Gradient Pursuit-Based Channel Estimation for MmWave Massive MIMO Systems with One-Bit ADCs

In this paper, channel estimation for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) is considered. In the mmWave band, the number of propagation paths is small, which results in sparse virtual channels. To estimate sparse virtual channels based on the maximum a posteriori (MAP) criterion, sparsity-constrained optimization comes into play. In general, optimizing objective functions with sparsity constraints is NP-hard because of their combinatorial complexity. Furthermore, the coarse quantization of one-bit ADCs makes channel estimation a challenging task. In the field of compressed sensing (CS), the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms were proposed to approximately solve sparsity-constrained optimization problems iteratively by pursuing the gradient of the objective function via hard thresholding. The accuracy guarantee of these algorithms, however, breaks down when the objective function is ill-conditioned, which frequently occurs in the mmWave band. To prevent the breakdown of gradient pursuit-based algorithms, the band maximum selecting (BMS) technique, which is a hard thresholder selecting only the "band maxima," is applied to GraSP and GraHTP to propose the BMSGraSP and BMSGraHTP algorithms in this paper.Comment: to appear in PIMRC 2019, Istanbul, Turke

Channel Estimation via Gradient Pursuit for MmWave Massive MIMO Systems with One-Bit ADCs

In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, one-bit analog-to-digital converters (ADCs) are employed to reduce the impractically high power consumption, which is incurred by the wide bandwidth and large arrays. In practice, the mmWave band consists of a small number of paths, thereby rendering sparse virtual channels. Then, the resulting maximum a posteriori (MAP) channel estimation problem is a sparsity-constrained optimization problem, which is NP-hard to solve. In this paper, iterative approximate MAP channel estimators for mmWave massive MIMO systems with one-bit ADCs are proposed, which are based on the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms. The GraSP and GraHTP algorithms iteratively pursue the gradient of the objective function to approximately optimize convex objective functions with sparsity constraints, which are the generalizations of the compressive sampling matching pursuit (CoSaMP) and hard thresholding pursuit (HTP) algorithms, respectively, in compressive sensing (CS). However, the performance of the GraSP and GraHTP algorithms is not guaranteed when the objective function is ill-conditioned, which may be incurred by the highly coherent sensing matrix. In this paper, the band maximum selecting (BMS) hard thresholding technique is proposed to modify the GraSP and GraHTP algorithms, namely the BMSGraSP and BMSGraHTP algorithms, respectively. The BMSGraSP and BMSGraHTP algorithms pursue the gradient of the objective function based on the band maximum criterion instead of the naive hard thresholding. In addition, a fast Fourier transform-based (FFT-based) fast implementation is developed to reduce the complexity. The BMSGraSP and BMSGraHTP algorithms are shown to be both accurate and efficient, whose performance is verified through extensive simulations.Comment: to appear in EURASIP Journal on Wireless Communications and Networkin

FCFGS-CV-Based Channel Estimation for Wideband MmWave Massive MIMO Systems with Low-Resolution ADCs

In this paper, the fully corrective forward greedy selection-cross validation-based (FCFGS-CV-based) channel estimator is proposed for wideband millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs). The sparse nature of the mmWave virtual channel in the angular and delay domains is exploited to convert the maximum a posteriori (MAP) channel estimation problem to an optimization problem with a concave objective function and sparsity constraint. The FCFGS algorithm, which is the generalized orthogonal matching pursuit (OMP) algorithm, is used to solve the sparsity-constrained optimization problem. Furthermore, the CV technique is adopted to determine the proper termination condition by detecting overfitting when the sparsity level is unknown.Comment: to appear in IEEE Wireless Communications Letter

SVM-Based Channel Estimation and Data Detection for One-Bit Massive MIMO systems

The use of low-resolution Analog-to-Digital Converters (ADCs) is a practical solution for reducing cost and power consumption for massive Multiple-Input-Multiple-Output (MIMO) systems. However, the severe nonlinearity of low-resolution ADCs causes significant distortions in the received signals and makes the channel estimation and data detection tasks much more challenging. In this paper, we show how Support Vector Machine (SVM), a well-known supervised-learning technique in machine learning, can be exploited to provide efficient and robust channel estimation and data detection in massive MIMO systems with one-bit ADCs. First, the problem of channel estimation for uncorrelated channels is formulated as a conventional SVM problem. The objective function of this SVM problem is then modified for estimating spatially correlated channels. Next, a two-stage detection algorithm is proposed where SVM is further exploited in the first stage. The performance of the proposed data detection method is very close to that of Maximum-Likelihood (ML) data detection when the channel is perfectly known. We also propose an SVM-based joint Channel Estimation and Data Detection (CE-DD) method, which makes use of both the to-be-decoded data vectors and the pilot data vectors to improve the estimation and detection performance. Finally, an extension of the proposed methods to OFDM systems with frequency-selective fading channels is presented. Simulation results show that the proposed methods are efficient and robust, and also outperform existing ones

A survey on hybrid beamforming techniques in 5G : architecture and system model perspectives

The increasing wireless data traffic demands have driven the need to explore suitable spectrum regions for meeting the projected requirements. In the light of this, millimeter wave (mmWave) communication has received considerable attention from the research community. Typically, in fifth generation (5G) wireless networks, mmWave massive multiple-input multiple-output (MIMO) communications is realized by the hybrid transceivers which combine high dimensional analog phase shifters and power amplifiers with lower-dimensional digital signal processing units. This hybrid beamforming design reduces the cost and power consumption which is aligned with an energy-efficient design vision of 5G. In this paper, we track the progress in hybrid beamforming for massive MIMO communications in the context of system models of the hybrid transceivers' structures, the digital and analog beamforming matrices with the possible antenna configuration scenarios and the hybrid beamforming in heterogeneous wireless networks. We extend the scope of the discussion by including resource management issues in hybrid beamforming. We explore the suitability of hybrid beamforming methods, both, existing and proposed till first quarter of 2017, and identify the exciting future challenges in this domain

Energy efficient and low complexity techniques for the next generation millimeter wave hybrid MIMO systems

The fifth generation (and beyond) wireless communication systems require increased capacity, high data rates, improved coverage and reduced energy consumption. This can be potentially provided by unused available spectrum such as the Millimeter Wave (MmWave) frequency spectrum above 30 GHz. The high bandwidths for mmWave communication compared to sub-6 GHz microwave frequency bands must be traded off against increased path loss, which can be compensated using large-scale antenna arrays such as the Multiple-Input Multiple- Output (MIMO) systems. The analog/digital Hybrid Beamforming (HBF) architectures for mmWave MIMO systems reduce the hardware complexity and power consumption using fewer Radio Frequency (RF) chains and support multi-stream communication with high Spectral Efficiency (SE). Such systems can also be optimized to achieve high Energy Efficiency (EE) gains with low complexity but this has not been widely studied in the literature. This PhD project focussed on designing energy efficient and low complexity communication techniques for next generation mmWave hybrid MIMO systems. Firstly, a novel architecture with a framework that dynamically activates the optimal number of RF chains was designed. Fractional programming was used to solve an EE maximization problem and the Dinkelbach Method (DM) based framework was exploited to optimize the number of active RF chains and the data streams. The DM is an iterative and parametric algorithm where a sequence of easier problems converge to the global solution. The HBF matrices were designed using a codebook-based fast approximation solution called gradient pursuit which was introduced as a cost-effective and fast approximation algorithm. This work maximizes EE by exploiting the structure of RF chains with full resolution sampling unlike existing baseline approaches that use fixed RF chains and aim only for high SE. Secondly, an efficient sparse mmWave channel estimation algorithm was developed with low resolution Analog-to-Digital Converters (ADCs) at the receiver. The sparsity of the mmWave channel was exploited and the estimation problem was tackled using compressed sensing through the Stein's unbiased risk estimate based parametric denoiser. The Expectation-maximization density estimation was used to avoid the need to specify the channel statistics. Furthermore, an energy efficient mmWave hybrid MIMO system was developed with Digital-to- Analog Converters (DACs) at the transmitter where the best subset of the active RF chains and the DAC resolution were selected. A novel technique based on the DM and subset selection optimization was implemented for EE maximization. This work exploits the low resolution sampling at the converting units and provides more efficient solutions in terms of EE and channel estimation than existing baselines in the literature. Thirdly, the DAC and ADC bit resolutions and the HBF matrices were jointly optimized for EE maximization. The flexibility in choosing the bit resolution for each DAC and ADC was considered and they were optimized on a frame-by-frame basis unlike the existing approaches, based on the fixed resolution sampling. A novel decomposition of the HBF matrices to three parts was introduced to represent the analog beamformer matrix, the DAC/ADC bit resolution matrix and the baseband beamformer matrix. The alternating direction method of multipliers was used to solve this matrix factorization problem as it has been successfully applied to other non-convex matrix factorization problems in the literature. This work considers EE maximization with low resolution sampling at both the DACs and the ADCs simultaneously, and jointly optimizes the HBF and DAC/ADC bit resolution matrices, unlike the existing baselines that use fixed bit resolution or otherwise optimize either DAC/ADC bit resolution or HBF matrices