IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 48, NO. 12, DECEMBER 2000 3569 Correspondence________________________________________________________________________ Generalized Forward/Backward Subaperture Smoothing Techniques for Sample Starved STAP S. Unnikrishna Pillai, Younglok L. Kim, and Joseph R. Guerci Abstract—A major issue in space-time adaptive processing (STAP) for moving target indicator (MTI) radar is the so-called sample support problem. Often, the available sample support for estimating the requisite interference covariance matrix is inadequate, thereby precluding STAP beamforming utilizing many adaptive degrees-of-freedom (DOFs). Al- though deterministic rank-reduction methods can reduce sample support requirements, they are invariably suboptimal from a signal-to-interfer- ence-plus-noise-ratio (SINR) standpoint. In this paper, a new generealized subspatial and subtemporal aperture smoothing method employing forward and backward data vectors is in- troduced to overcome the data deficiency problem. It is shown that multi- plicative improvement in data samples can be obtained at the expense of negligible loss in space-time aperture of the steering vector. Index Terms—Array processing, MTI radar, space-time adaptive radar. I. INTRODUCTION A major issue in space-time adaptive processing (STAP) for moving target indicator (MTI) radar is the so-called sample support problem [1], [2]. This arises from the need to estimate, on the fly, the requisite interference statistics. For max signal-to-interference-plus-noise-ratio (SINR) beamforming, the relevant statistic is the interference-only co- variance matrix [3]–[6]. Since spatio-temporal adaptive beamforming often involves many adaptive degrees-of-freedom (DOFs), many vector (snapshot) samples are required to form a useful covariance estimate. For example, the DARPA Mountain Top radar [7] has the capability of supporting spatial (antenna channels) and tem- poral (coherent pulses), for a total of adaptive DOFs. If the sample matrix inverse (SMI) method is employed, a wide sense stationary (WSS) sample support of approximately is required (for the Gaussian case) to obtain SINR performance within 3 dB of optimum [4]. Since the instantaneous operating RF bandwidth of the radar is only 200 kHz, this translates into a WSS requirement on the ground clutter of approximately km, which is clearly not reasonable. For high interference-to-noise-ratio (INR) cases, principal compo- nents and appropriately diagonally loaded sample covariance estimates can reduce this requirement to , where is the dimension of the dominant subspace [8]–[12]. However, this can still lead to unrealistic WSS assumptions, particularly in the presence of subspace leakage phenomenon (e.g., internal clutter motion, antenna dispersion, trans- mitter instabilities, etc.) that have the effect of increasing the rank of the dominant interference [13], [14]. For the aforementioned Mountain Manuscript received February 22, 1999; revised August 25, 2000. This work was supported in part by the Office of Naval Research under Contract N-00014-89-J-1512P-5. The associate editor coordinating the review of this paper and approving it for publication was Dr. Sergio Barbarossa. S. U. Pillai is with the Department of Electrical Engineering, Polytechnic University, Brooklyn, NY 11202 USA (e-mail: pillai@hora.poly.edu). Y. L. Kim is with InterDigital Communications Corp., Melville, NY 11747 USA. J. R. Guerci is with the Defense Advanced Research Projects Agency (DARPA), Arlington, VA 22203 USA. Publisher Item Identifier S 1053-587X(00)10146-1. Top radar example, in the absence of antenna “crab” [5] and any other subspace leakage phenomenon, [15], which translates into a WSS requirement of approximately 58 km, which is still quite large. In a practical setting, this lower bound would be unattainable due to unavoidable subspace leakage. In this paper, a comprehensive forward/backward (F/B) smoothing methodology that generalizes previous results [16]–[19] is introduced and yields a strategy for gracefully trading spatio-temporal aperture for increased effective sample support. Similar to previous F/B methods, symmetry of the antenna array and temporal sampling (uniform pulse repetition interval) are exploited to yield an increased effective sample support via synthesized F/B data vectors. However, in the present method, additional sample support is obtained by subspatial and subtemporal aperture smoothing. The remaining paper is organized as follows. In Section II, a brief STAP problem formulation is presented. In Section III, the generalized F/B method is detailed. Subtemporal aperture smoothing is introduced in Section III-A, and subspatial aperture smoothing is presented in Sec- tion III-B. Combined subspatio-temporal smoothing is then detailed in Section III-C. Conclusions and areas for future research are contained in Section IV. II. STAP PROBLEM FORMULATION Consider the radar scenario where the returned space-time snapshot signal may consist of a target echo and interferences such as jammer, clutter, and thermal noise given by (1) where and are the complex target attenuation factor and target steering vector, respectively, associated with the spa- tial and Doppler parameters and of the moving target, and represents the total interference signal. Here, represents the concatenated space-time data vector formed from the array output vectors corresponding to pulse returns that are present in a coherent processing interval (CPI) with interpulse interval equal to . Thus, using antenna elements, if represents the th sensor output at th pulse), then (2) and . . . (3) represent the array output and space-time snapshot data vectors, respec- tively. In the point-Doppler detection problem, the optimum weight vector (in a max SINR sense) is given by [3] (4) where is the total interference plus noise covariance matrix. For a uniform linear array (ULA) with interelement spacing equal to , the spatio-temporal steering vector can be expressed as [5] (5) 1053–587X/00$10.00 © 2000 IEEE