Sensitivity analysis of MVDR and MPDR beamformers

A sensitivity analysis of two distortionless beamformers is presented in this paper1. Specifically, two well-known variants, namely the minimum power distortionless response (MPDR) and minimum variance distortionless response (MVDR) beamformers, are considered. In our scenario, which is typical to many modern communications systems, waves emitted by multiple point sources are received by an antenna array. An analytical expression for the signal to interference and noise ratio (SINR) improvement obtained by both beamformers under steering errors is derived. These expression are experimentally evaluated and compared with the robust Capon beamformer (RCB), a robust variant of the MPDR beamformer. We show that the MVDR beamformer, which uses the noise correlation matrix in its minimization criterion, is more robust to steering errors than its counterparts, that use the received signal correlation matrix. Furthermore, even if the noise correlation matrix is erroneously estimated due to steering errors in the interference direction, the MVDR advantage is still maintained for reasonable range of steering errors. These conclusions conform with Cox [1] findings. Only line of sight propagation regime is considered in the current contribution. Ongoing research extends this work to fading channels.