On unique localization of constrained-signals sources

Conditions for unique localization of radiating sources by passive sensor arrays are presented. Unlike in previous analyses, the case wherein the signals are constrained to certain loci in the complex plane is addressed. Two types of constraints are considered. The first includes the case of constant-amplitude signals and the second includes the case of complex-exponential signals. The conditions specify the maximum number of sources that can be uniquely localized by a general array satisfying some mild geometrical constraints in terms of the number of sensors and the rank of the correlation matrix of the sources. This number exceeds substantially the corresponding number for the unconstrained-signals case