Abstract
Capon's Minimum Variance Distortionless Response beamformer requires the ensemble covariance matrix to compute the array weights [Capon, in Proc. IEEE (1969)]. In practice, adaptive beamformers compute their array weights from the estimated sample covariance matrix (SCM). In many scenarios, the environment changes too rapidly for the SCM to be full rank. The Dominant Mode Rejection (DMR) beamformer [Abraham and Owsley, IEEE Oceans (1990)] mitigates this problem by imposing a structure on the eigenvalues of the SCM. DMR assumes that the background noise is spatially white, and enforces this assumption by replacing the weak SCM eigenvaues by their average. However, DMR still must estimate the appropriate subspace dimension for the dominant signals to minimize the expected beamformer output power. Estimating the DMR output power as a function of subspace dimension from the SCM results in a substantial negative bias for the output power caused by overfitting. Random matrix theory results on eigenvector fidelity allow us to approximate this bias in the output power, and compensate for the overfitting. This compensation yields a more accurate estimate of the beamformer output power as a function of subspace dimension. [Work funded by ONR 321US.]