A novel sparse recovery space-time adaptive processing algorithm using the log-sum penalty to approximate the ℓ0 − norm penalty

Applying the sparse recovery (SR) technique to airborne radar space-time adaptive processing (STAP) can greatly reduce the number of required training samples, which is advantageous in detecting targets in non-homogeneous and non-stationary clutter environments. However, the poor performance, the slow convergence speed or the high computational complexity of the traditional SR STAP algorithms limit their practical application. To tackle this problem, a novel efficient SR STAP algorithm is proposed. The newly proposed SR STAP algorithm utilises the log-sum penalty to approximate the ${\ell }_0-\text{norm}$ penalty, which exhibits improved convergence performance and clutter suppression performance compared to the traditional SR STAP algorithms. Besides, the proposed algorithm can ensure the convergence in each iteration by offering a closed-form analytic solution. Furthermore, the result of the mathematical derivation demonstrates the essential equivalence between our method and the iterative reweighted ${\ell }_2$ method. By utilising this equivalence, two additional methods are proposed that incorporate the knowledge of the clutter Capon spectrum and the clutter spectrum of the iterative adaptive approach (IAA) as the components of weighted values, resulting in further performance improvement of the proposed algorithm. Finally, simulation results with both simulated data and Mountain-Top data demonstrate the high effectiveness and performance of the proposed methods.