Efficient Adaptive Matrix Spatial Filter with Nulling

Beamspace adaptive matrix spatial filters have been extensively studied for their superior nulling performance and mathematical elegance. However, a major drawback of current spatial filters is the high computational cost—often reaching O(M4.5)—due to their formulation as second-order cone programming (SOCP) problems that rely on iterative interior-point methods. This paper proposes a robust and efficient matrix filtering framework with adaptive nulling capabilities to suppress interference. The proposed method is formulated as a convex optimization problem that admits a non-iterative, closed-form solution, thereby reducing the complexity to O(M3). Consequently, it can be efficiently implemented on resource-constrained embedded platforms. Furthermore, the algorithm incorporates an explicit passband flatness constraint, which significantly improves compatibility with downstream Direction-of-Arrival (DOA) estimation modules. To achieve even greater efficiency, we introduce a novel dual sequential rank-1 update strategy, further lowering the overall computational complexity to O(M2).