L1 REGULARIZED STAP ALGORITHM WITH A GENERALIZED SIDELOBE CANCELER ARCHITECTURE FOR AIRBORNE RADAR
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1 L1 REGULARIZED STAP ALGORITHM WITH A GENERALIZED SIDELOBE CANCELER ARCHITECTURE FOR AIRBORNE RADAR Zhaocheng Yang, Rodrigo C. de Lamare and Xiang Li Communications Research Group Department of Electronics University of York, UK rcdl500@york.ac.uk Electronics Science and Engineering School, National University of Defense Technology, China yangzhaocheng@gmail.com and lixiang01@vip.sina.com
2 Outline Motivation Prior Work Contributions Signal Model Proposed L1 Regularized Algorithm Simulations Conclusions
3 Motivation Full-rank STAP: Existing problems: large-sample support and expensive computation. Faster convergence, lower computational complexity and improved robustness against non-homogeneous interference. Main idea: to devise a new STAP algorithm that exploits the sparsity of the receive data and the filter weights. How does it work? Imposing a sparse regularization (L1-norm type) to the minimum mean-square error (MMSE) criterion. The goal is to find an appropriate solution for this kind of mixed L1-norm and L2-norm optimization problem.
4 Prior Work Compressive sensing type STAP: Global matched filter to STAP data, Maria and Fuchs. (2006s). CS-STAP, Sun, Zhang, etc. (2009s). Selesnick, Pillai, etc. (2010s). Parker and Potter. (2010s) All these works focus on the recovery of the clutter power in angle-doppler plane.
5 Contributions Modify the MSE cost function (imposing a sparse regularization to the MSE criterion). Propose a L1-based online coordinate descent (OCD) adaptive algorithm to compute the weights. Do not need matrix inversion (nearly the same computation complexity as RLS algorithm). Show faster convergence and better performance than conventional RLS algorithm.
6 Signal Model and Problem Statement where Detection problem: H 0 : r=r u H 1 : r=α t r t +r u. H 0 denotes target absence, H 1 denotes target present, r u is a MN x 1 the undesired interference vector, r t is a MN x 1 the normalized target space-time steering vector, α t is a complex gain of the target, M is the number of antenna elements, N is the number of pulses in one CPI
7 GSC-STAP for Airborne Radar Blocking matrix : STAP filter: Main problem: design of
8 Optimal Linear MMSE Design for GSC-STAP Optimization problem: Optimal GSC-STAP filter weights: where Associated output SINR:
9 Proposed L1 Regularized STAP Modified MMSE cost function: λ where is a positive scalar. Computing the gradient terms with respect to where How to solve?
10 Proposed L1 Regularized STAP Optimal weights by shrinkage method: where and is the soft-thresholding operator, given by
11 L1-based OCD Adaptive Algorithm The noise-subspace data covariance matrix and the crosscorrelation vector (i is sample index): The updated filter weights: where
12 Complexity Analysis
13 Simulation: Scenario and Parameters
14 Simulations: SINR vs Snapshots
15 Simulations: SINR vs Doppler Frequency
16 Simulations: Probability of Detection
17 Conclusions A new L1 regularized STAP algorithm is proposed with GSC architecture for airborne radar. A L1-based OCD adaptive algorithm is developed to compute the filter weights. Nearly the same computational complexity as RLS algorithm, without the need for a matrix inversion. The proposed algorithm outperforms the conventional RLS STAP algorithm.
18 References [1] W.L. Melvin, "A stap overview," IEEE A\&E Sys. Mag., vol.19, no.1, pp.19-35, [2] J. S. Goldstein, I. S. Reed and P. A. Zulch, "Multistage Partially Adaptive STAP CFAR Detection Algorithm," IEEE Trans. Aes. Ele. Sys., vol.35, no.2, pp , [3] R. Fa, R.C. de Lamare and L. Wang, "Reduced-rank STAP schemes for airborne radar based on swithced joint interpolation, decimation and filtering algorithm," IEEE Trans. Sig. Proc., vol.58, no.8, pp , [4] R. C. de Lamare and R. Sampaio-Neto, Adaptive reduced-rank processing based on joint and iterative interpolation, decimation, and filtering, IEEE Trans. Sig. Proc., vol. 57, No. 7, July 2009, pp [5] M. Zibulevsky and M. Elad, "L1-L2 optimization in signal and image processing," IEEE Sig. Proc. Mag., vol. 27, no. 3, pp , May [6] D. Angelosante, J.A. Bazerque and G.B. Giannakis, "Online adaptive estimation of sparse signals: where RLS meets the L_1-norm," IEEE Trans. Sig. Proc., vol. 58, no. 7, pp , [7] J. Friedman, T. Hastie and R. Tibshirani, "Regularization paths for generalized linear models via coordinate descent," Journal of Statistical Software, vol. 33, no. 1, pp. 1-22, 2010.
SPACE-TIME adaptive processing (STAP) techniques have
4182 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL 58, NO 8, AUGUST 2010 Reduced-Rank STAP Schemes for Airborne Radar Based on Switched Joint Interpolation, Decimation Filtering Algorithm Rui Fa, Rodrigo
This work is funded by the Ministry of Defence (MoD), UK. Project MoD, Contract No. RT/COM/S/021.
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