A new approach to array geometry for improved spatial spectrum estimation

Abstract

In this paper, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Carathedory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorreleated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of eiement positions, with dimension greater than the number of array eiements. The auBmented matrix ie then used in any of the known apectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the iarger dynamic range for spectral peak to background level, the lower eidelobes and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.A recurring question in array design for both signal reception mod spatial spectrum estimation is that of how to beneficially deploy the elements of a sparse array. Toward this purpose, we consider the problem of eetiaatinE the directions of arrival of E uncorreiated narrowband sources 5k(t) for k = 1, 2...K, which are spatially distributed in the directions 2' .O. Let d. represent the ith eieaent location with resect to a reference point for an M element linear array. Then the ith element output at time t can be written as [1) K -jk drosS 01 k x.(t)= kkl 5k(t)e +n.(t); il,2,...M (i) where k represents the wavenumber common to ali sources°and n.(t) stands for additive white noise of eprectral àeneiry N. In vector form (i) becomes * X(r)=A s(t)+n(r) (2) where K (r) + [x1(t), x0(t), . ..xM (t)JT s (t) = [sjt), s2(t), ...eK (r)]T and n (t) = [ni(t) n2(t), ...nN(t)I Here T stands for the transpose and * reprente the compiex conjugate. Also A = [1(01) , 1(02)

Gridless compressed sensing for fully augmentable arrays

“…Similar to the SPARROW formulation, our proposed algorithm does not require the sources to be uncorrelated. By simulations, we show that our proposed algorithm outperforms the algorithms in [9], [10] for correlated sources. The CRB is used to assess the performance of the DOA estimation algorithm.…”

“…e.g., direct augmentation [10] and subspace truncation [9] approaches, are proposed to achieve DOA estimation in such a case.…”

“…In the superior case, where the number of sources is larger than the number of sensors in the array, conventional DOA estimation algorithms fail to identify the sources. In [10], DOA estimation in the superior case has been achieved by constructing the augmented covariance matrix (ACM) and using it for the MUSIC algorithm instead of the direct data covariance matrix. In [9] and [11], DOA estimation algorithms for FAAs and PAAs are presented, respectively.…”

Comparison of sparse sensor array configurations with constrained aperture for passive sensing

“…5. Due to their co-array equivalence with the ULA, all of the considered sparse configurations can match this performance using co-array based array processing methods, such as covariance matrix augmentation [18] or intensity image addition [2]. The sparse arrays can likewise resolve up to N ULA − 1 = 29 incoherent sources using e.g.…”

Joint Phased-MIMO and Nested-Array Beamforming for Increased Degrees-of-Freedom

“…To compensate the sacrificed DOFs of phased-MIMO radar, it is necessary to increase the DOFs in the receiver. In earlier works, the problem of increasing the DOFs of linear arrays has been investigated in [13,14], but the augmented covariance matrix is not positive semidefinite anymore. The authors of [14] increase the DOFs with the minimum redundancy arrays [15] and constructing an augmented covariance matrix.…”