Low-complexity optimization for Two-Dimensional Direction-of-arrival Estimation via Decoupled Atomic Norm Minimization

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANM in terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy

Gridless Two-dimensional DOA Estimation With L-shaped Array Based on the Cross-covariance Matrix

The atomic norm minimization (ANM) has been successfully incorporated into the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for super-resolution. However, its computational workload might be unaffordable when the number of snapshots is large. In this paper, we propose two gridless methods for 2-D DOA estimation with L-shaped array based on the atomic norm to improve the computational efficiency. Firstly, by exploiting the cross-covariance matrix an ANM-based model has been proposed. We then prove that this model can be efficiently solved as a semi-definite programming (SDP). Secondly, a modified model has been presented to improve the estimation accuracy. It is shown that our proposed methods can be applied to both uniform and sparse L-shaped arrays and do not require any knowledge of the number of sources. Furthermore, since our methods greatly reduce the model size as compared to the conventional ANM method, and thus are much more efficient. Simulations results are provided to demonstrate the advantage of our methods

DNN-DANM: A High-Accuracy Two-Dimensional DOA Estimation Method Using Practical RIS

Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) has been an attractive technology for future wireless communication and sensing systems. However, in the practical RIS, the mutual coupling effect among RIS elements, the reflection phase shift, and amplitude errors will degrade the RIS performance significantly. This paper investigates the two-dimensional direction-of-arrival (DOA) estimation problem in the scenario using a practical RIS. After formulating the system model with the mutual coupling effect and the reflection phase/amplitude errors of the RIS, a novel DNNDANM method is proposed for the DOA estimation by combining the deep neural network (DNN) and the decoupling atomic norm minimization (DANM). The DNN step reconstructs the received signal from the one with RIS impairments, and the DANM step exploits the signal sparsity in the two-dimensional spatial domain. Additionally, a semi-definite programming (SDP) method with low computational complexity is proposed to solve the atomic minimization problem. Finally, both simulation and prototype are carried out to show estimation performance, and the proposed method outperforms the existing methods in the two-dimensional DOA estimation with low complexity in the scenario with practical RIS.Comment: 11 pages, 12 figure

Channel Estimation for RIS-Aided MIMO Systems: A Partially Decoupled Atomic Norm Minimization Approach

Channel estimation (CE) plays a key role in reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) communication systems, while it poses a challenging task due to the passive nature of RIS and the cascaded channel structures. In this paper, a partially decoupled atomic norm minimization (PDANM) framework is proposed for CE of RIS-aided MIMO systems, which exploits the three-dimensional angular sparsity of the channel. In particular, PDANM partially decouples the differential angles at the RIS from other angles at the base station and user equipment, reducing the computational complexity compared with existing methods. A reweighted PDANM (RPDANM) algorithm is proposed to further improve CE accuracy, which iteratively refines CE through a specifically designed reweighing strategy. Building upon RPDANM, we propose an iterative approach named RPDANM with adaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phases based on previously estimated channel parameters to facilitate CE, achieving superior CE accuracy while reducing training overhead. Numerical simulations demonstrate the superiority of our proposed approaches in terms of running time, CE accuracy, and training overhead. In particular, the RPDANM-APC approach can achieve higher CE accuracy than existing methods within less than 40 percent training overhead while reducing the running time by tens of times.Comment: 35 pages, 9 figures. Part of this paper has been submitted to the 2023 IEEE Global Communications Conference (GLOBECOM

A Coordinate Descent Approach to Atomic Norm Minimization

Atomic norm minimization is of great interest in various applications of sparse signal processing including super-resolution line-spectral estimation and signal denoising. In practice, atomic norm minimization (ANM) is formulated as a semi-definite programming (SDP) which is generally hard to solve. This work introduces a low-complexity, matrix-free method for solving ANM. The method uses the framework of coordinate descent and exploits the sparsity-induced nature of atomic-norm regularization. Specifically, an equivalent, non-convex formulation of ANM is first proposed. It is then proved that applying the coordinate descent framework on the non-convex formulation leads to convergence to the global optimal point. For the case of a single measurement vector of length N in discrete fourier transform (DFT) basis, the complexity of each iteration in the coordinate descent procedure is O(N log N ), rendering the proposed method efficient even for large-scale problems. The proposed coordinate descent framework can be readily modified to solve a variety of ANM problems, including multi-dimensional ANM with multiple measurement vectors. It is easy to implement and can essentially be applied to any atomic sets as long as a corresponding rank-1 problem can be solved. Through extensive numerical simulations, it is verified that for solving sparse problems the proposed method is much faster than the alternating direction method of multipliers (ADMM) or the customized interior point SDP solver