Communications Performance Analysis of Wireless Multiple Access Channel with Specially Correlated Sources

TL;DR

This work analyzes a two-user MAC with specially correlated sources in a continuous alphabet (Gaussian) wireless setting, emphasizing the need to model dependence via Copula theory. It extends the Slepian–Wolf capacity framework to Gaussian/wireless MACs and derives achievable rate regions for both DM-MAC and wireless SW-MAC with correlated sources. By applying the FGM copula to model correlated fading coefficients, the authors obtain closed-form outage probability expressions $P_{ ext{out}}$ that reveal negative dependence can reduce outages, supported by numerical simulations. The results provide guidance for MAC design under dependence, with future work suggested on alternative fading models (e.g., Rician) and copula families to further improve efficiency in complex multiuser environments.

Abstract

From both practical and theoretical viewpoints, performance analysis of communication systems using information-theoretic results is very important. In this study, first, we obtain a general achievable rate for a two-user wireless multiple access channel (MAC) with specially correlated sources as a more general version for continuous alphabet MACs, by extending the known discrete alphabet results to the wireless continuous alphabet version. Next, the impact of wireless channel coefficients correlation on the performance metrics using Copula theory, as the most convenient way for describing the dependence between several variables, is investigated. By applying the Farlie-Gumbel-Morgenstern (FGM) Copula function, we obtain closed-form expressions for the outage probability (OP) under positive/negative dependence conditions. It is shown that the fading correlation improves the OP for a negative dependence structure. Specifically, whenever the dependence structure tends to negative values, the OP decreases and the efficiency of the channel increases. Finally, the efficiency of the analytical results is illustrated numerically.

Figures (4)

• Figure 1: Multiple Access Channel with Rayleigh Fading Coefficients.
• Figure 2: Outage Probability vs $R_0$ For $P2=5$ and $10$ watts, and $P1=1$ watt, and Various Dependence Parameters.
• Figure 3: Outage Probability vs $R_0$ For $P1=1$ watt, and $P2=1$ watt, and Various Dependence Parameters.
• Figure 4: Outage Probability vs $R_0$ For $P1=5$ and $10$ watts, and $P2=1$ watt, and Various Dependence Parameters.

Theorems & Definitions (10)

• Definition 1: Copula Function
• Theorem 1: Sklar's theorem
• Definition 2: FGM Copula
• Theorem 2: Two-User DM-MAC with Specially Correlated Sources
• proof : Proof of Theorem \ref{['thm2']}
• Theorem 3: Two-User Gaussian MAC with Specially Correlated Sources
• proof : Proof of Theorem \ref{['thm3']}
• Definition 3: OP
• Theorem 4: The OP in wireless specially correlated sources MAC is given
• proof : Proof of Theorem \ref{['thm4']}