DOA and power estimation using a sparse representation of second-order statistics vector and [formula omitted]-norm approximation

Abstract

This paper focuses on the problem of joint direction-of-arrival (DOA) and power estimation based on sparse signal reconstruction. In this scheme, we utilize the second-order statistics (SOS) domain data of array output to construct a kind of special column vector, which also contains sufficient information on DOA and power parameters. Our aim is to transform the multiple measurement vectors (MMV) or “group sparsity” problem to the virtual single measurement vector (VSMV) problem in sparse signal representation framework. Concerning accuracy and complexity of estimation, we exploit a surrogate-TLP (truncated ℓ1 function) to approximate ℓ0-norm, and successively demonstrate how the nonconvex minimization problem can be treated by the DC (Difference of Convex functions) decomposition and the iterative approach. Theoretically, we prove that the proposed reconstruction algorithm can provide a stable and satisfactory performance, provided that the tuning parameter is selected properly and the noise is bounded. In addition, we also introduce an appropriate parameter selection strategy to make the algorithm robust. Numerical simulations show that the proposed algorithm not only has high resolution and good robustness to noise, but also provides an almost unbiased power estimation.