FDA-MIMO radar covariance matrix estimation via shrinkage processing

Abstract

Frequency diverse array multiple-input multiple-output (FDA-MIMO) produces an angle-range-dependent and time-varying transmit beampattern due to the small frequency increment across its array elements, which provides potential applications in new radar techniques. Due to this particularity, multiple signal classification (MUSIC) algorithm can be used to simultaneously estimate the angle and range of the target through a two-dimensional search. The MUSIC need to estimate the covariance matrix. In this paper, we introduce a shrinkage processing for estimating large covariance matrices when the number of samples is substantially fewer than the number of variables which is more common in FDA-MIMO than phase array (PA). Firstly, we propose a receiving model of multi-channel mixing multi-matched filter to eliminate time-varying effect. Secondly, the taper processing, Toeplitz rectification processing and shrinkage-to-identity processing are analyzed. Then, we propose two algorithms, namely, shrinkage-to-taper and shrinkage-to-Toeplitz-rectification on the basis of these algorithms. The proposed processing method improves upon both shrinkage and Toeplitz rectification or tapering processing by shrinking the sample covariance matrix (SCM) to its Toeplitz rectification or tapered version. Thirdly, a closed form expression of shrinkage coefficient for the shrinkage-to-Toeplitz-rectification, and shrinkage-to-taper are used. Finally, simulations results for FDA-MIMO radar show that the proposed algorithm is superior to the sample covariance matrix, shrinkage LW algorithm proposed by Ledoit-Wolf and shrinkage RBLW algorithm which is improved shrinkage LW according to the Rao-Blackwell theorem, in the sense of minimum mean-squared error (MMSE).