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.>

The relationship between Cadzow's signal subspace algorithm and the spatially smoothed minimum-norm algorithm of Tufts-Kumaresan is investigated. It is shown that Cadzow's algorithm can be realized by subarray averaging lower rank approximations to the array covariance matrix. A data-domain algorithm that is applicable in a correlated signal environment is formulated. This algorithm offers the advantage of lower word length requirements, and obviates the necessity of computing higher order statistics. It may also be extended in a straightforward way to incorporate signal enumeration. Simulation results are given that contrast the performance of this algorithm to the signal eigenvector approach.>

A method for determining the number of sources impinging on a uniform linear array, which is applicable even in the extreme case of fully correlated sources, is presented. This technique uses modified rank sequences, a modification of the construction implicit in the matrix decomposition methods of A. Di (1985). The authors prove that if a particular rank sequence stabilizes to a value strictly less than the common row size of the defining block matrices, then this value equals the number of sources provided that the number has not exceeded a Bressler-Macovski (1986) type bound. Using the above characterization of stability, they formulate an algorithm that either determines the number of sources or indicates that the resolution capability of the algorithm has been exceeded. Rank determinations are based on an additive perturbation model. A threshold that approximates the largest singular value of the error matrix is determined and used to separate the large and small singular values of the matrices that induce the rank sequence.>

A range and error analysis is developed for a discrete Fourier transform (fast Fourier transform) computed using the ring of cyclotomic integers. Included are derivations of both deterministic and statistical upper bounds for the range of the resulting processor and formulas for the ratio of the mean square error to mean square signal, in terms of the pertinent parameters. Comparisons of theoretical predictions with empirical results are also presented.

A new method is described for computing anN = R^{m} = 2^{\upsilon m}-point complex discrete Fourier transform that uses quantization within a dense ring of algebraic integers in conjunction with a residue number system over this ring. The algebraic and analytic foundations for the technique are derived and discussed. The architecture for a radix-Rfast Fourier transform algorithm using a residue number system overZ[\omega], where\omegais a primitiveRth root of unity, is developed; and range and error estimates for this algorithm are derived.