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

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

Advanced Techniques for High-Throughput Cellular Communications

The next generation wireless communication systems require ubiquitous high-throughput mobile connectivity under a range of challenging network settings (urban versus rural, high device density, mobility, etc). To improve the performance of the system, the physical layer design is of great importance. The previous research on improving the physical layer properties includes: a) highly directional transmissions that can enhance the throughput and spatial reuse; b) enhanced MIMO that can eliminate contention, enabling linear increase of capacity with number of antennas; c) mmWave technologies which operate on GHz bandwidth to over substantially higher throughput; d) better cooperative spectrum sharing with cognitive radios; e) better multiple access method which can mitigate multiuser interference and allow more multi-users. This dissertation addresses several techniques in the physical layer design of the next generation wireless communication systems. In chapter two, an orthogonal frequency division with code division multiple access (OFDM-CDMA) systems is proposed and a polyphase code is used to improve multiple access performance and make the OFDM signal satisfy the peak to average ratio (PAPR) constraint. Chapter three studies the I/Q imbalance for direct down converter. For wideband transmitter and receiver that use direct conversion for I/Q sampling, the I/Q imbalance becomes a critical issue. With higher I/Q imbalance, there will be higher degradation in quadrature amplitude modulation, which degrades the throughput tremendously. Chapter four investigate a problem of spectrum sharing for cognitive wideband communication. An energy-efficient sub-Nyquist sampling algorithm is developed for optimal sampling and spectrum sensing. In chapter ve, we study the channel estimation of millimeter wave full-dimensional MIMO communication. The problem is formulated as an atomic-norm minimization problem and algorithms are derived for the channel estimation in different situations. In this thesis, mathematical optimization is applied as the main approach to analyze and solve the problems in the physical layer of wireless communication so that the high-throughput is achieved. The algorithms are derived along with the theoretical analysis, which are validated with numerical results

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