This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.@en

This paper develops an efficient solution for super-resolution two-dimensional (2D) harmonic retrieval from multiple measurement vectors (MMV). Given the sample covariance matrix constructed from the MMV, a gridless compressed sensing approach is proposed based on the atomic norm minimization (ANM). In the approach, our key step is to perform a redundancy reduction (RR) transformation that effectively reduces the large problem size at hand, without loss of useful frequency information. For uncorrelated sources, the transformed 2D covariance matrices in the RR domain retain a salient structure, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. Accordingly, the decoupled ANM (D-ANM) framework can be applied for super-resolution 2D frequency estimation. Moreover, the resulting RR-enabled D-ANM technique, termed RR-D-ANM, further allows an efficient relaxation under certain conditions, which leads to low computational complexity of the same order as the 1D case. Simulation results verify the advantages of our solutions over benchmark methods, in terms of higher computational efficiency and detectability for 2D harmonic retrieval.

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This paper proposes an efficient direction of departure (DOD) and direction of arrival (DOA) estimation method for multi-input multi-output (MIMO) systems. For uncorrelated scenarios, the redundancy of the covariance matrix is first exploited by establishing its concise representation through redundancy reduction, which transforms the original large-size covariance matrix into a smaller-size matrix without loss of useful angle information. Then, the resulting transformed matrix, which retains a salient structure, permits efficient two-dimensional (2D) angle estimators working on a reduced-size problem for DOD and DOA estimation. Compared with conventional subspace-based methods, the proposed method incorporating an appropriate 2D angle estimator is more computationally efficient and can achieve higher estimation accuracy for small numbers of snapshots and low signal-to-noise ratios, which are verified by simulation results.

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In this paper, we study the problem of wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs), where a number of uncorrelated wideband signals impinge on an SLA and the data is collected from multiple frequency bins. To boost the performance and perform underdetermined DoA estimation, the difference co-array response matrices for all frequency bins are constructed first. Then, to merge the data from different frequency bins, we resort to the Jacobi-Anger approximation to transform the co-array response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. The major advantage of this approach is that the transformation matrices are all signal independent. For the special case where all sources share an identical distribution of the power spectrum, we develop two super-resolution off-the-grid DoA estimation approaches based on atomic norm minimization (ANM), one with and one without prior knowledge of the power spectrum. Our solution is able to resolve more sources than the number of antennas but also more than the number of degrees of freedom (DoF) of the difference co-array of the SLA. For the general case where each source has an arbitrary power spectrum, we propose a multi-task ANM method to exploit the joint sparsity from all frequency bins. Simulation results show that our proposed methods present a clear performance advantage over existing methods, and achieve an estimation accuracy close to the associated Cramér-Rao bounds (CRBs).@en

This paper aims at developing low-complexity solutions for super-resolution two-dimensional (2D) harmonic retrieval via covariance reconstruction. Given the collected sample covariance, a novel gridless compressed sensing approach is designed based on the atomic norm minimization (ANM) technique. The key is to perform a redundancy reduction (RR) transformation that effectively reduces the large problem size at hand, without loss of useful frequency information. For uncorrelated sources, the transformed 2D covariance matrices in the RR domain retain a salient structure, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. Accordingly, the decoupled ANM (DANM) framework can be applied for super-resolution 2D frequency estimation, at low computational complexity on the same order of the 1D case. An analysis of the complexity reduction of the proposed RR-D-ANM compared with benchmark methods is provided as well, which is verified by our simulation results @en

This paper develops an enhanced low-rank structured covariance reconstruction (LRSCR) method based on the decoupled atomic norm minimization (D-ANM), for super-resolution two-dimensional (2D) harmonic retrieval with multiple measurement vectors. This LRSCR-D-ANM approach exploits a potential structure hidden in the covariance by transferring the basic LRSCR to an efficient D-ANM formulation, which permits a sparse representation over a matrix-form atom set with decoupled 1D frequency components. The new LRSCR-D-ANM method builds upon the existence of a generalized Vandermonde decomposition of its solution, which otherwise cannot be guaranteed by the basic LRSCR unless a very conservative condition holds. Further, a low-complexity solution of the LRSCR-D-ANM is provided for fast implementation with negligible performance loss. Simulation results verify the advantages of the proposed LRSCR-D-ANM over the basic LRSCR, in terms of the wider applicability and the lower complexity.@en

This paper concerns wideband direction of arrival (DoA) estimation with sparse linear arrays (SLAs). We rely on the assumption that the power spectrum of the wideband sources is the same up to a scaling factor, which could in theory allow us to resolve not only more sources than the number of antennas but also more sources than the number of degrees of freedom (DoF) of the difference co-array of the SLA. We resort to the Jacobi-Anger approximation to transform the coarray response matrices of all frequency bins into a single virtual uniform linear array (ULA) response matrix. Based on the obtained model, two super-resolution DoA estimation approaches based on atomic norm minimization (ANM) are proposed, one with and one without prior knowledge of the power spectrum. Simulation results show that our proposed methods outperform the state of the art and are indeed capable of resolving more sources than the number of DoF of the difference co-array.@en

This paper develops efficient channel estimation techniques for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under practical hardware limitations, including an arbitrary array geometry and a hybrid hardware structure. Taking on an angle-based approach, this work adopts a generalized array manifold separation approach via Jacobi-Anger approximation, which transforms a non-ideal, non-uniform array manifold into a virtual array domain with a desired uniform geometric structure to facilitate super-resolution angle estimation and channel acquisition. Accordingly, structure-based optimization techniques are developed to effectively estimate both the channel covariance and the instantaneous channel state information (CSI) within a short sensing time. The different time-varying scales of channel path angles versus path gains are capitalized to design a two-step CSI estimation scheme that can quickly sense fading channels. Theoretical results are provided on the fundamental limits of the proposed technique in terms of sample efficiency. For computational efficiency, a fast iterative algorithm is developed via the alternating direction method of multipliers. Other related issues such as spurious-peak cancellation in non-uniform linear arrays and extensions to higher-dimensional cases are also discussed. Simulations testify the effectiveness of the proposed approaches in hybrid mmWave massive MIMO systems with arbitrary arrays.

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Compressed sensing deals with the reconstruction of signals from sub-Nyquist samples by exploiting the sparsity of their projections onto known subspaces. In contrast, this article is concerned with the reconstruction of second-order statistics, such as covariance and power spectrum, even in the absence of sparsity priors. The framework described here leverages the statistical structure of random processes to enable signal compression and offers an alternative perspective at sparsity-agnostic inference. Capitalizing on parsimonious representations, we illustrate how compression and reconstruction tasks can be addressed in popular applications such as power-spectrum estimation, incoherent imaging, direction-of-arrival estimation, frequency estimation, and wideband spectrum sensing.@en