Broadband Spatial Spectrum Estimation Based on Space-Time Minimum Variance Distortionless Response and Frequency Derivative Constraints

Abstract

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.