Adaptive nulling for multiple desired signals based on signal waveform estimation

The authors consider adaptive nulling of noise and interference in the presence of multiple desired signals. They reformulate the adaptive nulling problem as a signal estimation problem and derive several adaptive nulling algorithms which require varying amounts of prior information about the desired signals. The information required by the algorithms may include signal directions of arrival, relative power levels, and/or probability density functions for signal directions of arrival when they are not known exactly. It is shown that the optimal signal estimators derived are equivalent to the classical adaptive nulling techniques of Howells-Applebaum, least-mean-square, and Frost when supplied with certain prior information, and that in several cases, the resulting expressions for the optimal weights have forms to which well-known adaptation procedures can be readily applied