Variational Bayes Algorithms for mmWave and Massive MIMO-OFDM Systems with Low Resolution ADCs

Abstract

In this thesis, we develop novel low-complexity algorithms for massive multiple-input multiple-output (MIMO) systems under practical non-idealities and theoretically analyze their performance. The first problem we consider is that of joint channel estimation and data decoding in uplink massive multiple-input-multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs) at the base station. The nonlinearities introduced by the ADCs make the problem challenging: in particular, the existing linear detectors perform poorly. Also, the channel coding used in commercial wireless systems necessitates soft symbol detection to obtain satisfactory performance. In this part of the thesis, we present a low-complexity variational Bayesian (VB) inference procedure to jointly solve the (possibly correlated) channel estimation and soft symbol decoding problem. We present the approach in progressively more complex scenarios, including the case where even the channel statistics are not available at the receiver. Then, we combine the VB procedure with a belief propagation (BP) based channel decoder, which further enhances the performance without any additional complexity. We numerically evaluate the bit error rate (BER) and the normalized mean squared error (NMSE) in the channel estimates obtained by our algorithm as a function of various system parameters, and benchmark the performance against genie-aided and state-of-the-art receivers. The results show that the VB procedure is a promising approach for developing low-complexity advanced receivers in low-resolution ADC based systems.

In the second problem, we consider the delay-domain sparse channel estimation and data decoding problems in a massive MIMO orthogonal frequency division multiplexing (MIMO-OFDM) wireless communication system with low-resolution ADCs. The high non-linear distortion due to coarse quantization leads to severe performance degradation in conventional OFDM receivers, which necessitates novel receiver techniques. Firstly, we derive the Bayesian Cramer-Rao lower bound (CRLB) on the mean squared error (MSE) in recovering jointly compressible vectors from quantized noisy underdetermined measurements. Secondly, we formulate the pilot-assisted channel estimation as a multiple measurement vector (MMV) sparse recovery problem, and develop a VB algorithm to infer the posterior distribution of the channel. We benchmark the MSE performance of our algorithm with that of the CRLB, and numerically show that the VB algorithm meets the CRLB. Thirdly, we present a soft symbol decoding algorithm that infers the posterior distributions of the data symbols given the quantized observations. We utilize the posterior statistics of the detected data symbols as virtual pilots, and develop an iterative soft symbol decoding and data-aided channel estimation procedure. Finally, we present a variant of the iterative algorithm that utilizes the output bit log-likelihood-ratios (LLRs) of the channel decoder to adapt the data prior to further improve the performance. We provide interesting insights into the impact of the various system parameters on the MSE and BER of the developed algorithms, and benchmark them against the state-of-the-art.

In the third problem, we present a novel model-and-data-driven channel estimation procedure in a millimeter-wave MIMO-OFDM wireless communication system. The transceivers employ a hybrid analog-digital architecture. We adapt techniques from a wide range of signal processing methods, such as compressed sensing and Bayesian inference, to learn the unknown sparsifying dictionary in the beamspace domain, as well as the delay-and-beamspace sparse channel. We train the model-based algorithm with a site-specific training dataset generated using a realistic ray tracing-based wireless channel simulation tool. We assess the performance of the developed channel estimation algorithm with the same site's test data. We benchmark the performance of our procedure in terms of NMSE error against an existing fast greedy method and two state-of-the-art algorithms, and empirically show that model-based approaches combined with data-driven customization outperform purely model based techniques by a large margin. This algorithm was selected as one of the top three solutions in the "ML5G-PHY Channel Estimation Global Challenge 2020" organized by the International Telecommunication Union.

In the last problem considered in this thesis, we study the problem of downlink (DL) sum rate maximization in codebook-based multiuser (MU) MIMO systems. The user equipments (UEs) estimate the DL channels using pilot symbols sent by the access point (AP) and feedback the estimates to the AP over a control channel. We present a closed form expression for the achievable sum rate of the MU-MIMO broadcast system with codebook constrained precoding based on the estimated channels, where multiple data streams are simultaneously transmitted to all users. Next, we present novel, computationally efficient, minorization-maximization (MM) based algorithms to determine the selection of beamforming vectors and power allocation to each beam that maximizes the achievable sum rate. Our solution involves multiple uses of MM in a nested fashion. Based on this approach, we present and contrast two algorithms, which we call the square-root-MM (SMM) and inverse-MM (IMM) algorithms. The algorithms are iterative and converge to a locally optimal beamforming vector selection and power allocation solution from any initialization. We evaluate the performance and complexity of the algorithms for various values of the system parameters, compare them with existing solutions, and provide further insights into how they can be used in system design.