Jointly Sparse Recovery of Multiple Snapshots in STAP Zeqiang Ma, Yimin Liu*, Huadong Meng, Xiqin Wang Department of Electronic Engineering Tsinghua University Beijing 100084, P R China Yiminliu@tsinghua.edu.cn Abstract— A novel STAP algorithm based on jointly sparse recovery technique using multiple snapshots, called JSR-STAP, is proposed in this paper. The new algorithm uses the combined l 2,1 norm minimization to estimate the sparse spatial-temporal spectrum of measure data from the airborne array radar. Compared with traditional sparse recovery based STAP methods introduced in literature, the JSR-STAP extract a more reliable support set of clutter reflection from multiple snapshots so that the sparse recovery quality is evidently improved, and thus leads to a better result of clutter restrain. Both simulation and experimental results are provided to illustrate the performance of our new method. I. INTRODUCTION Space-Time Adaptive Processing (STAP) is a widely used technique in airborne radar signal processing which was originally developed for low-velocity moving targets detection in clutter environments [1]. The key step of STAP is to get an accurate estimation of clutter covariance matrix R [2][3]. Traditional method of estimating R usually based on the maximum likelihood estimation using large number of homogeneous training data which are obtained from the range cells beside the detect range cell. The compressive sensing theory [4][5] provides another point of view on this issue . By the implementation of sparse recovery theory, high-resolution spatial-temporal spectrum estimation with a few snapshots (or even only one single snapshot) is possible [6][7]. However, the information within the adjacent snapshot were not sufficiently utilized, which leads to a potential sacrifice of sparse recovery performance. In this paper, the Jointly Sparse Recovery STAP (JSR- STAP) algorithm, which is a new STAP approach based on the Jointly Sparse Recovery of multiple spatial-temporal snapshots, is proposed. In the new algorithm, a combined l 2,1 norm minimization model for multiple snapshots is built, and then the jointly sparse recovery is adopted to solve the combined l 2,1 norm minimization problem, which help us to get a more accurate spatial-temporal spectrum estimation of the clutter than traditional methods. And then the qualified spatial-temporal spectrum is used to construct the clutter covariance matrix, for a better performance of clutter restrain and low velocity target detection. The remainder of this paper is organized as follows. Section II describes the basic signal model. Section III introduces the principles of jointly sparse recovery and the JSR-STAP algorithm. In Section IV, both simulation and experimental results are given to illustrate the advantage of the newly proposed method. II. SIGNAL MODEL Suppose an airborne radar system that transmits coherent pulses through a uniform linear array (ULA) consisting of N array elements. The echo sample data is a N×M×L data cube, where M denotes the coherent pulse number and L denotes the range cell number. Let y l denote the vectored data matrix of the l th range cell. Then for a specific angle of arrival θ and related normalized Doppler frequency f d , the spatial-temporal steering vector is constructed as follows, ( ) ( ) ( ) , , d t d s f f θ θ = ⊗ t a a (1) where ⊗ denotes Kronecker product, and the spatial steering vector ( ) ( ) 1,exp( 2 ),...,exp( 2 1 ) T s s s s j f j N f θ π π = - ⎡ ⎤ ⎣ ⎦ a , (2) and the temporal steering vector is ( ) ( ) ( ) ( ) 1, exp 2 ,...,exp 2 1 T t d d d f j f j M f π π ⎡ ⎤ = - ⎣ ⎦ a . (3) In equation(2)(3), f s denotes spatial frequency, f s =d/λsinθ s , and the symbol θ s means the angle of arrival. Consider there are N c clutter scatterers in the l th range cell, then the sample data vector can be written as, ( ) 1 , c N l i di i l i x f θ = = + ∑ y t n , (4) where x i denotes the amplitude of the i th clutter scatterer and n l denotes the noise vector. The above equation can be rewritten in the form of matrix as, This work was supported in part by the National Natural Science Foundation of China under Grant 61201356, and in part by the 973 Program under Grant 0CB731901. 2013 IEEE Radar Conference (RadarCon13) 978-1-4673-5794-4/13/$31.00 ©2013 IEEE