International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 171808, 10 pages

http://dx.doi.org/10.1155/2015/171808

## Direct Data Domain Sparsity-Based STAP Utilizing Subaperture Smoothing Techniques

^{1}Research Institute of Space Electronics, Electronics Science and Engineering School, National University of Defense Technology, Changsha 410073, China^{2}Department of Electrical Engineering and Electronics, The University of Liverpool, Liverpool L69 3GJ, UK

Received 25 April 2014; Revised 6 October 2014; Accepted 16 October 2014

Academic Editor: Hang Hu

Copyright © 2015 Zhaocheng Yang 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

We propose a novel direct data domain (D3) sparsity-based space-time adaptive processing (STAP) algorithm utilizing subaperture smoothing techniques for airborne radar applications. Different from either normal sparsity-based STAP or D3 sparsity-based STAP, the proposed algorithm firstly uses only the snapshot in the cell under test (CUT) to generate multiple subsnapshots by exploiting the space-time structure of the steering vector and the uncorrelated nature of the components of the interference covariance matrix. Since the interference spectrum is sparse in the whole angle-Doppler plane, by employing a sparse regularization, the generated multiple subsnapshots are jointly used to recover the interference spectrum. The interference covariance matrix is then estimated from the interference spectrum, followed by the space-time filtering and the target detection. Simulation results illustrate that the proposed algorithm outperforms the generalized forward/backward method, the conventional D3 least squares STAP algorithm, and the existing D3 sparsity-based STAP algorithm. Furthermore, compared with the normal sparsity-based STAP algorithm using multiple snapshots, the proposed algorithm can also avoid the performance degradation caused by discrete interferers merely appearing in the CUT.

#### 1. Introduction

Space-time adaptive processing (STAP) is considered to be an effective tool for detection of weak targets by airborne radar systems in strong interference environments [1–4]. The problem is essentially that it usually assumes a homogeneous environment over the range cells. However, the assumptions are often not satisfied in realistic radar scenarios. Many factors, such as clutter edges, moving scatterers, shadowing and obstruction, and chaff, can render the clutter returns nonhomogeneous, resulting in performance degradation of conventional STAP algorithms [4].

Direct data domain least-squares (D3-LS) STAP approach is considered to be a powerful and effective method in nonhomogeneous environments [5–8]. It only uses the snapshot in the cell under test (CUT) rather than training data, which can avoid the nonhomogeneity in the training data and eliminate the impacts of nonhomogeneous environments. However, this configuration degrades the system performance since the system degrees of freedom (DOFs) are reduced. By combining the STAP algorithms using the training data and the D3-LS STAP algorithms, the hybrid detection approach is introduced with improved robustness to nonhomogeneous environments [9, 10]. Knowledge-aided (KA) STAP approaches using digital land classification data and digital elevation data were proposed to select training data to obtain improved STAP performance [11]. Another KA-STAP method, called model-based approach (see [12–19] and the references therein), basically employs some prior knowledge to form the simplified general clutter model (GCM) and then blends the GCM with the measured observations to design the STAP filter or directly uses it to design the STAP filter. This method can obtain good performance in a small-sample-support condition with accurate prior knowledge. However, the formed GCM usually does not contain the information of discrete interferers because the discrete interferers can appear at arbitrary positions in the angle-Doppler plane, which results in the increase of false alarms. Moreover, in practice, one cannot guarantee the accuracy of the prior knowledge, which is very important to the performance.

Recently, sparse recovery (SR) methods have been considered for STAP problems, such as sparsity-based STAP algorithms in [20–29] and L1-regularized STAP filters in [30, 31]. The sparsity-based STAP algorithms are highly related to the model-based approach but do not require the knowledge (such as the clutter ridge) to form the GCM and can be applied to arbitrary array geometries and random slow-time samples [21]. In fact, supposing that no prior knowledge of the interference is available, they discretize the whole angle-Doppler plane into many small grids, exploit the sparsity of the interference spectrum in all discretized angle-Doppler grids, and utilize the sparse recovery algorithms to recover the interference spectrum. Usually, there are two types of sparsity-based STAP in the literature: one type is the D3 STAP based on sparse recovery (D3-SR-STAP) algorithm which uses only the snapshot in the CUT [20–24]; the other is the normal STAP based on sparse recovery (NSR-STAP) that uses multiple snapshots adjacent to the CUT [24–29]. Both types exhibit significantly better performance than conventional STAP algorithms in limited training situations. However, for the D3-SR-STAP, the estimated interference covariance matrix is not stable since only one snapshot is employed; for the NSR-STAP, the presence of discrete interferers merely in the CUT will degrade the performance significantly.

In this paper, we propose a new D3-SR-STAP using the subaperture smoothing (SASM) techniques, which can overcome aforementioned drawbacks of both types of sparsity-based STAP. The proposed algorithm uses only snapshot in the CUT as conventional D3-SR-STAP does. Additionally, it uses the decimation techniques [32, 33] to generate multiple subsnapshots by exploiting the space-time structure of steering vector and the uncorrelated nature of the components of the interference covariance matrix. Then, the generated multiple subsnapshots are jointly used to recover the interference spectrum. Inspired by the SASM techniques used in the spectral estimation [34], the proposed algorithm can reduce the variance of the estimated interference spectrum resulting in improved signal-to-interference-plus-noise ratio (SINR). Moreover, thanks to the rapid convergence of sparsity-based STAP algorithms [25, 26, 28], the proposed algorithm does not reduce much the number of DOFs to increase the subsnapshots, which will benefit the recovery of the interference spectrum from single subsnapshot. It should be noted that another method, called the generalized forward/backward (F/B) method [35], also employs the SASM techniques and uses multiple training snapshots adjacent to the CUT to generate multiplicative improvement in the snapshots resulting in improved performance in sample limited cases. However, when the training snapshots have different statistics with that in the CUT, the performance of the generalized F/B method will degrade significantly. Simulation results illustrate the effectiveness of the proposed algorithm.

The rest of the paper is organized as follows. In Section 2, the STAP signal model and the principle of sparsity-based STAP algorithms are introduced. Section 3 details the proposed SASM D3-SR-STAP algorithm. Simulated data are used to evaluate the performance of the proposed algorithm in Section 4. Section 5 provides the summary and conclusions.

#### 2. Signal Model and Problem Formulation

In this section, we will introduce the signal model used in the paper and discuss the principle of the sparsity-based STAP algorithms.

##### 2.1. Signal Model

In airborne radar systems, ignoring the impact of range ambiguities, a general model for the space-time interference (clutter and discrete interferers) plus noise snapshot in a target-free range cell is given by [3] where is the Gaussian white noise vector with the noise power on each channel and pulse; and denote the numbers of independent clutter patches and independent discrete interferers over the iso-range of interest; , , and are the random complex amplitude, the angle-of-arrival (AOA), and the Doppler frequency of the th clutter patch, respectively; , , and are the random complex amplitude, the AOA, and the Doppler frequency of the th discrete interferer, respectively; is the space-time steering vector with the AOA and the Doppler frequency and is defined by (for a uniform linear array (ULA)) where is the number of pulses in a coherent process interval (CPI), is the number of array elements, and corresponds to the spatial frequency related to the AOA . Let the inner spacing of array elements be ; then the relationship between the spatial frequency and the AOA is , where is the operating wavelength.

##### 2.2. Principle of Sparsity-Based STAP Algorithms

Recently developed sparsity-based STAP algorithms provide an effective approach to estimate interference (clutter, discrete interferers) covariance matrix. It first discretizes the whole angle-Doppler plane into , () grids, where and are the number of angle and Doppler bins, respectively. Then the received data in (1) can be rewritten as [22–29] where denotes the angle-Doppler profile with nonzero elements representing the interference, and the matrix is the overcompleted space-time steering dictionary including all the possible space-time steering vectors, as given by Here, the symbols , and , denote the uniformly quantized Doppler frequencies and the AOAs. Herein, the interference plus noise covariance matrix can be expressed as where and is the interference spectral distribution vector under the assumptions of statistical independence between the clutter patches, the discrete interferers, and the noise [3, 4]. Here, stands for a diagonal matrix with the main diagonal taken from the elements of the vector , and denotes the Hadamard product.

To estimate , the sparsity-based STAP algorithms try to calculate the parameter using the computed angle-Doppler profile from the CUT or angle-Doppler profiles from adjacent target-free range cells, which can be obtained via the sparse recovery algorithms by exploiting the intrinsic sparsity of the interference spectral distribution, for example, the sparse interference spectrum computed by using the Mountain Top dataset [36], as shown in Figure 1. The whole angle-Doppler plane shows a high degree of sparsity and only a small number of angle-Doppler grids of the interference spectrum are occupied. Mathematically, the angle-Doppler profile can be estimated by solving the following minimal optimization problem known as the least absolute shrinkage and selection operator (LASSO) [23–26] or the basis pursuit denoising (BPDN) [20, 22, 24, 26, 27, 29], given as where () denotes the -norm, is the noise error allowance, and is a positive regularization parameter that provides a tradeoff between the approximation error and the sparsity.