In this paper, we consider a real-time deep learning-based symbol detection approach for MIMO-OFDM systems. To exploit the temporal correlation of the wireless channel and the time-frequency structure of OFDM signals, a recurrent neural network (RNN) with deep feedforward output layers is introduced, where the recurrent layers and feedforward output layers are designed to process time-domain and frequency-domain information respectively. Reservoir computing (RC), a special type of RNN, and extreme learning machine (ELM), a special type of feedforward neural network, are chosen as the corresponding building blocks to facilitate over-the-air training. An online training loss objective is introduced to recursively update the neural weights in real-time. We believe this is the first work in the literature to realize real-time machine learning for MIMO-OFDM symbol detection, i.e., conducting NN-based symbol detection on an OFDM symbol basis. We demonstrate that (1) theIEEEstandardized WiFi training sequence can be directly applied as the real-time training sequence (2) the symbol detection performance can be further improved by using our theoretically derived pilot pattern. Evaluation results show that our RC-ELM-based symbol detection method outperforms traditional model-based techniques as well as state-of-the-art learning-based approaches in highly dynamic channel environments for real-time symbol detection.

In this paper, we introduce a structure-based neural network architecture, namely RC-Struct, for MIMO-OFDM symbol detection. The RC-Struct exploits the temporal structure of the MIMO-OFDM signals through reservoir computing (RC). A binary classifier leverages the repetitive constellation structure in the system to perform multi-class detection. The incorporation of RC allows the RC-Struct to be learned in a purely online fashion with extremely limited pilot symbols in each OFDM subframe. The binary classifier enables the efficient utilization of the precious online training symbols and allows an easy extension to high-order modulations without a substantial increase in complexity. Experiments show that the introduced RC-Struct outperforms both the conventional model-based symbol detection approaches and the state-of-the-art learning-based strategies in terms of bit error rate (BER). The advantages of RC-Struct over existing methods become more significant when rank and link adaptation are adopted. The introduced RC-Struct sheds light on combining communication domain knowledge and learning-based receive processing for 5G/5G-Advanced and Beyond.

In this paper, we introduce a new neural network (NN) structure, multi-mode reservoir computing (Multi-Mode RC). It inherits the dynamic mechanism of RC and processes the forward path and loss optimization of the NN using tensor as the underlying data format. Multi-Mode RC exhibits less complexity compared to conventional RC structures (e.g. single-mode RC), and offers comparable generalization performance to its single-mode counterpart. Furthermore, we introduce an alternating least square-based learning algorithm as well as the associated theoretical analysis for Multi-Mode RC. The result can be utilized to guide the configuration of NN parameters to sufficiently circumvent over-fitting issues. As a key application, we consider the symbol detection task in multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems with massive MIMO employed at the base stations (BSs). Thanks to the tensor structure of massive MIMO-OFDM signals, our online learning-based symbol detection method generalizes well in terms of bit error rate even using a limited online training set. Evaluation results suggest that the Multi-Mode RC-based learning framework can efficiently and effectively combat practical constraints of wireless systems (i.e. channel state information (CSI) errors and hardware non-linearity) to enable robust and adaptive communications over the air.

Orthogonal Time Frequency Space (OTFS) is a novel framework that processes modulation symbols via a time-independent channel characterized by the delay-Doppler domain. The conventional waveform, orthogonal frequency division multiplexing (OFDM), requires tracking frequency selective fading channels over the time, whereas OTFS benefits from full time-frequency diversity by leveraging appropriate equalization techniques. In this paper, we consider a neural network-based supervised learning framework for OTFS equalization. Learning of the introduced neural network is conducted in each OTFS frame fulfilling an online learning framework: the training and testing datasets are within the same OTFS-frame over the air. Utilizing reservoir computing, a special recurrent neural network, the resulting one-shot online learning is sufficiently flexible to cope with channel variations among different OTFS frames (e.g., due to the link/rank adaptation and user scheduling in cellular networks). The proposed method does not require explicit channel state information (CSI) and simulation results demonstrate a lower bit error rate (BER) than conventional equalization methods in the low signal-to-noise (SNR) regime under large Doppler spreads. When compared with its neural network-based counterparts for OFDM, the introduced approach for OTFS will lead to a better tradeoff between the processing complexity and the equalization performance.

In this paper, we investigate online learning-based MIMO-OFDM symbol detection strategies focusing on a special recurrent neural network (RNN) - reservoir computing (RC). We first introduce the Time-Frequency RC to take advantage of the structural information inherent in OFDM signals. Using the time domain RC and the time-frequency RC as building blocks, we provide two extensions of the shallow RC to RCNet: 1) Stacking multiple time domain RCs; 2) Stacking multiple time-frequency RCs into a deep structure. The combination of RNN dynamics, the time-frequency structure of MIMO-OFDM signals, and the deep network enables RCNet to handle the interference and nonlinear distortion of MIMO-OFDM signals to outperform existing methods. Unlike most existing NN-based detection strategies, RCNet is also shown to provide a good generalization performance even with a limited online training set (i.e, similar amount of reference signals/training as standard model-based approaches). Numerical experiments demonstrate that the introduced RCNet can offer a faster learning convergence and as much as 20% gain in bit error rate over a shallow RC structure by compensating for the nonlinear distortion of the MIMO-OFDM signal, such as due to power amplifier compression in the transmitter or due to finite quantization resolution in the receiver.

Conventional reservoir computing (RC) is a shallow recurrent neural network (RNN) with fixed high dimensional hidden dynamics and one trainable output layer. It has the nice feature of requiring limited training which is critical for certain applications where training data is extremely limited and costly to obtain. In this paper, we consider two ways to extend the shallow architecture to deep RC to improve the performance without sacrificing the underlying benefit: (1) Extend the output layer to a three layer structure which promotes a joint time-frequency processing to neuron states; (2) Sequentially stack RCs to form a deep neural network. Using the new structure of the deep RC we redesign the physical layer receiver for multiple-input multiple-output with orthogonal frequency division multiplexing (MIMO-OFDM) signals since MIMO-OFDM is a key enabling technology in the 5th generation (5G) cellular network. The combination of RNN dynamics and the time-frequency structure of MIMO-OFDM signals allows deep RC to handle miscellaneous interference in nonlinear MIMO-OFDM channels to achieve improved performance compared to existing techniques. Meanwhile, rather than deep feedforward neural networks which rely on a massive amount of training, our introduced deep RC framework can provide a decent generalization performance using the same amount of pilots as conventional model-based methods in 5G systems. Numerical experiments show that the deep RC based receiver can offer a faster learning convergence and effectively mitigate unknown non-linear radio frequency (RF) distortion yielding twenty percent gain in terms of bit error rate (BER) over the shallow RC structure.

The Reservoir Computing, a neural computing framework suited for temporal information processing, utilizes a dynamic reservoir layer for high-dimensional encoding, enhancing the separability of the network. In this paper, we exploit a Deep Learning (DL)-based detection strategy for Multiple-input, Multiple-output Orthogonal Frequency-Division Multiplexing (MIMO-OFDM) symbol detection. To be specific, we introduce a Deep Echo State Network (DESN), a unique hierarchical processing structure with multiple time intervals, to enhance the memory capacity and accelerate the detection efficiency. The resulting hardware prototype with the hybrid memristor-CMOS co-design provides the in-memory computing and parallel processing capabilities, significantly reducing the hardware and power overhead. With the standard 180nm CMOS process and memristive synapses, the introduced DESN consumes merely 105mW of power consumption, exhibiting 16.7% power reduction compared to shallow ESN designs even with more dynamic layers and associated neurons. Furthermore, numerical evaluations demonstrate advantages of the DESN over state-of-the-art detection techniques in the literate for MIMO-OFDM systems even with a very limited training set, yielding a 47.8% improvement against conventional symbol detection techniques.

In this paper, we introduce a reservoir computing (RC) structure, namely, windowed echo state network (WESN), for multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) symbol detection. We show that adding buffers in input layers is able to bring an enhanced short-term memory (STM) to the standard echo state network. A unified training framework is developed for the introduced WESN MIMO-OFDM symbol detector using both comb and scattered patterns, where the training set size is compatible with those adopted in 3GPP LTE/LTE-Advanced standards. Complexity analysis demonstrates the advantages of WESN based symbol detector over state-of-the-art symbol detectors when the number of OFDM sub-carriers is large, where the benchmark methods are chosen as linear minimum mean square error (LMMSE) detection and sphere decoder. Numerical evaluations suggest that WESN can significantly improve the symbol detection performance as well as effectively mitigate model mismatch effects using very limited training symbols.