Performance Analysis of Dominant Mode Rejection Beamforming

Dominant Mode Rejection (DMR) adaptive beamforming replaces the covariance matrix for the Minimum Variance Distortionless Response (MVDR) beamformer with a modified sample covariance matrix (SCM). DMR modifies the SCM by first segmenting the eigenvalues into the signal (large eigenvalues) and noise (small eigenvalues) subspaces. The modified SCM uses the large signal eigenvalues but replaces the small noise eigenvalues with the average of these noise eigenvalues. The performance of the DMR beamformer in practical scenarios depends on the quality of the estimates of the rank of the signal subspace, as well as the quality of the estimated signal eigenvalues and associated eigenvectors. Therefore, an important challenge in practical applications of DMR is correctly estimating the rank of the signal subspace. Nadakuditi and Edelman recently developed an extension of the Akaike Information Criteria (AIC) for estimating the number of high dimensional signals from a relatively small number of observations exploiting results from infinite random matrix theory. The accuracy of the new Nadakuditi & Edelman AIC (N/E AIC) in estimating the dominant subspace rank was compared with the traditional AIC and Minimum Description Length (MDL) techniques. These simulations examined uniform linear arrays with one signal and varying numbers of array elements, snapshots and signal-to-noise ratios (SNRs). The N/E AIC performed better than the traditional AIC and MDL approaches in achieving a higher probability of correct rank estimation at a lower SNR in each case evaluated. Additionally, the N/E AIC performs well even in snapshot deficient cases where there are fewer snapshots than sensors. Both the standard AIC and MDL fail in snapshot deficient cases. The N/E AIC performance was also evaluated in simulations including a loud interfering source (+40 dB) and a relatively quiet source (-10 dB below the noise floor) observed by a uniform linear array with half-wavelength sampling over a range of array apertures and numbers of snapshots. The observed Signal to Interferer and Noise Ratio (SINR) for the standard DMR with N/E AIC suffered from a substantial degradation due to mismatch as the number of array elements grew. When the DMR algorithm was modified to incorporate the Cox/Pitre robust DMR method as well as the N/E AIC, the SINR closely tracked the performance of the omniscient beamformer with prior knowledge of the signal subspace rank.