An analysis of the projection method for robust adaptive beamforming

Two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error. These causes were discussed by Feldman and Griffihs (see IEEE Trans. Signal Processing, vol.42, p.867, April, 1994), which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error. This paper contains an analysis 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 error or sample covariance error occurs. A less accurate analysis based on a zeroth-order Taylor series expansion includes results presented by Jablon (1986) and Chang and Yeh (see ibid., vol.40, no.11, p.1336, 1992) as special cases.