Array spatial thinning for interference mitigation by semidefinite programming

We study the problem of interference mitigation in a phased array, where a subset containing k out of a total of N receivers creates a virtual spatial null for an incoming interference. The signal-of-interest and interference are represented by their corresponding steering vectors, and an optimum subarray is chosen such that the two vectors are as orthogonal as possible. This optimization is a binary quadratic non-convex minimization. We propose a semidefinite programming method to find suboptimal solutions using an optimal randomized sampling strategy. We show that the proposed method provides solutions as good as an exhaustive search with a cubic computational complexity. Furthermore, the proposed algorithm outperforms existing methods by solving the problem in a higher dimensionality.