Applying the unit circle constraint to the diagonally loaded minimum variance distortionless response beamformer

Adaptive beamformers (ABF) are used when estimating the direction of arrival of a narrowband planewave with a uniform line array in an environment with loud, unwanted signals. Capon's minimum variance distortionless response (MVDR) suppresses interferers by steering beampattern nulls in their directions but maintains unity gain in the look direction. In practical situations, ABFs replace the ensemble covariance matrix (ECM) with a sample covariance matrix (SCM) estimated from array observations, or snapshots. If there are not enough snapshots available to average, the SCM is a poor estimate of the ECM, and may be rank deficient. Adding some diagonal loading (DL) to the SCM improves the beamformer's performance by increasing white noise gain, but may cost some in interferer suppression. Projecting the zeros of the beamformer's array polynomial onto the unit circle (UC) provides deeper nulls to suppress interferers but exhibits worse white noise behavior than DL. The UCDL beamformer adds DL to the SCM before applying UC constraint to calculate array weights that achieve better SINR than either the UC or DL beamformers alone. Even when the UCDL beamformer suffers mismatch on the DL level, the UCDL SINR rivals or betters the DL beamformer with the optimal DL level.