Spatial Compressive Sensing for MIMO Radar

TL;DR

This paper introduces a spatial compressive sensing framework for MIMO radar that reduces the number of elements needed for target localization while maintaining high resolution, outperforming classical methods in numerical tests.

Contribution

It develops a novel sparse localization method using random array placements and structured random matrices, providing theoretical guarantees for target recovery with fewer elements.

Findings

Achieves target localization with fewer MIMO elements than traditional arrays.

Provides theoretical bounds on measurement matrix coherence and recovery guarantees.

Demonstrates superior performance of compressive sensing algorithms over classical methods in simulations.

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, MN (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 MN 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.