Data orthogonalization in sensor array signal processing

This primarily tutorial paper presents a perspective on the development of adaptive data orthogonalization (ADO) for spatial sensor array sampled data vectors. The development of ADO methods is traced from a generalization of the split array, crosscorrelation arrival angle tracker for a single source, plane wave arrival to multiple coherent arrivals. Development is followed through to the more recent maximization of the ratio of two quadratic forms that expresses beamformer array gain. Specifically, the reduced complexity implementation of a signal model error robust minimum variance distortionless response (MVDR) adaptive beamformer (ABF) is described. This robust beamformer is a simple, explicit linear blend (combination) of the inherently robust shaded time delay-and-sum conventional beamformer (CBF) and the enhanced minimum variance (EMV) dominant mode rejection (DMR) ABF. This ABF construction places an easily implemented upper bound on the signal suppression caused by signal model mismatch and allows a tradeoff between spatial resolution and main lobe signal maintenance (MLM). Several methods for robust DMR ABF are compared.