Deep Learning-Based Auto-Encoder for Time-Offset Sub-Faster-Than-Nyquist Downlink NOMA With Timing Errors and Imperfect CSI

This paper presents architecture designs and performance evaluations for the encoding and decoding of transmitted and received sequences for downlink time-offset sub-faster-than-Nyquist non-orthogonal multiple access signaling (TO-sFTN-NOMA). A conventional singular value decomposition (SVD)-based scheme for TO-sFTN-NOMA is employed as a benchmark. While this SVD scheme provides reliable communication, our findings reveal that it is not optimal in terms of bit error rate (BER) performance. Moreover, the SVD scheme is sensitive to timing offset errors, and its complexity increases quadratically with the sequence length. To overcome these limitations and improve the TO-sFTN-NOMA's performance, we propose a convolutional neural network (CNN) auto-encoder (AE) technique for encoding and decoding with linear time complexity. We explain the design of the encoder and decoder architectures and the training criteria. By considering several variants of the proposed CNN AE, we show that the proposed CNN AE can achieve an excellent trade-off between performance and complexity. The proposed CNN AE surpasses the SVD method by approximately 10 dB in a TO-sFTN-NOMA system with no timing offset errors and no channel state information (CSI) estimation errors. In the presence of CSI error with variance of 1$\%$ and uniform timing error at $\pm$4% of the symbol interval, the proposed CNN AE provides up to 16 dB SNR gain over the SVD method. We also propose a novel modified training objective function consisting of a weighted summation of the cross-entropy (CE) loss and a Q-function metric related to the BER. Simulations show that the modified objective loss function achieves SNR gains of up to 1 dB over the CE loss function alone.