. S. Wengrovitz. Resolution threshold of beamspace music for two closely spaced emitters. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(9):1545–1559, Sep 1990. [43] S. Anderson. Optimal dimension reduction for sensor array signal processing. In Asilomar Conference on Signals, Systems and Computers, pages 918–922 vol.2, Nov 1991. [44] M. D. Zoltowski, G. M. Kautz, and S. D. Silverstein. Beamspace rootmusic. IEEE Transactions on Signal Processing , 41(1):344–, Jan 1993. [45] Guanghan Xu, S. D. Silverstein, R. H. Roy, and T. Kailath. Beamspace esprit. IEEE Transactions on Signal Processing , 42(2):349–356, Feb 1994. [46] M. D. Zoltowski, M. Haardt, and C. P. Mathews. Closed-form 2-d angle estimation with rectangular arrays in element space or beamspace via unitary esprit. IEEE Transactions on Signal Processing , 44(2):316–328, Feb 1996. [47] A. B. Gershman. Direction finding using beamspace root estimator banks. IEEE Transactions on Signal Processing , 46(11):3131–3135, Nov 1998. [48] A. Hassanien, S. A. Elkader, A. B. Gershman, and K. M. Wong. Convex optimization based beam-space preprocessing with improved robustness against out-of-sector sources. IEEE Transactions on Signal Processing , 54(5):1587–1595, May 2006. [49] H. Hung and M. Kaveh. Focussing matrices for coherent signalsubspace processing. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(8):1272–1281, Aug 1988. [50] V. Venkateswaran and A. J. van der Veen. Analog beamforming in mimo communications with phase shift networks and online channel estimation. IEEE Transactions on Signal Processing , 58(8):4131–4143, Aug 2010. [51] X. Huang, Y. J. Guo, and J. D. Bunton. A hybrid adaptive antenna array. IEEE Transactions on Wireless Communications, 9(5):1770–1779, May 2010. 14 [52] J. Nsenga, A. Bourdoux, and F. Horlin. Mixed analog/digital beamforming for 60 ghz mimo frequency selective channels. In IEEE International Conference on Communications, pages 1–6, May 2010. [53] L. C. Godara. Smart Antennas. CRC Press LLC, 2004. [54] T. E. Bogale and L. B. Le. Beamforming for multiuser massive mimo systems: Digital versus hybrid analog-digital. In IEEE Global Communications Conference, pages 4066–4071, Dec 2014. [55] Z. Pi and F. Khan. An introduction to millimeter-wave mobile broadband systems. IEEE Communications Magazine, 49(6):101–107, June 2011. [56] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath. Spatially sparse precoding in millimeter wave mimo systems. IEEE Transactions on Wireless Communications, 13(3):1499–1513, March 2014. [57] W. Roh, J. Y. Seol, J. Park, B. Lee, J. Lee, Y. Kim, J. Cho, K. Cheun, and F. Aryanfar. Millimeter-wave beamforming as an enabling technology for 5g cellular communications: theoretical feasibility and prototype results. IEEE Communications Magazine, 52(2):106–113, February 2014. [58] F. Athley. Threshold region performance of maximum likelihood direction of arrival estimators. IEEE Transactions on Signal Processing , 53(4):1359–1373, 2005. [59] E. Kreyszig. Advanced engineering mathematics. John Wiley and Sons, New York, 2005. [60] C. Helstrom. Calculating error probabilities for intersymbol and cochannel interference. IEEE Transactions on Communications, 34(5):430–435, 1986. [61] T. Coleman and Y. Li. On the convergence of reflective newton methods for large-scale nonlinear minimization subject to bounds. Mathematical Programming, 67(2):189–224, 1994. [62] T. Coleman and Y. Li. An interior trust region approach for nonlinear minimization subject to bounds. SIAM Journal on optimization, 6(2):418–445, 1996. [63] M. Ibrahim, F. R¨omer, and G. Del Galdo. An adaptively focusing measurement design for compressed sensing based doa estimation. In Signal Processing Conference (EUSIPCO), 2015 23rd Europea n, pages 859–863. IEEE, 2015. [64] A. M Mathai and S. B Provost. Quadratic forms in random variables: theory and applications. M. Dekker New York, 1992. [65] F. Athley. Threshold region performance of deterministic maximum likelihood doa estimation of multiple sources. In Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference on, volume 2, pages 1283–1287. IEEE, 2002. [66] G. L. Turin. The characteristic function of hermitian quadratic forms in complex normal variables. Biometrika, 47(1/2):199–201, 1960. [67] D. Raphaeli. Distribution of noncentral indefinite quadratic forms in complex normal variables. IEEE transactions on Information Theory, 42(3):1002–1007, 1996. [68] Y. Ma, T. L. Lim, and S. Pasupathy. Error probability for coherent and differential psk over arbitrary rician fading channels with multiple cochannel interferers. IEEE Transactions on Communications, 50(3):429–441, 2002.

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