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Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective

Sibo Zhang, Bruno Clerckx

TL;DR

The paper addresses interference in practical wireless systems where receivers employ suboptimal decoders due to limited channel knowledge or complexity. It develops the Finite-Alphabet Gaussian Channel under Interference (FAGCI) model and uses constellation-constrained MI and generalized mutual information (GMI) to analyze matched and mismatched decoding, linking decoding metrics to BICM demodulators. Two novel decoding metrics—the generalized Gaussian and interference decomposition metrics—are proposed, showing improved GMI over Gaussian-interference approximations and enabling low-complexity demodulators with practical gains. The authors extend the framework to MU-MISO, formulating GMI-based precoder optimization to maximize sum-rate under different decoding strategies, and demonstrate substantial, receiver-aware performance benefits through simulations. Overall, the work provides a theoretical and practical framework for accurately evaluating and enhancing interference handling with finite-alphabet signals in current and future wireless networks.

Abstract

Interference widely exists in communication systems and is often not optimally treated at the receivers due to limited knowledge and/or computational burden. Evolutions of receivers have been proposed to balance complexity and spectral efficiency, for example, for 6G, while commonly used performance metrics, such as capacity and mutual information (MI), fail to capture the suboptimal treatment of interference, leading to potentially inaccurate performance evaluations. Mismatched decoding is an information-theoretic tool for analyzing communications with suboptimal decoders. In this work, we use mismatched decoding to analyze communications with decoders that treat interference suboptimally, aiming at more accurate performance metrics. Specifically, we consider a finite-alphabet input Gaussian channel under interference, representative of modern systems, where the decoder can be matched (optimal) or mismatched (suboptimal) to the channel. The matched capacity is derived using MI, while a lower bound on the mismatched capacity under various decoding metrics is derived using generalized mutual information (GMI). We show that the decoding metric in the proposed channel model is closely related to the behavior of the demodulator in bit-interleaved coded modulation (BICM) systems. Simulations illustrate that GMI/MI accurately predicts the throughput of BICM-type systems {with various demodulators}. Finally, we extend the channel model and the GMI to multiple antenna cases, with an example of multi-user multiple-input-single-output (MU-MISO) precoder optimization problem considering GMI under different decoding strategies. In short, this work discovers new insights about the impact of interference, proposes novel receivers, and introduces a new design and performance evaluation framework that more accurately captures the effect of interference.

Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective

TL;DR

The paper addresses interference in practical wireless systems where receivers employ suboptimal decoders due to limited channel knowledge or complexity. It develops the Finite-Alphabet Gaussian Channel under Interference (FAGCI) model and uses constellation-constrained MI and generalized mutual information (GMI) to analyze matched and mismatched decoding, linking decoding metrics to BICM demodulators. Two novel decoding metrics—the generalized Gaussian and interference decomposition metrics—are proposed, showing improved GMI over Gaussian-interference approximations and enabling low-complexity demodulators with practical gains. The authors extend the framework to MU-MISO, formulating GMI-based precoder optimization to maximize sum-rate under different decoding strategies, and demonstrate substantial, receiver-aware performance benefits through simulations. Overall, the work provides a theoretical and practical framework for accurately evaluating and enhancing interference handling with finite-alphabet signals in current and future wireless networks.

Abstract

Interference widely exists in communication systems and is often not optimally treated at the receivers due to limited knowledge and/or computational burden. Evolutions of receivers have been proposed to balance complexity and spectral efficiency, for example, for 6G, while commonly used performance metrics, such as capacity and mutual information (MI), fail to capture the suboptimal treatment of interference, leading to potentially inaccurate performance evaluations. Mismatched decoding is an information-theoretic tool for analyzing communications with suboptimal decoders. In this work, we use mismatched decoding to analyze communications with decoders that treat interference suboptimally, aiming at more accurate performance metrics. Specifically, we consider a finite-alphabet input Gaussian channel under interference, representative of modern systems, where the decoder can be matched (optimal) or mismatched (suboptimal) to the channel. The matched capacity is derived using MI, while a lower bound on the mismatched capacity under various decoding metrics is derived using generalized mutual information (GMI). We show that the decoding metric in the proposed channel model is closely related to the behavior of the demodulator in bit-interleaved coded modulation (BICM) systems. Simulations illustrate that GMI/MI accurately predicts the throughput of BICM-type systems {with various demodulators}. Finally, we extend the channel model and the GMI to multiple antenna cases, with an example of multi-user multiple-input-single-output (MU-MISO) precoder optimization problem considering GMI under different decoding strategies. In short, this work discovers new insights about the impact of interference, proposes novel receivers, and introduces a new design and performance evaluation framework that more accurately captures the effect of interference.

Paper Structure

This paper contains 24 sections, 5 theorems, 58 equations, 15 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mismatched Decoding for Finite Alphabets
  3. Finite-Alphabet Gaussian Channel under Interference
  4. Encoding and Decoding
  5. Matched Capacity and a Lower Bound on Mismatched Capacity
  6. Approximation of mismatched capacity
  7. Numerical results on GMI for FAGCI model
  8. Improvement on Decoding metric
  9. Generalized Gaussian Decoding Metric
  10. Interference Decomposition Decoding Metric
  11. Results on GMI of the Proposed Decoding Metrics
  12. Practical Receivers
  13. Signal Processing with GMI
  14. Achievable Rate of MU-MISO Incorporating Decoding Strategy
  15. Sum-Rate Optimization
  16. ...and 9 more sections

Key Result

Proposition 1

With optimal decoding, i.e., using (matched decoding metric) as the decoding metric, the capacity of (FAG channel) is given by the constellation-constrained MI as in (matched capacity).

Figures (15)

  • Figure 1: Channel model with interference and noise.
  • Figure 2: GMI and MI with $\sigma_i^2=20$dBm, $\sigma_j^2=10$dBm and $\sigma_z^2=0$dBm.
  • Figure 3: Visualization of $\mathcal{X+I+J}$ at the three marked points in Figure \ref{['Fig: GMI_vs_MI_varying_X_pow']}.
  • Figure 4: GMI and MI with $\sigma_x^2=20$dBm, $\sigma_j^2=15$dBm and $\sigma_z^2=0$dBm.
  • Figure 5: GMI and MI with $\sigma_x^2=20$dBm, $\sigma_i^2=20$dBm and $\sigma_z^2=0$dBm.
  • ...and 10 more figures

Theorems & Definitions (9)

  • Remark 1
  • Proposition 1: Matched capacity
  • Proposition 2: A lower bound on mismatched capacity
  • Remark 2
  • Remark 3
  • Remark 4
  • Proposition 3: Approximation of the GMI
  • Proposition 4
  • Proposition 5