Optimal Array Phase Center Study for Frequency-Domain Constrained Space-Time Broadband Beamforming

The frequency-domain constrained broadband space-time beamformer has been widely used in many fields because of its excellent performance and no need for pre-steering delay. However, the beam response of the frequency-domain constrained space-time broadband beamformer depends heavily on the phase center location of the array. The wrong phase center location of the array will lead to undesirable wide main lobe and high side lobe. To choose the location of the phase center of the array correctly, this paper makes an in-depth theoretical discussion on this dependency based on the uniform linear array. First, the dependence of the quiescent beam response of the frequency-domain constrained space-time broadband beamformer on the phase center location of the array is theoretically derived, and it is proved that there is an optimal phase center location of the array which can make the beamformer obtain the best quiescent beam response. Then, a selection criterion of the optimal array phase center location is proposed, and based on this criterion, the closed-form solution of the optimal array phase center location is theoretically derived when the constraint matrix contains two pre-selected points. Finally, based on the closed-form solution, through correct extrapolation, the suboptimal solution for the optimal array phase center location is obtained when the constraint matrix contains any preselected points. Numerical simulations verify the correctness and effectiveness of the proposed methods.