An Effective Array Beamforming Scheme Based on Branch-and-Bound Algorithm

In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time, the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition, the beamformer weight vector is penalized with the modified reweighted
$l_{1}$
-norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the state-of-the-art methods in the case of a single expected signal and multiple desired signals.