Gridless DOA Estimation via. Alternating Projections

Wagner, Mark; Gerstoft, Peter; Park, Yongsung

doi:10.1109/icassp.2019.8682920

Cited by 15 publications

(17 citation statements)

References 24 publications

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“…They brought enhanced sparsity and resolution compared to convex atomic norm-based methods. Alternatively, alternating projections-based gridless methods [9][27] directly solved the atomic l 0 norm minimization problem to pursue higher resolution. However, the convergence performance is not guaranteed due to unclosed or nonconvex sets [9].…”

Section: B Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Yan¹,

Zhao²,

Zhang³

et al. 2021

Preprint

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Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic l0 norm (i.e., the continuous analog of l0 norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic l0 norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error.To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic l0 norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic l0 norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic l0 norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.

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Section: B Related Workmentioning

confidence: 99%

“…However, gridding gives rise to the well-known basis mismatch issue that limits the estimation accuracy. To avoid gridding, the so-called gridless type [7][8] [9] have been proposed, which can directly operate in the continuous frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Yan¹,

Zhao²,

Zhang³

et al. 2021

Preprint

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“…Summarizing above, we list the steps of the DOA estimation algorithm via the BS-ANM approach in Table 2. To apply the ADMM approach to DOA estimation, we propose a subspace based method, inspired from [32]. Consider the covariance matrix in Equation (43)…”

Section: Doa Estimation With Covariance Matrixmentioning

confidence: 99%

Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array

2020

Sensors

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Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.

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“…Both ongrid and offgrid methods are grid-based methods. Another method to deal with the offgrid problem is the gridless method [16][17][18], which directly operates in the continuous domain so that can completely avoid the grid mismatch problem. However, this kind of method needs strong theoretical guarantees.…”

Section: Introductionmentioning

confidence: 99%

Complex Multisnapshot Sparse Bayesian Learning for Offgrid DOA Estimation

Liu

Ding

et al. 2022

International Journal of Antennas and Propagation

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Direction of arrival (DOA) estimation has recently been developed based on sparse signal reconstruction (SSR). Sparse Bayesian learning (SBL) is a typical method of SSR. In SBL, the two-layer hierarchical model in Gaussian scale mixtures (GSMs) has been used to model sparsity-inducing priors. However, this model is mainly applied to real-valued signal models. In order to apply SBL to complex-valued signal models, a general class of sparsity-inducing priors is proposed for complex-valued signal models by complex Gaussian scale mixtures (CGSMs), and the special cases correspond to complex versions of several classical priors are provided, which is helpful to analyze the connections with different modeling methods. In addition, the expression of the SBL form of the real- and complex-valued model is unified by parameter values, which makes it possible to generalize and improve the properties of the SBL methods. Finally, the SBL complex-valued form is applied to the offgrid DOA estimation complex-valued model, and the performance between different sparsity-inducing priors is compared. Theoretical analysis and simulation results show that the proposed algorithm can effectively process complex-valued signal models and has lower algorithm complexity.

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Gridless DOA Estimation via. Alternating Projections

Cited by 15 publications

References 24 publications

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array

Complex Multisnapshot Sparse Bayesian Learning for Offgrid DOA Estimation

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