Spatial Compressive Sensing for MIMO Radar

Abstract

Abstract-We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, we develop a bound on the coherence of the resulting measurement matrix, and obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, we show that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, M N (which is also the number of degrees of freedom), scales with K (log G) 2 , where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product M N scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. In the numerical results we show that, in the proposed framework, compressive sensing recovery algorithms are capable of better performance than classical methods, such as beamforming and MUSIC.

Target parameter estimation for spatial and temporal formulations in MIMO radars using compressive sensing

“…It is shown in [12] that for Toeplitz matrix exhibiting structure and μ( ) 0.9, Bayesian reconstruction is more efficient than convex optimization methods. Furthermore, the matrix A R has Vandermonde structure and its usage for sparse recovery with a similar matrix to A R is also discussed in [17]. Ref [29] analyzed Fourier-based structured matrices for compressed sensing.…”

“…In [16], the minimization problem is solved based on the covariance matrix estimation approach which requires a large number of snapshots. The work in [17] does not provide a fast parameter estimation algorithm and assumes that the number of targets, sparsity rate, and noise variance are known. The authors in [18] have used CVX (a package to solve convex problems) to solve the minimization problem obtained by CS formulation of MIMO radar.…”

Compressive sensing and sparse antenna arrays for indoor 3-D microwave imaging

“…Research into using sparse linear arrays and CS to capture 2-D images for radar applications [6] [7] has assumed that the scene is mostly empty except for one or two aircraft or other objects, which occupy only a few pixels in the image. Prior attempts to use CS with sparse planar antenna arrays for 3-D imaging [8] again assumed that the scene being imaged is sparse in the spatial domain.…”

Cognitive sub-Nyquist hardware prototype of a collocated MIMO radar

“…In other words, the conventional processing resolution is limited by the number of elements and the receiver sampling rate. Several methods have been proposed to address the problem of preserving the MIMO radar resolution when either the number of antennas [3] or the number of received samples [4][5][6] is reduced. Most exploit the fact that the target scene is sparse facilitating the use of compressed sensing (CS) methods [7,8].…”

“…The Xamples are expressed as a matrix of unknown target parameters and the reconstruction algorithm is derived by extending the orthogonal matching pursuit (OMP) [8] to simultaneously solve a system of CS matrix equations. In sub-Nyquist MIMO, the radar antenna elements are randomly placed within the aperture (see [11] for introduction and [3] for recent updates on random arrays), and signal orthogonality is achieved by frequency division multiplexing (FDM). In a conventional MIMO radar, the use of non-overlapping FDM waveforms results in a strong range-azimuth coupling [12][13][14] in the receiver processing, and therefore, it is common to use orthogonal code signals (i.e.…”