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.INDEX TERMS Quiescent beam response, array phase center, space-time broadband beamformer, frequency-domain constraints.

The two-dimensional optimization capability of the space-time minimum variance distortionless response (STMVDR) can improve the spatial spectrum estimation performance of the broadband beamformer with limited samples, but its high sensitivity to frequency errors may lead to the suppression of some narrowband signals not at the grid point of the frequency response calculation. In order to reduce the sensitivity of STMVDR to frequency errors, a broadband spatial spectrum estimation method based on STMVDR and frequency derivative constraints is proposed in this paper. First, based on the beam response of the STMVDR beamformer, an arbitrary order frequency derivative constraint is derived. Second, combining the gain constraint and frequency derivative constraint, the linear constrained minimum variance problem is established to solve the optimal weight of the beamformer. Finally, the calculation method of the broadband spatial spectrum is derived. Numerical simulations show that the proposed method not only solves the problem of frequency mismatch caused by the insufficient number of points for calculating frequency response, but also does not cause the spatial response related peaks to deviate from the true direction due to the broadening of the main lobe of frequency response. In addition, the proposed method can reduce the computational complexity of the algorithm by more than half by increasing the interval of the frequency calculation grid points, and does not significantly loss in the angular resolution capability and estimation accuracy of the algorithm.