Nonunique sinusoidal Vandermonde bases

A simple constructive procedure is provided for producing unfavorable signal scenarios, that is, collections of fewer than M signals which cannot be resolved by any detection method. Given any pair of integers M and D, with D larger than M/2, and any set of D angles of arrival, it is shown how to produce two distinct signals scenarios for which the corresponding noise-free snapshot matrices are identical. The behavior of several contemporary detection algorithms is illustrated for scenarios whose signal covariance matrices lie in a neighborhood of an unfavorable signal covariance matrix. Detection performance degrades in rather large neighborhoods of these matrices, especially at low signal-to-noise ratios