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Optical Communications with Relative Intensity Noise: Channel Modeling and Information Rates

Felipe Villenas, Yunus Can Gültekin, Alex Alvarado

Abstract

We consider optical communications with intensity modulation and direct detection affected by laser relative intensity noise (RIN). Starting from a continuous-time waveform model, we derive an equivalent discrete-time channel model. As a result of RIN, the resulting channel model exhibits signal-dependent noise with memory. Unlike the commonly-assumed model in the literature, the conditional variance of this noise term has a polynomial dependence on the symbol of interest. Finally, we study achievable information rates for this channel under practically-relevant system parameters. We take a mismatched decoding approach and compute the generalized mutual information (GMI) using a memoryless decoding metric. Our numerical results show that when the memory in the channel is ignored by the receiver, GMI saturates as the constellation size increases, and thus, dense constellations do not offer gains. We also show that this saturation results from nonsymmetric nonvanishing contributions of the symbols to the GMI.

Optical Communications with Relative Intensity Noise: Channel Modeling and Information Rates

Abstract

We consider optical communications with intensity modulation and direct detection affected by laser relative intensity noise (RIN). Starting from a continuous-time waveform model, we derive an equivalent discrete-time channel model. As a result of RIN, the resulting channel model exhibits signal-dependent noise with memory. Unlike the commonly-assumed model in the literature, the conditional variance of this noise term has a polynomial dependence on the symbol of interest. Finally, we study achievable information rates for this channel under practically-relevant system parameters. We take a mismatched decoding approach and compute the generalized mutual information (GMI) using a memoryless decoding metric. Our numerical results show that when the memory in the channel is ignored by the receiver, GMI saturates as the constellation size increases, and thus, dense constellations do not offer gains. We also show that this saturation results from nonsymmetric nonvanishing contributions of the symbols to the GMI.
Paper Structure (8 sections, 2 theorems, 21 equations, 6 figures, 1 table)

This paper contains 8 sections, 2 theorems, 21 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Signal-dependent Noise Analysis
  5. Information-Theoretic Analysis
  6. Lower Bound via Generalized Mutual Information
  7. Numerical Results
  8. Conclusions

Key Result

Theorem 1

The discrete-time equivalent channel model for the system in Fig. fig:system_IMDD is given by where $Q_k$ are independent and identically distributed Gaussian samples $Q_k\!\sim\!\mathcal{N}\left(0,\frac{1}{2}N_0^\mathrm{th} G^2 \|h\|_2^2\right)$ and $Z_k$ is a signal-dependent noise term given by

Figures (6)

  • Figure 1: Equivalent high-speed IM-DD system with laser RIN and external modulation.
  • Figure 2: Histogram of the samples $Y_k$. The contributions of the thermal noise $Q_k$ and signal-dependent noise $Z_k$ are also plotted independently.
  • Figure 3: Conditional variance $\mathsf{E}\left[Z_k^2|A_k\!=\!\mathsf{a}_n\right]$ using \ref{['eq:Zk_var']} as function of $\ell$.
  • Figure 4: GMI vs. OMA for the system in Fig. \ref{['fig:system_IMDD']} using the parameters in Table \ref{['tab:sim_param']}.
  • Figure 5: GMI at $\text{OMA}=25$ dBm vs. $M$. The GMI converges as $M\to\infty$ (dashed lines). The maximum value is obtained for $M=16$.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Theorem 1: Channel Model
  • proof
  • Example 1: Signal-dependent Noise Simulations
  • Theorem 2: Conditional Variance of $Z_k$
  • proof
  • Example 2: Conditional Variance Convergence