Statistics of adaptive nulling and modeling inhomogeneities in adaptive processing

This paper exarmines the integrity of the generalized eigenrelation (GER) as an approach to modeling inhomogeneities in adaptive processing. In the process, some fundamental properties of adaptive nulling are established, and novel statistics are derived for the sample covariance-based (SCB) minimum variance distortionless response (MVDR) beamformer. In particular, it is shown that the mean and variance of the adaptive beam response of an SCB MVDR beamformer evaluated in the direction of a jammer on which it has trained are inversely proportional to the power of the jammer, whereas one not trained on this jammer has mean and variance independent of the jammer's power. A novel generalized exact expression for the variance of the SCR MVDR beamformer output is derived under nonhomogeneous conditions, which shows that as the power of the jammer increases, the output variance of the SCR MVDR beamformer trained on this jammer is upper bounded due to appropriate null formation, whereas for one not trained on the jammer, the output variance grows linearly with the jammer's power. A formal treatment of some stochastic convergence properties that are pivotal to adaptive nulling for this well-known beamformer is provided. @ 199g IEEE.