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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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