In this work we first analyze two methods of finding low rank solutions: Steering Independent Conjugate Gradient (SI-CG) and Steering Dependent Conjugate Gradient (SD-CG). These low-rank beamformers have a rank where the output SINR is maximized and a large drop in the output SINR can occur if the beamformer operates at an improper rank. Indirect Dominant Mode Rejection (IDMR) is proposed wherein one first employs a high-resolution spatial spectrum estimation technique to estimate the directions and powers of the dominant interferers. Subsequently, this information is used to construct an estimate of the signal-free (interference plus noise only) autocorrelation matrix (for a given look-direction.) In this process, any residual correlations between the interferers and the signal arriving from the look-direction due to finite sample averaging is effectively removed. Simulations reveal that IDMR yields a dramatic improvement in output SINR relative to CG and PCI/DMR, even when the latter operate at the optimal rank. In the case of correlated signals IDMR shows not to degrade the output SINR, different from CG and PCI/DMR.
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