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Influence of Behavioral Models on Multiuser Channel Capacity

Erik Agrell, Magnus Karlsson

TL;DR

This work investigates how interferer behavioral models in a multiuser WDM optical link shape the achievable rate of a single subchannel. By analyzing a simple three-channel, weakly nonlinear model, it derives upper and lower bounds on $C_1(P_1)$ under three distinct interferer behaviors and shows that capacity can grow unbounded with power under certain conditions, especially when interferers are discrete and can be canceled at the receiver. The results demonstrate that the chosen behavioral model has a profound influence on capacity predictions, sometimes yielding unbounded growth or power-dependent peaks, which challenges common assumptions in optical capacity analyses. The study highlights the need to explicitly specify behavioral models in single-user channel analyses and suggests directions for extending the framework to more realistic, strongly nonlinear, and dispersion-including settings with more channels.

Abstract

In order to characterize the channel capacity of a wavelength channel in a wavelength-division multiplexed (WDM) system, statistical models are needed for the transmitted signals on the other wavelengths. For example, one could assume that the transmitters for all wavelengths are configured independently of each other, that they use the same signal power, or that they use the same modulation format. In this paper, it is shown that these so-called behavioral models have a profound impact on the single-wavelength achievable information rate. This is demonstrated by establishing, for the first time, upper and lower bounds on the maximum achievable rate under various behavioral models, for a rudimentary WDM channel model.

Influence of Behavioral Models on Multiuser Channel Capacity

TL;DR

This work investigates how interferer behavioral models in a multiuser WDM optical link shape the achievable rate of a single subchannel. By analyzing a simple three-channel, weakly nonlinear model, it derives upper and lower bounds on under three distinct interferer behaviors and shows that capacity can grow unbounded with power under certain conditions, especially when interferers are discrete and can be canceled at the receiver. The results demonstrate that the chosen behavioral model has a profound influence on capacity predictions, sometimes yielding unbounded growth or power-dependent peaks, which challenges common assumptions in optical capacity analyses. The study highlights the need to explicitly specify behavioral models in single-user channel analyses and suggests directions for extending the framework to more realistic, strongly nonlinear, and dispersion-including settings with more channels.

Abstract

In order to characterize the channel capacity of a wavelength channel in a wavelength-division multiplexed (WDM) system, statistical models are needed for the transmitted signals on the other wavelengths. For example, one could assume that the transmitters for all wavelengths are configured independently of each other, that they use the same signal power, or that they use the same modulation format. In this paper, it is shown that these so-called behavioral models have a profound impact on the single-wavelength achievable information rate. This is demonstrated by establishing, for the first time, upper and lower bounds on the maximum achievable rate under various behavioral models, for a rudimentary WDM channel model.

Paper Structure

This paper contains 11 sections, 8 theorems, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System model
  3. Behavioral models in multiuser communications
  4. Information theory
  5. Upper bounds
  6. Lower bounds
  7. Results
  8. Behavioral model (a)---fixed interferer distributions
  9. Behavioral model (b)---adaptive interferer power
  10. Behavioral model (c)---adaptive interferer distribution
  11. Conclusions and discussion

Key Result

Lemma 1

If $X$ and $Z$ are independent, then

Figures (3)

  • Figure 1: A single-user channel model can be seen as a combination of a multiuser channel model and a behavioral model for all users but one. Transmitter and receiver are marked Tx and Rx, respectively.
  • Figure 2: The achievable rates ${C_1}(P_1)$ of user 1 in a WDM system, with the three behavioral models (a), (b), and (c), defined in Sec. \ref{['sec:behavioral']}, as a function of the signal power $P_1$. Dashed lines give upper bounds and solid lines lower bounds. Shaded regions indicate the amount of uncertainty. Behavioral models (a) and (b) both have two versions, depending on the type of interferer distributions. In (c), the lower bound is obtained as the envelope of multiple bounds, indicated with gray curves. Dotted vertical lines correspond to curves in Fig. \ref{['mi-psk']}.
  • Figure 3: The mutual information according to Theorem \ref{['th:mi-discrete']} for $M$-PSK constellations with uniform probabilities, for the indicated values of $P_1/P_\text{ase}$. The peak of each curve yields the lower bound in Fig. \ref{['miplots']} (c).

Theorems & Definitions (8)

  • Lemma 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Lemma 6
  • Lemma 7
  • Theorem 8