Cross‐spectral matrix estimation effects on adaptive beamforming

Adaptive beamforming algorithms that use cross‐spectral matrix (CSM) data to calculate optimum weights are sensitive to the number of unsmoothed CSM samples used in the CSM estimate. Assuming that the samples used in the CSM estimate are independent identically Gaussian distributed with zero mean, it is shown that the output power of a minimum variance distortionless response (MVDR) beamformer using the estimated CSM is biased low relative to the output power of a MVDR beamformer using the true CSM. Using data from a horizontal line array deployed in a shallow water, high noise environment, the MVDR beamformer output power has been measured with various numbers of samples used in the CSM estimate. The number of CSM samples was varied by changing the time‐bandwidth product. The measured median beam noise levels are compared with the theory. Conclusions are drawn about the number of samples that should be used to obtain a reliable CSM estimate, and about how stationary the data are within the time‐bandwidth integration used in the CSM estimates.