Robust Sidelobe Control for Adaptive Beamformers Against Array Imperfections via Subspace Approximation-Based Optimization

Conventional adaptive beamformers usually suffer from serious performance degradation when the receive array is imperfect and unknown sporadic interferences appear. To enhance robustness against array imperfections and simultaneously suppress sporadic interferences, this paper studies robust adaptive beamforming (RAB) with accurate sidelobe level (SLL) control, where the imperfect array steering vector (SV) is expressed as a spherical uncertainty set. Under the maximum signal-to-interference-plus-noise ratio (SINR) criterion and robust SLL constraints, we formulate the resultant RAB into a second-order cone programming problem, which is computationally prohibitive due to numerous robust quadratic SLL constraints. To tackle this issue, we provide a subspace approximation-based method to approximate the whole sidelobe space, thus replacing all robust SLL constraints with a single subspace constraint. Moreover, we leverage the Gauss–Legendre quadrature-based scheme to generate the sidelobe space in a computationally efficient manner. Additionally, we give an explicit approach for determining the norm upper bound of SV uncertainty sets under various imperfection scenarios, addressing the challenge of obtaining this upper bound in practice.Simulation results showed that the proposed subspace approximation-based RAB beamformer had a better SINR performance than typical counterparts and was much more computationally efficient.