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Geometric constellation shaping for wireless optical intensity channels: An information-theoretic approach

Suhua Zhou, Tianqi Li, Zhaoxi Fang, Jing Zhou, Wenyi Zhang

TL;DR

This work tackles bandwidth-efficient transmission for IM/DD optical wireless channels by proposing a geometric constellation shaping method that yields exponential-like level distributions. It constructs constellations via centroids of equiprobable exponential intervals, then improves finite-M performance through shifting and scaling, and finally regularizes levels to be representable with $b+2$ bits, preserving asymptotic optimality as $M=2^b$. The approach guarantees that high-SNR capacity $C(\textsf{SNR})$ can be approached by increasing constellation size, with a demonstrated shaping gain of about $0.65$ dB in a practical 16-level LDPC-coded modulation. The method reduces DAC resolution requirements while maintaining near-optimal information rates, and can be extended to more specific IM/DD channel models that admit a near-optimal continuous input distribution.

Abstract

A simple geometric shaping method is proposed for optical wireless communication systems based on intensity modulation and direct detection (IM/DD) from an information-theoretic perspective. Constellations consisting of equiprobable levels with exponential-like distribution are obtained, which possesses asymptotic optimality in the sense that the high-SNR capacity of average-intensity constrained optical intensity channel can be approached by such constellations with increasing size. All $2^b$ levels ($b\in\mathbb N$) of the obtained constellation can be represented by a basic level and $b+2$ bits, thereby reducing the required resolution of the digital-to-analog converter (DAC) without affecting the asymptotic optimality. Achievable information rate evaluations verify the asymptotic optimality. As an example, error performance results of a simple $16$-level LDPC coded modulation scheme show that a shaping gain of $0.65$ dB can be obtained by applying the proposed constellation design. This method can also be applied to more specific IM/DD channel models, since it only requires a near-optimal continuous input distribution.

Geometric constellation shaping for wireless optical intensity channels: An information-theoretic approach

TL;DR

This work tackles bandwidth-efficient transmission for IM/DD optical wireless channels by proposing a geometric constellation shaping method that yields exponential-like level distributions. It constructs constellations via centroids of equiprobable exponential intervals, then improves finite-M performance through shifting and scaling, and finally regularizes levels to be representable with bits, preserving asymptotic optimality as . The approach guarantees that high-SNR capacity can be approached by increasing constellation size, with a demonstrated shaping gain of about dB in a practical 16-level LDPC-coded modulation. The method reduces DAC resolution requirements while maintaining near-optimal information rates, and can be extended to more specific IM/DD channel models that admit a near-optimal continuous input distribution.

Abstract

A simple geometric shaping method is proposed for optical wireless communication systems based on intensity modulation and direct detection (IM/DD) from an information-theoretic perspective. Constellations consisting of equiprobable levels with exponential-like distribution are obtained, which possesses asymptotic optimality in the sense that the high-SNR capacity of average-intensity constrained optical intensity channel can be approached by such constellations with increasing size. All levels () of the obtained constellation can be represented by a basic level and bits, thereby reducing the required resolution of the digital-to-analog converter (DAC) without affecting the asymptotic optimality. Achievable information rate evaluations verify the asymptotic optimality. As an example, error performance results of a simple -level LDPC coded modulation scheme show that a shaping gain of dB can be obtained by applying the proposed constellation design. This method can also be applied to more specific IM/DD channel models, since it only requires a near-optimal continuous input distribution.
Paper Structure (10 sections, 17 equations, 3 figures, 1 table)

This paper contains 10 sections, 17 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Optical Intensity Channel and Constellation Shaping
  3. Proposed Geometric Shaping Method
  4. Level Generation: From Quantile to Centroid
  5. Level Optimization: Shifting and Scaling
  6. Level Regularization: Representation by $b+2$ Bits
  7. Numerical Results
  8. Achievable Information Rate
  9. Coded Modulation Performance Results
  10. Conclusion

Figures (3)

  • Figure 1: Optical SNR gain obtained by shifting and scaling.
  • Figure 2: Comparison of proposed and standard PAM constellations. Increase of PAPR can be indicated by the largest levels (emphasized by circles).
  • Figure 3: Achievable information rate comparison.