基于lp 范数的离格稀疏空时自适应处理算法

稀疏恢复（Sparse Recovery， SR）空时自适应信号处理（Space Time Adaptive Processing， STAP）仅需要少量的杂波样本即可有效抑制杂波，但是稀疏恢复空时自适应信号处理依赖于空时字典，当载机运动方向与天线放置方向存在偏航角时，杂波脊偏离空时字典格点，出现离格问题，从而导致杂波抑制性能下降。已有的基于l1范数类的离格稀疏恢复算法在存在噪声时性能下降，没有充分利用杂波的稀疏性，文章提出一种基于lp(0<p<1)范数的离格空时自适应处理算法，首先将建立基于空时字典更新的稀疏恢复空时自适应模型，然后将该模型松弛为lp(0<p<1)范数的非凸优化问题，最后利用主函数最大化算法将该优化问题转化成凸优化问题，利用两层迭代求解的方法得到该问题的解，最后利用模型的解估计杂波协方差矩阵。通过仿真实验表明，提出的算法能够提高存在离格问题时的杂波恢复精度，抑制杂波的性能也优于已有的基于变分推断的算法。 

lp Norm Based Off-grid Sparse Space Time Adaptive Processing

Sparse recovery（SR） space time adaptive processing（STAP） could suppress clutter using a small number of clutter samples， but it highly relies on the space time dictionary. When there was a yaw angel between the direction of the aircraft crab and the antenna placement， the clutter would deviate from the dictionary grids， what we called off-grid. It would cause the degradation of clutter suppression. In this paper， as the reason of some sparse recovery off-grid algorithms don’t performance well when there exists noise and they don’t use the sparsity of clutter well. We proposed a l_p norm based STAP algorithm. Firstly， a dynamic dictionary SR STAP model is built. Then the model is relaxed to a l_p norm nonconvex problem. Finally， the problem is transformed to a weighted l₁ norm problem， and a two-step iterative method is proposed to find the solution. Numerical results show proposed algorithm can recover the clutter accurately， and has better performance in clutter suppression than the variational inference based algorithm.