Data record size requirements of MVDR-optimized adaptive antenna arrays

We investigate the data-record-size requirements of the minimum-variance-distortionless-response beamformer to meet a given performance objective in signal detection and direction-of-arrival estimation problems. For signal detection problems we consider the output-energy performance measure while for direction-of-arrival estimation problems we adopt a spectrum-based measure defined as the ratio between the estimated and the ideal spectrum. In both cases, closed form expressions are derived that provide the data record size that is necessary to achieve a given performance confidence level in a neighborhood of the optimal performance point. This is done by utilizing close approximations of the involved probability density functions and Markoff-type inequalities. The practical significance of the derived expressions lies in the fact that the expressions are functions of the number of antenna elements only, while they are independent of the ideal input covariance matrix which is not known in most realistic applications