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International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 903902, 12 pages

http://dx.doi.org/10.1155/2015/903902

## Multitarget Direct Localization Using Block Sparse Bayesian Learning in Distributed MIMO Radar

School of Electronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China

Received 16 April 2014; Revised 14 August 2014; Accepted 22 August 2014

Academic Editor: Michelangelo Villano

Copyright © 2015 Bin Sun 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

The target localization in distributed multiple-input multiple-output (MIMO) radar is a problem of great interest. This problem becomes more complicated for the case of multitarget where the measurement should be associated with the correct target. Sparse representation has been demonstrated to be a powerful framework for direct position determination (DPD) algorithms which avoid the association process. In this paper, we explore a novel sparsity-based DPD method to locate multiple targets using distributed MIMO radar. Since the sparse representation coefficients exhibit block sparsity, we use a block sparse Bayesian learning (BSBL) method to estimate the locations of multitarget, which has many advantages over existing block sparse model based algorithms. Experimental results illustrate that DPD using BSBL can achieve better localization accuracy and higher robustness against block coherence and compressed sensing (CS) than popular algorithms in most cases especially for dense targets case.

#### 1. Introduction

Multiple-input multiple-output (MIMO) radar study has received considerable attention over the past few years [1–7]. MIMO radar is typically used in two antenna configurations, namely, colocated [1, 2] and distributed [3, 4]. Colocated MIMO radar with closely spaced antennas exploits the waveform diversity and increased degrees of freedom (DOF) to obtain better angular resolution due to the virtual aperture [1]. The proximity of the antenna arrays allows considering the same target response for each transmitter-receiver pair [8]. Unlike colocated MIMO radar, distributed MIMO radar exploits angular diversity by capturing information from different aspect angles of target with widely spaced antennas [3] and supports accurate target location and velocity estimation [9]. In distributed MIMO radar, targets display different radar cross-sections (RCS) in different transmit-receive channels, and thus better detection performance is ensured by averaging the target scintillations from different angles [3]. In this paper, we are concerned with solving multiple stationary targets localization problem using distributed MIMO radar.

Location estimation technique is one important problem for MIMO radar systems due to its great potential to enable different kinds of localization applications. The traditional approach to solve the localization problem consists of a two-step procedure. The signal parameters such as direction of arrival (DOA), time of arrival (TOA), and time difference of arrival (TDOA) are estimated firstly at several receivers independently and then the coordinates of targets are calculated by exploiting the explicit geometric relationship. The authors in [10, 11] studied target localization with MIMO radar systems by utilizing bistatic TOA for multilateration and the Cramêr-Rao bound (CRB) for the target localization accuracy was derived. It has been shown that localization by coherent MIMO radar provides significantly better performance than noncoherent processing where the phase information is ignored. Coherent processing, however, entails the challenge of ensuring multisite systems phase synchronization [12] and the impact of static phase errors at the transmitters and receivers over the CRB has been well analyzed [13, 14]. Literature [15] has demonstrated that even the noncoherent MIMO radar provides significant performance improvement over a monostatic phased array radar with high range and azimuth resolutions. Although most publications on localization algorithms concentrate on the two-step method, it is suboptimal in general [16]. The problem becomes more complicated and challenging for multiple dense targets scenario using the method given in [11], where parameters as TOAs should be assigned to the correct targets, which is called “Data Association” [17] and it is an important problem especially for multiple target applications. A multiple-hypothesis- (MH-) based algorithm for multitarget localization was proposed to estimate the number and states of targets [18].

On the contrary, the direct position determination (DPD) method suggested by Weiss in [16] and Bar-Shalom and Weiss in [19] does not need intermediate parameters as DOAs or TOAs. The position estimates of interest are obtained directly by minimizing a cost function using the grid-search method, which can improve the estimation accuracy with respect to the two-step method. A maximum likelihood (ML) based DPD method dealing with one moving target is developed [20]. Moreover, the DPD method can provide superior localization capability in the context of multitarget scenarios since the data association step is avoided. Despite these advantages, the DPD method did not receive enough attention due to its intensive computation load. Recently, sparsity-based representation DPD framework is exploited for target/source localization problem. In fact, since the number of unknown targets is small in the radar scene, it can be modeled as an ideal sparse vector in the localization problem. Therefore, sparse modeling for distributed MIMO radar is firstly presented in [21] and the location estimates can be obtained by searching for the block sparse solution of underdetermined model using block matching pursuit (BMP) method. In [22], the multisource localization problem using TDOA measurements is formulated to be a sparse recovery problem and the problem of the data association and multisource localization is solved in a joint fashion. The method of block sparse Bayesian learning (BSBL) method in [23] motivates us to consider its application to multitarget localization problem in distributed MIMO radar. By exploiting the intrablock correlation, BSBL can achieve a superior performance over other algorithms for off-grid DOA estimation [24]. Simulation results showed that the BSBL method significantly outperforms competitive algorithms in different experiments.

In this paper, motivated by [21], we propose to apply the BSBL algorithm [23] for solving multitarget direct localization problem by employing block sparse modeling and we demonstrate the superiority of BSBL for multitarget localization problem through sufficient numerical experiments from many aspects. Specifically, we demonstrate the robustness of BSBL against compressed sampling and capability of dealing with dense targets localization. The effect of parameter estimation based on the off-grid model is also shown.

The remainder of the paper is organized as follows. We introduce the signal model for a distributed MIMO radar and formulate the block sparse representation of signal in Section 2. In Section 3, we review existing sparse recovery algorithms for this problem. Then, the sparsity-aware multitarget localization using BSBL is presented in Section 4. The comparison of performance based on Monte Carlo simulations is shown in Section 5. Finally, concluding remarks and future work are addressed in Section 6.

Notations used in this paper are as follows. Boldface letters are reserved for vectors and matrices. and denote the norm and norm, respectively. , are the determinant and trace of a matrix **,** respectively. denotes a block matrix with principal diagonal blocks being the in turn. means each elements in the vector is nonnegative. denotes vector of all ones and denotes identity matrix.

#### 2. Signal Model

Consider a distributed MIMO radar network consisting of transmitters, located at , receivers, located at , and targets, located at in a two-dimensional (2D) plane. Without loss of generality, we can extend the analysis in this paper to the three-dimensional (3D) case. A set of orthogonal narrowband waveforms are transmitted from different transmitters where denotes the fast time. Suppose that the th transmitter generates a linearly frequency-modulated (LFM) signal where denotes the window function, , is the chirp rate, represents the bandwidth, denotes the pulse duration, and is the carrier frequency of the th transmitter. Further, we assume that the cross correlations between these waveforms are close to zeros for different delays; namely, where denotes the conjugate operator. Let denote the complex RCS value corresponding to the th target between the th transmitter and the th receiver and each target is modeled as a collection of various reflection coefficients. In this work, we are interested in Rician target model [25], which describes one dominant scatterer together with a number of small scatterers, and target returns are assumed to be deterministic and unknown.

For coherent processing, we obtain the bandpass signal arriving at the th receiver taking account of the phase errors as where is the time delay corresponding to the th target in the th transmit-receive pair and is the speed of the propagation of the wave in the medium. and in (4) denote the phase error induced by the th transmitter or th receiver, respectively. The noise is assumed to be complex Gaussian with power spectral density (PSD) and is assumed to be independent for different .

The received signals at each receiver can be decomposed by a bank of matched filters. Then we take samples within a range bin centered at in the th transmit-receive pair as where and denote the sample index and sampling interval, respectively, , is selected as the center of targets, is the sampling start time of corresponding range gate, and is the noise component at the output of the matched filter. Note that unknown phase errors are absorbed in the unknown reflection coefficient as . Plus, the waveform term is no longer present in this equation as it is integrated out of the matched filter being a sinc function. This model is more practical than that in [21] by taking account of the effect of sampling deviation from the location of peaks.

We discretize the planar area into a grid of uniform cells where each of the targets is located at one of the cells. If there are targets in the area and is given a fine grid of cells such that the cell’s occupancy is exclusive, the distribution of the targets in the plane is sparse; that is, out of cells only contain the targets. This implies the spatial sparsity model as depicted in Figure 1. Denoting the signal attributed to the target located at cell at sample index as and concatenating the signals corresponding to each cells, the signal vector coming from all the 2D plane can be formed as , where and stands for the transpose operator. Further, is defined as