Mathematical Problems in Engineering

Volume 2016, Article ID 3986903, 9 pages

http://dx.doi.org/10.1155/2016/3986903

## A Novel STAP Algorithm for Airborne MIMO Radar Based on Temporally Correlated Multiple Sparse Bayesian Learning

^{1}Air Force Engineering University, Xi’an 710051, China^{2}National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China

Received 1 March 2016; Revised 28 June 2016; Accepted 20 July 2016

Academic Editor: Cornel Ioana

Copyright © 2016 Hanwei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In a heterogeneous environment, to efficiently suppress clutter with only one snapshot, a novel STAP algorithm for multiple-input multiple-output (MIMO) radar based on sparse representation, referred to as MIMOSR-STAP in this paper, is presented. By exploiting the waveform diversity of MIMO radar, each snapshot at the tested range cell can be transformed into multisnapshots for the phased array radar, which can estimate the high-resolution space-time spectrum by using multiple measurement vectors (MMV) technique. The proposed approach is effective in estimating the spectrum by utilizing Temporally Correlated Multiple Sparse Bayesian Learning (TMSBL). In the sequel, the clutter covariance matrix (CCM) and the corresponding adaptive weight vector can be efficiently obtained. MIMOSR-STAP enjoys high accuracy and robustness so that it can achieve better performance of output signal-to-clutter-plus-noise ratio (SCNR) and minimum detectable velocity (MDV) than the single measurement vector sparse representation methods in the literature. Thus, MIMOSR-STAP can deal with badly inhomogeneous clutter scenario more effectively, especially suitable for insufficient independent and identically distributed (IID) samples environment.

#### 1. Introduction

Space-time adaptive processing (STAP) is a crucial technique which is used in airborne phased array radar to suppress clutter for target detection [1]. However, the fully adaptive STAP processor is difficult to be applied in practice, due to the lack of sufficient independent and identically distributed (IID) training samples in seriously nonhomogeneous environment. Focused on nonhomogeneous clutter scenario, many strategies have been proposed [2–8], that is, STAP algorithms based on reduce-dimension (RD), reduce-rank (RR), direct data domain (DDD), and space-time autoregressive filtering (STAR). However, the abovementioned methods’ clutter covariance matrix based on maximum-likelihood estimation, called traditional STAP methods, requires twice the degree of freedom (DOF) of IID training samples if it is intended to acquire less than 3 dB loss of optimal performance [9]. Ginolhac et al. [7, 8] proposed a new LR-STAP filter by cleverly taking into account the persymmetric structure of the noise covariance matrix (CM) and the low-rank (LR) structure of the clutter. The resulting STAP filter is shown, both theoretically and experimentally, to exhibit 3 dB SINR loss performance with only secondary data (where is the clutter rank). The IID training samples support can be further reduced. Thus, it can be seen that reducing the number of secondary data used to estimate the CM for STAP technique is still an active research topic.

Inspired by the rapid development of sparse representation (SR) and compressed sensing (CS) theory, clutter covariance matrix (CCM) can be estimated by utilizing SR technique [10, 11] which needs much fewer training samples compared with traditional STAP methods, and it is referred to as SR-STAP in [10–12]. However, using the data of single snapshot in SR-STAP [12] may lead to estimation errors, such as clutter spectrum disconnection and “pseudopeaks.” Hence, to prevent a potential sacrifice of sparse representation performance happening and make sufficient use of the adjacent multiple snapshots, it would better transform from the single measurement vector (SMV) sparse solution problem into the multiple measurement vectors (MMV) joint sparse solution problem. The MMV problem caught many scholars’ attention [11]. Moreover, to suppress the seriously heterogeneous clutter, direct data domain (D3) method has been proposed. In [13], owing to the intrinsic sparsity of the spectral distribution, a new direct data domain approach is examined, which seeks to estimate the high-resolution spectrum by using focal underdetermined system solution (FOCUSS) and L1 norm minimization. In [10], by exploiting the space-time smoothing techniques, one snapshot of the cell under test (CUT) generates multiple subsnapshots. And then, the angle-Doppler profile is estimated by using the least absolute shrinkage and selection operator (LASSO) solution.

However, there are two problems in view of the aforementioned facts. Firstly, the stationarity is hard to be guaranteed; for example, short-range clutter environment in non-side-looking airborne radar is seriously nonhomogeneous, which results in clutter distribution varying with range and training samples in different range cell unsatisfying IID. Conventional SR-STAP cannot be used. Secondly, the accuracy of clutter space-time spectrum estimation has a great impact on the clutter suppression performance, and the calculation error due to sparse recovery in noise background should be further reduced. To resolve the above issues, a novel STAP algorithm for airborne MIMO radar based on Temporally Correlated Multiple Sparse Bayesian Learning is proposed, which can effectively suppress clutter with only one snapshot. The proposed method maintains further accuracy and robustness to noise so that it can achieve better performance of output signal-to-clutter ratio (SCR) and minimum detectable velocity (MDV) than current single measurement vector sparse representation.

The rest of the paper is organized as follows. The principle of SR-STAP is briefly introduced and the signal model of the problem is formulated in Section 2. In Section 3, multiple snapshot generation is studied. Then, the novel STAP algorithm for airborne MIMO radar is proposed to mitigate the strong ground clutter based on Temporally Correlated Multiple Sparse Bayesian Learning (TMSBL). In Section 4, simulation results are provided to assess the effectiveness of the proposed method. Finally, conclusions are presented in Section 5.

#### 2. Principle of SR-STAP and Problem Formulation

In airborne radar systems, ignoring the range ambiguity, a general model of the space-time clutter plus noise can be expressed aswhere is the Gaussian white noise vector, is the number of independent clutter patches that are evenly distributed in azimuth, and , , and are the complex-valued scattering coefficient, spatial frequency, and Doppler frequency of the th clutter patch, respectively. is the space-time steering vector, and it is given byThe whole angle-Doppler plane is discretized into grids, where and ( and denote the resolution) are the number of angle and Doppler bins, respectively. Afterwards, the received signal in (1) can be rewritten aswhere is the redundant space-time completed dictionary and is the angle-Doppler profile with nonzero elements representing the clutter.

According to [14–16], solving (3) for its sparse solution can be transformed to optimization problem as follows:

As to (4), it has been proven to be an NP-hard problem. Fortunately, by optimization, we could find the solution of (4) with some characteristic of sparsity. There are a lot of algorithms to solve this type of problem [17–19], such as OMP algorithm [17], FOCUSS algorithm [18], and SBL algorithm [19].

Based on the above discussion, the clutter covariance matrix can be estimated bywhere is the noise power and denotes the identity matrix. As the estimated clutter space-time spectrum is not stable with only one snapshot, CCM estimation is inaccurate and the clutter suppression performance degrades significantly. To make sufficient use of the multiple snapshots and obtain a better clutter suppression performance, multisnapshots are employed in synergy, which is called sparse solution with multiple measurement vectors [20–22] (MMV). As stated in [11], selecting IID training range cells from both sides of the cell under test, (3) can be rewritten bywhere , , and . The estimated clutter space-time spectrum can be obtained as . The clutter covariance matrix can be estimated by (5).

Finally, the weight vector of STAP processor can be calculated by where is the space-time steering vector of target.

The calculation error may be serious in the procedure of sparse representation for STAP, because the single selected snapshot contains random noise and clutter. Utilizing multiple IID snapshots improves the robustness of the method. However, IID samples are difficult to acquire in seriously nonhomogeneous clutter environment.

#### 3. MIMOSR-STAP Method Based on TMSBL

MIMO radar has the superiority of waveform diversity and increases the dimension of receiving data. A novel STAP algorithm for airborne MIMO radar based on TMSBL is presented in this section. The single snapshot of range cell data in MIMO radar can be equivalent to multiple snapshots data in conventional phased array radar. The procedure of multiple snapshot generation is shown in Figure 1, and the method is described in detail as follows.