Deep Learning Based Channel Estimation in Wireless Communications

Abstract

Deep learning techniques which employ trained neural networks to solve problems have witnessed widespread adoption in diverse fields like medicine, architecture, robotics, autonomous vehicles, wireless communications, and many more. This widespread adop- tion of neural networks (NNs) is a result of significant advancements on both hardware and software fronts. In wireless communications, deep learning techniques have been extensively adopted for symbol detection, beam tracking, constellation design, optimal resource allocation, channel estimation, and several other tasks. Learning based solutions offered by well trained NNs have shown robustness to model mismatches/non-idealities witnessed in communication systems. This thesis addresses the problem of channel es- timation using deep learning techniques for different signalling schemes under various channel conditions. Specifically, we consider learning based techniques for 1) channel prediction in time-varying channels, 2) channel estimation in orthogonal frequency divi- sion multiplexing (OFDM) systems in doubly-selective channels, 3) delay-Doppler (DD) domain channel estimation for orthogonal time frequency space (OTFS) systems with different pilot frame structures, and 4) DD channel estimation for Zak transform based OTFS systems. The details of the contributions made in the thesis are summarised below. Deep channel prediction in time-varying channels: In the first part of the thesis, we consider the problem of channel prediction in time-varying fading channels. In time-varying fading channels, channel coefficients are estimated using pilot symbols that are transmitted every coherence interval. For channels with high Dopplers, the rapid channel variations over time will require these pilots to be transmitted often. We propose a novel receiver architecture using deep recurrent neural networks (RNNs) that learns the channel variations and, thereby, reduces the number of pilot symbols required for channel estimation. Specifically, we design and train an RNN to learn the correlation in the time-varying channel and predict the channel coefficients into the future with good accuracy over a wide range of Dopplers and signal-to-noise ratios (SNRs). Also, the robustness of prediction for different Dopplers and SNRs is achieved by adapting the number of predictions into the future based on the Doppler and SNR. We also propose a data decision driven receiver architecture using RNNs, wherein the data symbols detected using the channel predictions are treated as pilots to enable more predictions, thereby the pilot overhead is further reduced in every coherence interval. Numerical results show that the proposed RNN based receiver achieves good bit error performance in time-varying fading channels, while being spectrally efficient. Channel estimation in OFDM in doubly-selective channels: In the second part of the thesis, we consider the problem of channel estimation in doubly-selective (i.e., time-selective and frequency-selective) channels in OFDM systems in the presence of oscillator phase noise (PN). Methods reported in the literature to estimate the channel incur significant overhead in terms of the number of training/pilot symbols needed to ef- fectively estimate the channel in the presence of PN. We propose a learning based channel estimation scheme for OFDM systems in the presence of both PN and doubly-selective fading. We view the channel matrix as an image and model the channel estimation problem as an image completion problem where the information about the image is sparsely available. Towards this, we devise and employ two-dimensional convolutional neural networks (CNNs) for learning and estimating the channel coefficients in the entire time-frequency (TF) grid, based on pilots sparsely populated in the TF grid. Further, using the estimated channel coefficients, we devise a simple and effective PN estimation and compensation scheme. Our results demonstrate that the proposed network and the PN compensation scheme achieve robust OFDM performance in the presence of PN and doubly-selective fading. DD domain channel estimation in OTFS: Unlike OFDM, which is not robust to highly time-selective channels due to inter-carrier interference, OTFS modulation has been shown to be robust to rapidly time-varying channels with high Doppler spreads (in the order of kHz of Doppler). In OTFS, information symbols are multiplexed in the DD domain and the channel is also viewed in the DD domain (as opposed to the TF domain in OFDM). In the third part of the thesis, we consider the problem of DD domain channel estimation in OTFS systems using deep learning techniques. Widely considered pilot frame structures for DD channel estimation in OTFS include exclusive pilot frame, embedded pilot frame, interleaved pilot frame, and superimposed pilot frame. We devise suitable learning based architectures for channel estimation using these pilot frames as detailed below. First, we propose a learning based architecture for estimating the DD channel for both exclusive pilot frame and embedded pilot frame. The proposed learning network, called DDNet, is based on a multi-layered RNN framework that works seamlessly for both frames. Our results demonstrate that the proposed DDNet achieves better mean square error (MSE) and bit error rate (BER) performance compared to other schemes in the literature. Next, we consider DD channel estimation for interleaved pilot (IP) frame, where pilot symbols are interleaved with data symbols in a lattice type fashion, without any guard symbols. For this IP frame structure, we propose an RNN based channel estimation scheme. The proposed network is called IPNet. Our results show that the proposed IPNet architecture achieves good BER performance while being spectrally efficient. The rate loss in the pilot frame structures considered above can be avoided by superimposing pilot symbols over data symbols. We propose a sparse superimposed pilot (SSP) scheme, where pilot and data symbols are superimposed in a few bins and the remaining bins carry data symbols only. For the SSP scheme, we propose an RNN based learning architecture (referred to as SSPNet) trained to provide accurate channel estimates overcoming the leakage effects in channels with fractional delays and Dopplers. Our results show that the proposed SSP scheme with the proposed SSPNet based channel estimation performs better than a fully superimposed pilot (FSP) scheme reported in the literature. DD domain channel estimation in OTFS using TF domain learning: In the fourth and final part of the thesis, we propose a novel learning based approach for channel estimation in OTFS systems, where learning is done in the TF domain for DD domain channel estimation. Learning in the TF domain is motivated by the fact that the range of values in the TF channel matrix is favorable for training as opposed to the large swing of values in the DD channel matrix which is not favourable for training. A key beneficial outcome of the proposed approach is its low complexity along with very good performance. We develop this TF learning approach for two types of OTFS systems, namely, 1) two-step OTFS, where the information symbols in the DD domain are converted to time domain for transmission in two steps (DD domain to TF domain conversion followed by TF domain to time domain conversion), and 2) single-step OTFS (also called as Zak OTFS), where the DD domain symbols are directly converted to time domain in one step using inverse Zak transform. Our results show that the proposed TF learning-based approach achieves almost the same performance as that of the state-of- the-art algorithm, while being drastically less complex making it practically appealing.