Model-based Deep Learning Algorithms in Mimo Receivers : Channel Estimation & Symbol Detection

Abstract

With the advent of Massive multiple-input-multiple-output (MIMO) wireless communication systems, users can now enjoy high spectral efficiency and throughput leading to a better quality of service. The efficacy of these systems largely hinge on being able to accurately estimate parameters such as the state of the wireless channel and transmitted data symbols. Traditional estimation techniques fall in either of the categories - (i) optimal/close to optimal but computationally intensive, and (ii) suboptimal but simple, linear estimators. Model-based Deep Learning aims to fill in the gap between these two by providing near-optimal performance at a fraction of the complexity (at inference time). Unfolding, a technique to incorporate model-based deep learning with limited data and algorithmic interpretability, involves converting the iterations of a traditional (non deep learning) algorithm into neural network layers by introducing learnable parameters and nonlinear activation functions. In this thesis, we aim to exploit the lean framework of unfolding, coupled with its transparent architecture, to obtain channel and symbol estimates in both quantized and unquantized receivers. \par

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \textbf{Unfolding for Coherent Symbol Detection: } In Chapter \ref{Chapter:Chap2_FastNet}, we propose an unfolded symbol detection algorithm titled Fast Detection Network \textbf{(FastNet)} for estimating the transmitted data symbols with the assumption of perfect channel knowledge at the receiver. The proposed FastNet has a nonhomogeneous framework that allows its constituent layers to have different structures - few of the layers can involve a massive amount of matrix-vector multiplications with high dimensional trainable projection matrices that allow better separability of features, while the rest of the layers can have a simpler structure to bring down the computational burden and occupied memory space. Simulations showed that a judicious choice of the number of such simpler layers, instead of the existing unfolded network with a homogeneous structure that contains high dimensional matrix projections in all of its layers, can lead to significant reduction in the complexity in the range of $\textbf{35}-\textbf{50}\%$, with marginal change in performance.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \par \textbf{Unfolding for Joint Channel Estimation and Symbol Detection: } Chapter \ref{Chapter:Chap3_JEDADNet} proposes a Joint Channel Estimation and Symbol Detection (JED) scheme based on the iterations of Alternating Direction Method of Multipliers (ADMM), referred to as \textbf{JED-ADMM}, that outperforms existing non deep learning JED methods by exploiting the non-smooth constraint arising from Quadrature Amplitude Modulation (QAM) data symbols. We then unfold JED-ADMM into a model-based neural network \textbf{Joint Estimation and Detection using Alternating Direction Method of Multipliers Network (JED-ADNet)} by converting each JED-ADMM iteration into a neural network layer comprising learnable parameters and activations. Furthermore, to lessen the computational burden, the matrix inversion updates of JED-ADMM are replaced with simpler first-order updates. Numerical simulations conclude that the proposed JED-ADNet promises upto $\mathbf{2}$ dB improvement in Signal-to-Noise Ratio (SNR), with the Bit Error Rate (BER) as the performance metric, compared to existing unfolded JED techniques in Rayleigh channels and exhibits comparable performance as state-of-the-art diffusion models, at a fraction of the complexity, in realistic Third Generation Partnership Project (3GPP) channels for low to mid SNR range.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \par \textbf{mmWave Channel Estimation in $1$-bit Quantized Receivers: } Analog-to-digital converters (ADCs) for millimetre-wave (mmWave) systems have to operate at a very high sampling rate due to the high bandwidth involved. This leads to a massive strain on the power budget, especially if full resolution ADCs are used for conversion of the incoming analog signals into digital domain (for further processing by modern digital receivers). One way to reduce the power consumption is to design low resolution ADCs, $1$-bit in the extreme case, that leads to an exponential reduction in the power consumption. However, channel estimation in such receivers is a challenging task due to the non-linearity introduced by the quantization operation of ADCs. Existing methods have utilised the low-rank property of mmWave channels to formulate an optimization problem in order to retrieve the channel state information. In Chapter \ref{Chap4:spcom}, we propose two methods - (i) \textbf{Projected Gradient Ascent with Nuclear, Infinity norm and Sparsity (PGA-NIS), and (ii) Projected Gradient Ascent with Nuclear, Infinity norm and Sparsity with Log-Barrier (PGA-NIS-L)}. The aforementioned proposed techniques incorporate additional constraints of maximum absolute entry and angular sparsity to improve the normalised mean square error of the channel estimates, by upto $\mathbf{4.5}$ dB, for a range of SNR values and antenna configurations.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \par \textbf{Unfolding for Symbol Detection in Task-based Quantized Receivers: } Chapter \ref{Chapter:Chap5_tamnet} proposes a \textbf{Task-based Alternating Direction Method of Multipliers unfolded Network (TAMNet)} for symbol detection from $b$-bit quantized measurements at the receiver. Task-based systems apply a tailored pre-processing on the incoming analog signal, to possibly counteract the nonlinear quantization effects, before it is converted into its digital equivalent via sampling and quantization. The resulting signal has a more informative finite-level representation that makes it more amenable for processing in the symbol detector block in order to recover the transmitted constellation data symbols. We provide a closed-form expression for a suitable pre-processing block and then modify its structure to let it be trained by the incoming data. The quantized symbol is then sent to an unfolded symbol detector that is based on the ADMM iterations. Numerical results demonstrate that TAMNet yields an SNR improvement of upto $\mathbf{3.5}$ dB over the existing unfolded conventional quantized receivers, in achieving a symbol error rate (SER) of $\approx 3\times10^{-4}$.