In this letter, we consider the problem of direction of arrival estimation using sparsity enforced reconstruction methods. Co-prime arrays with M + N sensors are utilized to increase the degrees of the freedom from O(M + N) to O(MN). The key to the success of sparse-based direction of arrival estimation is that every target must fall on the predefined grid. Off-grid targets can highly jeopardize the reconstruction performance. In this letter, we use joint sparsity reconstruction methods to explore the underlying structure between the sparse signal and the gird mismatch. Two types of sparse reconstruction methods, the greedy method and the convex relaxation method, are considered. By implementing numerical experiments, we demonstrate that our proposed methods can fully utilize the virtual aperture created by co-prime arrays and also outperform the previously proposed MUSIC method with spatial smoothing.

Sparse Direction of Arrival Estimation Using Co-Prime Arrays with Off-Grid Targets

Different from conventional phased-array radars, the frequency diverse array (FDA) radar offers a range-dependent beampattern capability that is attractive in various applications. The spatial and range resolutions of an FDA radar are fundamentally limited by the array geometry and the frequency offset. In this paper, we overcome this limitation by introducing a novel sparsity-based multitarget localization approach incorporating both coprime arrays and coprime frequency offsets. The covariance matrix of the received signals corresponding to all sensors and employed frequencies is formulated to generate a space-frequency virtual difference coarrays. By using $\mathcal {O}(M+N)$ antennas and $\mathcal {O}(M+N)$ frequencies, the proposed coprime arrays with coprime frequency offsets enables the localization of up to $\mathcal {O}(M^2N^2)$ targets with a resolution of $\mathcal {O}(1/(MN))$ in angle and range domains, where $M$ and $N$ are coprime integers. The joint direction-of-arrival (DOA) and range estimation is cast as a two-dimensional sparse reconstruction problem and is solved within the Bayesian compressive sensing framework. We also develop a fast algorithm with a lower computational complexity based on the multitask Bayesian compressive sensing approach. Simulations results demonstrate the superiority of the proposed approach in terms of DOA-range resolution, localization accuracy, and the number of resolvable targets.

Frequency Diverse Coprime Arrays With Coprime Frequency Offsets for Multitarget Localization

The inherent limitation of the predefined spatial discrete grids greatly restricts the precision and feasibility of many sparse signal representation (SSR)-based direction-of-arrival (DOA) estimators. In this paper, we first propose a perturbed SSR-based model to alleviate this limitation by incorporating a bias parameter into the DOA estimation framework. Using this model, a perturbed sparse Bayesian learning-based algorithm, named PSBL, is developed to solve the DOA estimation problem, followed by a theoretical analysis of PSBL. We then present two algorithms based on the covariance matrix of the array output, named perturbed covariance matrix (PCM) and improved PCM (IPCM), respectively, to improve the convergence speed of PSBL. Extensive experiments show that the PSBL enjoys a high estimation accuracy in the cases of limited snapshots, low signal-to-noise-ratio, correlated, and spatially adjacent signals. In particular, PCM not only keeps the merits of PSBL, but also exhibits superiority over PSBL in terms of computational efficiency. IPCM has a better computational efficiency, but with a small sacrifice of its performance in a correlated signal scenario.

Direction of Arrival Estimation for Off-Grid Signals Based on Sparse Bayesian Learning

In this work, the grid mismatch problem for a single snapshot direction of arrival estimation problem is studied. We derive a Bayesian Cramer-Rao bound for the grid mismatch problem with the errors in variables model and propose a block sparse estimator for grid matching and sparse recovery.

Block Sparse Estimator for Grid Matching in Single Snapshot DoA Estimation

Compressed sensing (CS) is a promising emerging domain that outperforms the classical limit of the Shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix. Unfortunately, in realistic scenario, the knowledge of this basis or equivalently of the entire dictionary is often uncertain, i.e., corrupted by a Basis Mismatch (BM) error. The consequence of the BM problem is that the estimation accuracy in terms of Bayesian Mean Square Error (BMSE) of popular sparse-based estimators collapses even if the support is perfectly estimated and in the high Signal to Noise Ratio (SNR) regime. This saturation effect considerably limits the effective viability of these estimation schemes. In the first part of this work, the Bayesian Cramer-Rao Bound (BCRB) is derived for CS model with unstructured BM. We show that the BCRB foresees the saturation effect of the estimation accuracy of standard sparse-based estimators as for instance the OMP, Cosamp or the BP. In addition, we provide an approximation of this BMSE threshold. In the second part and in the context of the structured BM model, a new estimation scheme called Bias-Correction Estimator (BiCE) is proposed and its statistical properties are studied. The BiCE acts as a post-processing estimation layer for any sparse-based estimator and mitigates considerably the BM degradation. Finally, the BiCE i) is a blind algorithm, i.e., is unaware of the uncorrupted dictionary matrix, ii) is generic since it can be associated to any sparse-based estimator, iii) is fast, i.e., the additional computational cost remains low, and iv) has good statistical properties. To illustrate our results and propositions, the BiCE is applied in the challenging context of the compressive sampling of non-bandlimited impulsive signals.

/pdf/compressed-sensing-with-basis-mismatch-performance-bounds-1n2ahbymzo.pdf

Compressed Sensing with Basis Mismatch: Performance Bounds and Sparse-Based Estimator

Sparse signal recovery is often performed over an estimation grid whose choice affects the recovery performance The grid mismatch effect is posed as a total least squares problem based on the errors in variables (EIV) model An existing approach to model the mismatch namely the interpolation approach is interpreted as an EIV model The grid mismatch is solved by an alternating descent algorithm, which alternates between basis-pursuit (BP) and least squares (LS) as well as its extension wherein BP is solved by a Bayesian algorithm These algorithms are compared with respect to the SNR and grid offset for the Nyquist and upsampled grids

http://ieeexplore.ieee.org/iel5/6423297/6450609/06450709.pdf

Grid matching for sparse signal recovery in compressive sensing

Detection, estimation and grid matching of multiple targets with single snapshot measurements

The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behavior. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models. The aim in this work is to generalize the finite sample distribution properties of LASSO estimator for a real and linear measurement model in Gaussian noise. 
In this work, we derive an expression for the finite sample characteristic function of the LASSO estimator, we then use the Fourier slice theorem to obtain an approximate expression for the marginal probability density functions of the one-dimensional components of a linear transformation of the LASSO estimator.

The LASSO Estimator: Distributional Properties

Full-duplex wireless nodes can transmit and receive at the same time and in the same frequency band, thus effectively doubling the data rate. In these systems, the transmit signal interferes with the receive signal, a phenomena termed as self-interference. Self-interference is a major impediment to realising a full-duplex wireless node. In the recent years, there has been significant research on self-interference mitigation. In this paper, we survey important techniques for self-interference cancellation from the past few years. In particular, we focus on the various RF and baseband self-interference cancellation techniques for realising an ideal full-duplex node.

Rakshith Jagannath

Papers

Block Sparse Estimator for Grid Matching in Single Snapshot DoA Estimation

Grid matching for sparse signal recovery in compressive sensing

Detection, estimation and grid matching of multiple targets with single snapshot measurements

The LASSO Estimator: Distributional Properties

Self-interference cancellation in full-duplex wireless devices: A survey