Gridless SR-STAP algorithm based on square-root lasso for airborne radar clutter suppression

The grid-based sparse recovery space-time adaptive processing(SR-STAP) algorithm requires the angular Doppler plane to be discretised in order to construct an overcomplete basis matrix. This process can result in off-grid problem and lead to a decline in performance. To address this issue, a gridless SR-STAP algorithm based on square-root Lasso(SRL) is proposed in this paper. Firstly, by introducing auxiliary variables, we obtain an iterative solution to the SRL using alternating optimization. Secondly, substituting the above iterative solution into the original problem transforms the SRL into a trace minimization problem for the clutter covariance matrix(CCM). The trace minimization problem is convex and can be solved globally in the continuous domain, thus avoiding the off-grid problem. Thirdly, to accommodate the noise unknown environment, a closed-form solution for the noise power is derived. Finally, in order to improve the computational efficiency, we solve iteratively for the required parameters in the framework of alternating direction method of multipliers(ADMM). Simulation results demonstrate that the proposed algorithm can overcome the off-grid problem, exhibits better clutter suppression performance and lower computational complexity than typical grid-based SR-STAP algorithm.