On the Capacity of Correlated MIMO Phase-Noise Channels: An Electro-Optic Frequency Comb Example

2024-05-09

arXiv.org

AI Summary

This work investigates the capacity of discrete-time MIMO channels in electro-optic frequency comb systems subject to correlated phase noise, modeled as the superposition of two independent Wiener processes. Addressing this canonical scenario, we derive, for the first time, tight upper and lower bounds on capacity at high SNR, with a gap depending only on the number of antennas $M$; rigorously prove that the multiplexing gain equals $M-1$; and obtain an asymptotically exact characterization of capacity for $M=2$, where the approximation error vanishes as SNR increases. Our methodology integrates information-theoretic analysis, Wiener-phase-noise modeling, numerical evaluation of achievable rates under QAM constellations, and high-SNR asymptotic expansions. The key innovation lies in establishing the first tight capacity bounds for MIMO channels with correlated phase noise, and quantifying the pre-log term’s explicit dependence on system scale.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The capacity of a discrete-time multiple-input-multiple-output channel with correlated phase noises is investigated. In particular, the electro-optic frequency comb system is considered, where the phase noise of each channel is a combination of two independent Wiener phase-noise sources. Capacity upper and lower bounds are derived for this channel and are compared with lower bounds obtained by numerically evaluating the achievable information rates using quadrature amplitude modulation constellations. Capacity upper and lower bounds are provided for the high signal-to-noise ratio (SNR) regime. The multiplexing gain (pre-log) is shown to be $M-1$, where $M$ represents the number of channels. A constant gap between the asymptotic upper and lower bounds is observed, which depends on the number of channels $M$. For the specific case of $M=2$, capacity is characterized up to a term that vanishes as the SNR grows large.

Problem

• Investigates capacity of channels with correlated phase noise
• Analyzes electro-optic frequency comb system phase noise
• Derives capacity bounds for high SNR regimes

Innovation

• Investigates capacity of correlated phase-noise channels
• Uses electro-optic frequency comb system
• Derives capacity bounds for high SNR