A performance analysis of robust constrained beamforming with random errors

Two causes of performance degradation in linearly constrained minimum variance beamforming are perturbation error and sample covariance estimation error. These causes were discussed by the authors (1991), who proposed an approach, termed the projection method, to reduce the sensitivity of the beamformer performance to both types of error. An analysis is given of the expected performance of the beamformer when it is implemented either with or without using the projection method. Based on a second order Taylor series expansion of an approximate expression for the signal to interference-plus-noise ratio (SINR) at the beamformer output, the analysis provides accurate results when either perturbation errors or sample covariance errors occur. A less accurate analysis based on a zeroth order Taylor series expansion is found to include results presented by N.K. Jablon (1986) and L. Chang and C. Yeh (1993) as special cases.<>