Deep Learning-based Auto-encoder for Time-offset Faster-than-Nyquist Downlink NOMA with Timing Errors and Imperfect CSI

TL;DR

The paper tackles downlink T-NOMA under timing offsets and imperfect CSI by proposing a CNN-based auto-encoder with linear sequence-length complexity, outperforming the traditional SVD baseline in BER under practical impairments. A novel training objective that combines cross-entropy with a Q-function-based BER surrogate (Q-loss) further improves performance, while auxiliary MLPs for power allocation (MLP-PA) and CSI transformation (MLP-T) boost robustness. Empirical results show the CNN-AE achieving up to about 10 dB improvement over SVD in scenarios with timing and CSI errors, and roughly 2× throughput relative to a single-user link at the same BER. The work highlights the potential of end-to-end learning to realize efficient, robust T-NOMA systems, with future work extending to analytic AE-rate characterizations and practical coding schemes.

Abstract

We examine encoding and decoding of transmitted sequences for the downlink time-offset faster than Nyquist signaling non-orthogonal multiple access NOMA (T-NOMA) channel. We employ a previously proposed singular value decomposition (SVD)-based scheme 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). Additionally, the SVD is sensitive to timing offset errors, and its time complexity increases quadratically with the sequence length. We propose a convolutional neural network (CNN) auto-encoder (AE) for encoding and decoding with linear time complexity. We explain the design of the encoder and decoder architectures and the training criteria. By examining several variants of the CNN AE, we show that it can achieve an excellent trade-off between performance and complexity. The proposed CNN AE surpasses the SVD method by approximately 2 dB in a T-NOMA system with no timing offset errors or channel state information estimation errors. In the presence of channel state information (CSI) error variance of 1$\%$ and uniform timing error at $\pm$4\% of the symbol interval, the proposed CNN AE provides up to 10 dB SNR gain over the SVD method. We also propose a novel modified training objective function consisting of a linear combination of the traditionally used cross-entropy (CE) loss function and a closed-form expression for the bit error rate (BER) called the Q-loss function. Simulations show that the modified loss function achieves SNR gains of up to 1 dB over the CE loss function alone.

Figures (16)

• Figure 1: CNN autoencoder system. The encoder encodes the messages $\mathbf{x}$ for transmission as $\mathbf{v}$. The stochastic T-NOMA channel superimposes the transmitted sequences and uses faster than Nyquist signaling. The decoder at each user recovers the transmitted messages from the received sequence.
• Figure 2: CNN encoder block diagram. The non-linear activation functions $\psi_i$s enable non-linear encoding. The final layer normalizes the output to satisfy the rate and power constraints.
• Figure 3: CNN decoder block diagram for user $r$. The first convolutional layer accepts the complex sequences of sufficient statistics for 2D-processing. The outcome sequence is further processed by 1D convolutional layers and non-linear activations.
• Figure 4: BER comparison between SVD T-NOMA system simulation, one-user Rayleigh fading channel, T-NOMA with stronger/weaker user selection (per Appendix \ref{['AverageBERAnalysisAppendix']}), and CNN AE T-NOMA system simulation. All simulations assume perfect CSI and timing. Given the same average SNR per user, the CNN AE8 communicates at double the rate of a single-user system while maintaining the same BER when trained at SNRs of 15 and 30 dB.
• Figure 5: Learning curve.