Nonuniform Linear Antenna Arrays Research Articles

Detection-estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays. III. Detection-estimation nonidentifiability

For pt.II see ibid., vol.51, no.6, p.1492-507 (2003). We investigate nonidentifiability conditions for the detection-estimation problem with multiple uncorrelated plane waves incident upon a nonuniform (sparse) linear antenna array. Specifically, we define conditions under which a given Hermitian covariance matrix has a nonunique (multiple) decomposition into an admissible number of dyads weighted by the source powers and a white-noise identity matrix. Our method is based on the Proukakis-Manikas technique of generating ambiguity generator sets (AGSs) and allows ambiguous sets of sources associated with a given sparse antenna geometry to be determined.

Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays

Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the "conventional" case (m<M), traditional detection techniques such as Akaike's information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the "superior" case (m/spl ges/M), these standard techniques are not applicable. We introduce a new approach to the detection problem for "fully augmentable" arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix T/sub /spl mu// with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources /spl mu/. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m/spl circ/ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance.

Design of Nonuniform Linear Antenna Array Geometry and Signal Processing Algorithm for DOA Estimation of Gaussian Sources

Abramovich, Yuri I., and Spencer, Nicholas K., Design of Nonuniform Linear Antenna Array Geometry and Signal Processing Algorithm for DOA Estimation of Gaussian Sources, Digital Signal Processing10 (2000), 340–354.This paper discusses the problem of direction-of-arrival (DOA) estimation for Gaussian sources that have arbitrary correlation: from independent to fully correlated. For independent sources, the antenna array design is governed by two competing considerations: maximum aperture, which inclines toward increasing sparsity for a given number of array sensors, and identifiability, which tends to exclude extreme sparsity. For fully correlated sources, these two competing criteria are augmented by a third which allows for the initialization of DOA estimation by the generalized spatial smoothing (GSS) technique. The maximum number of fully correlated sources is in turn an important factor in the GSS algorithm and subsequent array geometry design. We present a geometry optimization technique that permits accurate DOA estimation of arbitrarily correlated sources.

Resolving manifold ambiguities in direction-of-arrival estimation for nonuniform linear antenna arrays

This paper addresses the problem of ambiguities in direction of arrival (DOA) estimation for nonuniform (sparse) linear arrays. Usually, DOA estimation ambiguities are associated with linear dependence among the points on the antenna array manifold, that is, the steering vectors degenerate so that each may be expressed as a linear combination of the others. Most nonuniform array geometries, including the so-called minimum redundancy arrays, admit such manifold ambiguities. While the standard subspace algorithms such as MUSIC fail to provide unambiguous DOA estimates under these conditions, we demonstrate that this failure does not necessarily imply that consistent and asymptotically effective DOA estimates do not exist. We demonstrate that in most cases involving uncorrelated Gaussian sources, manifold ambiguity does not necessarily imply nonidentifiability; most importantly, we introduce algorithms designed to resolve manifold ambiguity. We also show that for situations where the number of sources exceeds the number of array sensors, a new class of locally nonidentifiable scenario exists.