A new array geometry, which is capable of significantly increasing the degrees freedom linear arrays, proposed. This structure obtained by systematically nesting two or more uniform arrays and can provide <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(N^{2})$</tex></formula> using only Notation="TeX">$N$</tex> </formula> physical sensors when second-order statistics received data used. The concept...

This paper considers the sampling of temporal or spatial wide sense stationary (WSS) signals using a co-prime pair sparse samplers. Several properties and applications samplers are developed. First, for uniform with M N sensors where appropriate interelement spacings, difference co-array has O(MN) freedoms which can be exploited in beamforming direction arrival estimation. An -point DFT filter bank an N-point used at outputs two sensor arrays their combined such way that there effectively MN...

A new approach to super resolution line spectrum estimation in both temporal and spatial domain using a coprime pair of samplers is proposed. Two uniform with sample spacings MT NT are used where M N T has the dimension space or time. By considering difference set this (which arise naturally computation second order moments), locations which O(MN) consecutive multiples can be generated only O(M + N) physical samples. In efficiently use these virtual samples for spectral estimation, novel...

Coprime sampling and coprime sensor arrays have been introduced recently for the one-dimensional (1-D) case, applications in beamforming direction finding discussed. A pair of can be used to sample a wide-sense stationary signal sparsely, then reconstruct autocorrelation at significantly denser set points. All based on (e.g., spectrum DOA estimation) benefit from this property. It was also shown past that coprimality exploited frequency domain by using DFT filter banks, produce effect much...

A new class of two dimensional arrays with sensors on lattice(s) is proposed, whose difference co-array can give rise to a virtual array much larger number elements "dense" lattice. This structure obtained by systematically nesting arrays, one sparse lattice and the other dense where lattices bear certain relation each other. The such an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> xmlns:xlink="http://www.w3.org/1999/xlink">N</i>...

Coprime arrays, consisting of two uniform linear arrays whose inter-element separations are coprime, can resolve O(MN) sources using only O(M + N) sensors. However, holes in the coarray prevent us from full MUSIC algorithm for DOA estimation. Through interpolation, it may be possible to use remaining elements increase degrees freedom beyond what is captured contiguous ULA section coarray. Techniques like positive definite Toeplitz completion, array and sparse recovery, manage include all...

Recently, direction-of-arrival estimation (DOA) algorithms based on arbitrary even-order (2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> ) cumulants of the received data have been proposed, giving rise to new DOA algorithms, namely 2 MUSIC algorithm. In particular, it has shown that algorithm can identify xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( xmlns:xlink="http://www.w3.org/1999/xlink">Nq</i> statistically independent...

This paper explores the practical application of a new class two dimensional arrays, namely, nested in array processing problems like direction arrival estimation. Nested arrays constitute with physical sensors on lattice(s), whose difference co-array gives rise to virtual <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( xmlns:xlink="http://www.w3.org/1999/xlink">MN</i> ) elements, although number used is...

A new framework for the problem of sparse support recovery is proposed, which exploits statistical information about unknown signal in form its correlation. key contribution this paper to show that if existing algorithms can recover size s, then using such correlation information, guaranteed recoverable be increased O(s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), although itself may not recoverable. This proved possible by (a)...

The problem of direction arrival (DOA) estimation narrowband sources using an antenna array is considered where the number can potentially exceed sensors. In earlier works, authors showed that a suitable geometry, such as nested and coprime arrays, it possible to localize O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) M To this end, two different approaches have been proposed. One based on extension subspace methods MUSIC these...

Although Cramér-Rao Bounds (CRB) for direction-of-arrival (DOA) estimation have been extensively studied decades, existing results are mainly applicable when there fewer sources than sensors. In contrast, this letter considers an underdetermined signal model (more sensors) and investigates conditions under which CRB exist. Necessary sufficient derived the associated Fisher information matrix to be nonsingular, in turn, leads closed-form expressions CRBs DOA estimation. These highlight...

Based on the high-order difference co-array concept, an enhanced four-level nested array (E-FL-NA) is first proposed, which optimizes consecutive lags at fourth-order stage. To simplify sensor location formulations for comprehensive illustration and also convenient structure construction, a simplified (SE-FL-NA) then whose performance compromised but still better than (FL-NA). This further extended to higher order case with multiple sub-arrays, referred as level arrays (SE-ML-NAs), where...

Sparse linear arrays such as co-prime and nested can resolve more sources than the number of sensors. In contrast, uniform (ULA) cannot This paper demonstrates this using Bayesian learning (SBL) co-array MUSIC for single frequency beamforming. For approximately same sensors, are shown to outperform ULA in root mean squared error. shows that multi-frequency SBL significantly reduce spatial aliasing. The effects different sparse sub-arrays on performance compared qualitatively Noise...

Coprime sampling has, in the past, been used for signal processing applications such as range and doppler improvement radar, identifying sinusoids noise. This paper considers a coprime pair of samplers space or time from point view difference coarray, which is key to increased freedom available with arrays. First, two uniform linear arrays N M elements are considered. With interelement spacings given by Mλ/2 Nλ/2 where integers, it shown that coarray has O(MN) freedoms, so number freedoms...

This paper considers the problem of compressively sampling wide sense stationary random vectors with a low rank Toeplitz covariance matrix. Certain families structured deterministic samplers are shown to efficiently compress high-dimensional matrix size N × N, producing compressed sketch O(√r) O(√r).The reconstruction can be cast as that line spectrum estimation, whereby, in absence noise, matrices any exactly recovered from compressive sketches O(√r), no matter how large is. In presence...

The Multiple Measurement Vector (MMV) problem is central to sparse signal processing, where the goal recover common support of a set unknown vectors size N, from L compressed measurement vectors, each M ≪ N. Recent advances in correlation-aware and Bayesian techniques for MMV models show promising evidence that under appropriate assumptions, it possible supports (s) larger than dimension (M) vector. However, these results are primarily asymptotic L, cannot provide recovery guarantees finite...

Sparse support recovery techniques guarantee successful of sparse solutions to linear underdetermined systems provided the measurement matrix satisfies certain conditions. The maximum level sparsity that can be recovered with existing algorithms is O(M) where M denotes size vector. This paper shows how this improved O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) by assuming prior knowledge about correlation structure measurements....

Nested and coprime arrays are sparse which can identify O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) sources using only m sensors. Systematic algorithms have recently been developed for such identification. These traditionally implemented by performing MUSIC or a similar algorithm in the difference-coarray domain. This paper considers use of nested case where number is less than m. It will be demonstrated that there some...

In this paper, the problem of identifying common sparsity support multiple measurement vectors (MMV) is considered. The model given by y[n] = Ax <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> [n], 1 ≤ n L where {y[n]} xmlns:xlink="http://www.w3.org/1999/xlink">n=1</sub> <sup xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> denote vectors, A ∈ R xmlns:xlink="http://www.w3.org/1999/xlink">M×N</sup> matrix and x [n]...

This paper considers the problem of co-array interpolation for direction-of-arrival (DOA) estimation with sparse nonuniform arrays. By utilizing much longer difference associated these arrays, it is possible to perform DOA more sources than sensors. Since may contain holes (or missing lags), algorithms have been proposed fully utilize remaining elements beyond that captured in contiguous ULA segment. However, quality and stability performed by such (especially presence modeling errors) not...

A finite duration sequence exhibiting periodicities does not in general admit a sparse representation terms of the DFT basis unless period is divisor duration. This paper develops dictionary called Farey for efficient such sequences. It shown herein that this especially useful identifying hidden data record. The properties are studied, and to be superior conventional based uniform dictionary, from view point periods.

Sparse arrays have emerged as a popular alternative to the conventional uniform linear array (ULA) due enhanced degrees of freedom (DOF) and superior resolution offered by them. In passive setting, these advantages are realized leveraging correlation between received signals at different sensors. This has led belief that sparse require large number temporal measurements reliably estimate parameters interest from correlations, therefore they may not be preferred in sample-starved regime. this...

The nested and coprime arrays have recently been introduced as systematic structures to construct difference coar-rays with O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) elements, where m is the number of array elements. They are therefore able identify sources (or DOAs) under assumption that uncorrelated. In view their larger aperture compared uniform linear (ULAs) same these some advantages over conventional ULAs even in cases...

This letter offers several new insights into the maximum-likelihood direction-of-arrival (DOA) estimation problem, when number of sources exceeds sensors. Two problems are studied: one for estimating Toeplitz-structured coarray covariance matrix from measurements, and other DOAs directly measurements. We establish equivalence both is assumed to be unknown can potentially exceed Additionally, it shown that source waveforms satisfy certain orthogonality conditions, Toeplitz-constrained...

This paper provides new probabilistic guarantees for recovering the common support of jointly sparse vectors in multiple measurement vector (MMV) models. In recent times, Bayesian approaches signal recovery (such as learning and correlation-aware LASSO) have shown preliminary evidence that under appropriate conditions access to ideal covariance matrix measurements or certain restrictive orthogonality condition on signals), it is possible recover supports size (K) larger than dimension (M)...