Alternative proofs for “On unique localization of constrained-signal sources”

We provide simple proofs for the theorems in “On Unique Localization of Constrained-Signal Sources” by M. Wax (see ibid. vol.40, p.1542-1547, June 1992). The approach is based on the topological dimension of a set. All the possible observation matrices form the legitimate set. The observation matrices that can have nonunique solutions form the ambiguity set. The components of the legitimate and ambiguity set are random matrices. We find the conditions under which the dimensionality of the ambiguity set is smaller than the dimensionality of the legitimate set. In such a case, the probability of the ambiguity set is zero and with probability one, a unique solution can be found for the localization problem