Sparsity-Based DOA Estimation of Coherent and Uncorrelated Targets With Flexible MIMO Radar

This paper considers the direction of arrival (DOA) estimation of coherent and uncorrelated targets by exploiting a flexible multiple input multiple output radar. First, the proposed radar is generalized with two coprime expansion factors for enlarging the inter-element spacing of transmit and receive arrays, referred to as sparse arrays with flexible inter-element spacing (SA-FIS), which shows that the conventional nested or coprime ones are the special cases. The range of consecutive lags and the number of unique lags in the sum-difference coarray are derived in closed form. It is verified that SA-FIS can obtain the maximum unique lags and also suppress the mutual coupling effects. We then extend the FIS viewpoint to sparse nonuniform linear arrays, where the two-level nested and coprime arrays are employed to achieve a significant increase in degrees of freedom (DOFs). Furthermore, to fully utilize these unique lags, we propose a reduced-complexity two-step sparse representation algorithm. By modifying and removing the off-diagonal elements of the estimated target covariance matrix, the proposed method can just identify the diagonal ones, thereby leading to further improved performance with much lower computational complexity. Finally, the Cramér-Rao bound on DOAs and correlated coefficients for SA-FIS is derived. Numerical simulations demonstrate the superiority of the proposed method with SA-FIS in terms of DOFs, computations, estimation accuracy, and resolution capability compared with previous ones.