DOA and power estimation using a sparse representation of second-order statistics vector and ℓ0ℓ0-norm approximation

• We introduce a modified source parameter estimation algorithm using ℓ0ℓ0-norm approximation.
• We give theoretical evidence that the proposed algorithm is convergent and asymptotic unbiased.
• We present an appropriate strategy to select regularization and tuning parameters properly.
• The proposed algorithm has lower sensitivity to the number of snapshots.
• The proposed algorithm can provide higher estimation accuracy and better robustness to noise.

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 ℓ1ℓ1 function) to approximate ℓ0ℓ0-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.