Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces

Compressive Sensing for Multi-channel and Large-scale MIMO Networks

Compressive sensing (CS) is a revolutionary theory that has important applications in many engineering areas. Using CS, sparse or compressible signals can be recovered from incoherent measurements with far fewer samples than the conventional Nyquist rate. In wireless communication problems where the sparsity structure of the signals and the channels can be explored and utilized, CS helps to significantly reduce the number of transmissions required to have an efficient and reliable data communication. The objective of this thesis is to study new methods of CS, both from theoretical and application perspectives, in various complex, multi-channel and large-scale wireless networks. Specifically, we explore new sparse signal and channel structures, and develop low-complexity CS-based algorithms to transmit and recover data over these networks more efficiently. Starting from the theory of sparse vector approximation based on CS, a compressive multiple-channel estimation (CMCE) method is developed to estimate multiple sparse channels simultaneously. CMCE provides a reduction in the required overhead for the estimation of multiple channels, and can be applied to estimate the composite channels of two-way relay channels (TWRCs) with sparse intersymbol interference (ISI). To improve end-to-end error performance of the networks, various iterative estimation and decoding schemes based on CS for ISI-TWRC are proposed, for both modes of cooperative relaying: Amplify-and-Forward (AF) and Decode-and-Forward (DF). Theoretical results including the Restricted Isometry Property (RIP) and low-coherent condition of the discrete pilot signaling matrix, the performance guarantees, and the convergence of the schemes are presented in this thesis. Numerical results suggest that the error performances of the system is significantly improved by the proposed CS-based methods, thanks to the awareness of the sparsity feature of the channels. Low-rank matrix approximation, an extension of CS-based sparse vector recovery theory, is then studied in this research to address the channel estimation problem of large-scale (or massive) multiuser (MU) multiple-input multiple-output (MIMO) systems. A low-rank channel matrix estimation method based on nuclear-norm regularization is formulated and solved via a dual quadratic semi-definite programming (SDP) problem. An explicit choice of the regularization parameter and useful upper bounds of the error are presented to show the efficacy of the CS method in this case. After that, both the uplink channel estimation and a downlink data recoding of massive MIMO in the interference-limited multicell scenarios are considered, where a CS-based rank-q channel approximation and multicell precoding method are proposed. The results in this work suggest that the proposed method can mitigate the effects of the pilot contamination and intercell interference, hence improves the achievable rates of the users in multicell massive MIMO systems. Finally, various low-complexity greedy techniques are then presented to confirm the efficacy and feasibility of the proposed approaches in practical applications

Channel Estimation in Massive Multi-User MIMO Systems Based on Low-Rank Matrix Approximation

In recent years, massive Multi-User Multi-Input Multi-Output (MU-MIMO) system has attracted significant research interests in mobile communication systems. It has been considered as one of the promising technologies for 5G mobile wireless networks. In massive MU-MIMO system, the base station (BS) is equipped with a very large number of antenna elements and simultaneously serves a large number of single-antenna users. Compared to traditional MIMO system with fewer antennas, massive MU-MIMO system can offer many advantages such as significant improvements in both spectral and power efficiencies. However, the channel estimation in massive MU-MIMO system is particularly challenging due to large number of channel matrix entries to be estimated within a limited coherence time interval. This problem occurs in a single-cell case where both dimensions of the channel matrix grow large. Also, It happens in the multi-cell setting due to the pilot contamination effect. In this thesis, the problem of channel estimation in both single-cell and multi-cell time division duplex (TDD) massive MU-MIMO systems is studied. Thus, two-channel estimation namely “nuclear norm (NN)” and “iterative weighted nuclear norm (IWNN)” approximation techniques are proposed to solve the channel estimation problem in both systems. First, channel estimation in a single-cell TDD massive MU-MIMO system is formulated as a convex nuclear norm optimization problem with regularization parameter γ. In this study, the regularization parameter γ is selected based on the cross-validation (CV) curve method. The simulation results in terms of the normalized mean square error (NMSE) and uplink achievable sum-rate (ASR) are provided to show the effectiveness of the NN proposed scheme compared to the conventional least square (LS) estimator. Then, the IWNN approximation is proposed to improve the performance of the NN method. Thus, the channel estimation in a single-cell TDD massive MU-MIMO system is formulated as a weighted nuclear norm optimization problem. The simulation results show the effectiveness of the IWNN estimation approach compared to the standard NN and conventional LS estimation methods in terms of the NMSE and ASR. Second, both previous estimation techniques are extended to apply in a multi-cell TDD massive MU-MIMO system to mitigate pilot contamination effect. The simulation results in terms of the NMSE and uplink ASR show that the IWNN scheme outperforms the NN and LS estimations in the presence of high pilot contamination effect. Finally, a novel channel estimation scheme namely “Approximate minimum mean square error (AMMSE)” is proposed to reduce the computational complexity of the minimum mean square error (MMSE) estimator which was proposed for multi-cell TDD massive MU-MIMO system. Furthermore, a brief analysis of the computational complexity regarding the number of multiplications of the proposed AMMSE estimator is provided. It has been shown that the complexity of the proposed AMMSE estimator is reduced compared to the conventional MMSE estimator. The simulation results in terms of the NMSE and the uplink ASR performances show the proposed AMMSE estimation performance is almost the same as the conventional MMSE estimator under two different scenarios: noise-limited and pilot contamination

Compressive Sensing for Multi-channel and Large-scale MIMO Networks

Compressive sensing (CS) is a revolutionary theory that has important applications in many engineering areas. Using CS, sparse or compressible signals can be recovered from incoherent measurements with far fewer samples than the conventional Nyquist rate. In wireless communication problems where the sparsity structure of the signals and the channels can be explored and utilized, CS helps to significantly reduce the number of transmissions required to have an efficient and reliable data communication. The objective of this thesis is to study new methods of CS, both from theoretical and application perspectives, in various complex, multi-channel and large-scale wireless networks. Specifically, we explore new sparse signal and channel structures, and develop low-complexity CS-based algorithms to transmit and recover data over these networks more efficiently. Starting from the theory of sparse vector approximation based on CS, a compressive multiple-channel estimation (CMCE) method is developed to estimate multiple sparse channels simultaneously. CMCE provides a reduction in the required overhead for the estimation of multiple channels, and can be applied to estimate the composite channels of two-way relay channels (TWRCs) with sparse intersymbol interference (ISI). To improve end-to-end error performance of the networks, various iterative estimation and decoding schemes based on CS for ISI-TWRC are proposed, for both modes of cooperative relaying: Amplify-and-Forward (AF) and Decode-and-Forward (DF). Theoretical results including the Restricted Isometry Property (RIP) and low-coherent condition of the discrete pilot signaling matrix, the performance guarantees, and the convergence of the schemes are presented in this thesis. Numerical results suggest that the error performances of the system is significantly improved by the proposed CS-based methods, thanks to the awareness of the sparsity feature of the channels. Low-rank matrix approximation, an extension of CS-based sparse vector recovery theory, is then studied in this research to address the channel estimation problem of large-scale (or massive) multiuser (MU) multiple-input multiple-output (MIMO) systems. A low-rank channel matrix estimation method based on nuclear-norm regularization is formulated and solved via a dual quadratic semi-definite programming (SDP) problem. An explicit choice of the regularization parameter and useful upper bounds of the error are presented to show the efficacy of the CS method in this case. After that, both the uplink channel estimation and a downlink data precoding of massive MIMO in the interference-limited multicell scenarios are considered, where a CS-based rank-q channel approximation and multicell precoding method are proposed. The results in this work suggest that the proposed method can mitigate the effects of the pilot contamination and intercell interference, hence improves the achievable rates of the users in multicell massive MIMO systems. Finally, various low-complexity greedy techniques are then presented to confirm the efficacy and feasibility of the proposed approaches in practical applications

Atomic Norm decomposition for sparse model reconstruction applied to positioning and wireless communications

This thesis explores the recovery of sparse signals, arising in the wireless communication and radar system fields, via atomic norm decomposition. Particularly, we focus on compressed sensing gridless methodologies, which avoid the always existing error due to the discretization of a continuous space in on-grid methods. We define the sparse signal by means of a linear combination of so called atoms defined in a continuous parametrical atom set with infinite cardinality. Those atoms are fully characterized by a multi-dimensional parameter containing very relevant information about the application scenario itself. Also, the number of composite atoms is much lower than the dimension of the problem, which yields sparsity. We address a gridless optimization solution enforcing sparsity via atomic norm minimization to extract the parameters that characterize the atom from an observed measurement of the model, which enables model recovery. We also study a machine learning approach to estimate the number of composite atoms that construct the model, given that in certain scenarios this number is unknown. The applications studied in the thesis lay on the field of wireless communications, particularly on MIMO mmWave channels, which due to their natural properties can be modeled as sparse. We apply the proposed methods to positioning in automotive pulse radar working in the mmWave range, where we extract relevant information such as angle of arrival (AoA), distance and velocity from the received echoes of objects or targets. Next we study the design of a hybrid precoder for mmWave channels which allows the reduction of hardware cost in the system by minimizing as much as possible the number of required RF chains. Last, we explore full channel estimation by finding the angular parameters that model the channel. For all the applications we provide a numerical analysis where we compare our proposed method with state-of-the-art techniques, showing that our proposal outperforms the alternative methods.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Juan José Murillo Fuentes.- Secretario: Pablo Martínez Olmos.- Vocal: David Luengo Garcí

Low-Rank Channel Estimation for Millimeter Wave and Terahertz Hybrid MIMO Systems

Massive multiple-input multiple-output (MIMO) is one of the fundamental technologies for 5G and beyond. The increased number of antenna elements at both the transmitter and the receiver translates into a large-dimension channel matrix. In addition, the power requirements for the massive MIMO systems are high, especially when fully digital transceivers are deployed. To address this challenge, hybrid analog-digital transceivers are considered a viable alternative. However, for hybrid systems, the number of observations during each channel use is reduced. The high dimensions of the channel matrix and the reduced number of observations make the channel estimation task challenging. Thus, channel estimation may require increased training overhead and higher computational complexity. The need for high data rates is increasing rapidly, forcing a shift of wireless communication towards higher frequency bands such as millimeter Wave (mmWave) and terahertz (THz). The wireless channel at these bands is comprised of only a few dominant paths. This makes the channel sparse in the angular domain and the resulting channel matrix has a low rank. This thesis aims to provide channel estimation solutions benefiting from the low rankness and sparse nature of the channel. The motivation behind this thesis is to offer a desirable trade-off between training overhead and computational complexity while providing a desirable estimate of the channel

Atomic norm-based DOA estimation with sum and difference co-arrays in coexistence of circular and non-circular signals

Sparse arrays can increase the array aperture and degrees of freedom through the construction of either sum or difference co-arrays or both. In order to exploit the advantages of sparse arrays while estimating directions of arrival (DOAs) of a mixture of circular and non-circular signals, in this paper, a gridless DOA estimation method is proposed by employing a recently introduced enhanced nested array, whose virtual arrays have no holes. The virtual signals derived from both sum and difference co-arrays are constructed based on atomic norm minimization. It is shown that the proposed method also works when the circular and non-circular signals come from the same set of directions. Simulation results are provided to demonstrate the performance of the proposed method