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End-to-End NOMA with Perfect and Quantized CSI Over Rayleigh Fading Channels

Selma Benouadah, Mojtaba Vaezi, Ruizhan Shen, Hamid Jafarkhani

TL;DR

This work develops an end-to-end autoencoder for downlink NOMA in Rayleigh fading, enabling interference-aware, channel-adaptive signaling that can operate with perfect or quantized CSI. By conditioning the transmitter on instantaneous channel gains (or their quantized versions) and jointly learning transmit and receive mappings, the AE discovers flexible super-constellations that mitigate inter-user interference. The results show superior BER performance compared to analytical NOMA benchmarks, with Lloyd–Max quantization providing clear benefits over uniform feedback and a novel training scheme mitigating BER floors at high SNR. This approach advances practical NOMA deployment under realistic CSI constraints by leveraging end-to-end learning of channel-aware signaling strategies.

Abstract

An end-to-end autoencoder (AE) framework is developed for downlink non-orthogonal multiple access (NOMA) over Rayleigh fading channels, which learns interference-aware and channel-adaptive super-constellations. While existing works either assume additive white Gaussian noise channels or treat fading channels without a fully end-to-end learning approach, our framework directly embeds the wireless channel into both training and inference. To account for practical channel state information (CSI), we further incorporate limited feedback via both uniform and Lloyd-Max quantization of channel gains and analyze their impact on AE training and bit error rate (BER) performance. Simulation results show that, with perfect CSI, the proposed AE outperforms the existing analytical NOMA schemes. In addition, Lloyd-Max quantization achieves superior BER performance compared to uniform quantization. These results demonstrate that end-to-end AEs trained directly over Rayleigh fading can effectively learn robust, interference-aware signaling strategies, paving the way for NOMA deployment in fading environments with realistic CSI constraints.

End-to-End NOMA with Perfect and Quantized CSI Over Rayleigh Fading Channels

TL;DR

This work develops an end-to-end autoencoder for downlink NOMA in Rayleigh fading, enabling interference-aware, channel-adaptive signaling that can operate with perfect or quantized CSI. By conditioning the transmitter on instantaneous channel gains (or their quantized versions) and jointly learning transmit and receive mappings, the AE discovers flexible super-constellations that mitigate inter-user interference. The results show superior BER performance compared to analytical NOMA benchmarks, with Lloyd–Max quantization providing clear benefits over uniform feedback and a novel training scheme mitigating BER floors at high SNR. This approach advances practical NOMA deployment under realistic CSI constraints by leveraging end-to-end learning of channel-aware signaling strategies.

Abstract

An end-to-end autoencoder (AE) framework is developed for downlink non-orthogonal multiple access (NOMA) over Rayleigh fading channels, which learns interference-aware and channel-adaptive super-constellations. While existing works either assume additive white Gaussian noise channels or treat fading channels without a fully end-to-end learning approach, our framework directly embeds the wireless channel into both training and inference. To account for practical channel state information (CSI), we further incorporate limited feedback via both uniform and Lloyd-Max quantization of channel gains and analyze their impact on AE training and bit error rate (BER) performance. Simulation results show that, with perfect CSI, the proposed AE outperforms the existing analytical NOMA schemes. In addition, Lloyd-Max quantization achieves superior BER performance compared to uniform quantization. These results demonstrate that end-to-end AEs trained directly over Rayleigh fading can effectively learn robust, interference-aware signaling strategies, paving the way for NOMA deployment in fading environments with realistic CSI constraints.
Paper Structure (13 sections, 1 theorem, 10 equations, 6 figures)

This paper contains 13 sections, 1 theorem, 10 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Autoencoder for NOMA Rayleigh Channel
  4. Network Structure and Training
  5. Quantized CSI versus Perfect CSI
  6. Numerical Results
  7. Super-constellation Adaptation to Channel Gains
  8. Comparison with Theoretical and Benchmark BER Bounds
  9. Adaptability for Different Bit Lengths
  10. Quantized CSI Feedback: Uniform vs. Lloyd–Max
  11. Improving BER Floor at High SNR
  12. Conclusion
  13. BER for QPSK-QPSK NOMA under Rayleigh Fading

Key Result

Lemma 1

The average symbol error probability of a two-user NOMA system over a Rayleigh fading channel, where each user employs a QPSK constellation, is given by in which and average $\bar{\xi}_{k,j}$ are obtained by replacing $|h_k|^2$ with its expectation $2\sigma_{h_k}^2$ in the corresponding instantaneous expressions in eq:gamma_a--eq:gamma_d.

Figures (6)

  • Figure 1: The architecture of the implemented AE-NOMA. In this example, the output layer sizes of the decoders are $\ell_1=\ell_2=2$. In the full CSI case, $\hat{h}_k = h_k$, whereas in the quantized CSI case, $\hat{h}_k = f_Q(h_k)$ for $k \in \{1,2\}$.
  • Figure 2: Super-constellations with two different channel gains for UE1 and UE2.
  • Figure 3: Average BER performance of the proposed AE system and traditional approaches under Rayleigh fading.
  • Figure 4: Average BER performance of AE compared to traditional constellations for two cases: $\ell_1=2$ bits, $\ell_2=3$ bits and $\ell_1=1$ bit, $\ell_2=3$ bits.
  • Figure 5: Average BER for uniform (U) and Lloyd–Max (LM) quantized CSI feedback under various quantization levels and unquantized CSI. All graphs are for $l_1=l_2=2$ bits.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Lemma 1