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Outage Probability in Network Coding Based Cooperative Wireless Networks over Nakagami-m Fading Channels

Elias Benamira, Fatiha Merazka, Güneş Karabulut Kurt

TL;DR

This work addresses the outage performance of network-coded cooperative wireless networks operating under Nakagami-$m$ fading. It develops exact closed-form outage expressions for a two S-D pair, two-relay topology and extends the results to general $N$ S-D pairs and $M$ relays by deriving a product-form end-to-end outage probability and a corresponding diversity order. The authors validate the analytic expressions with Monte-Carlo simulations using the equivalent end-to-end SNR and analyze how the fading parameter $m$ on individual links shapes performance, revealing practical implications for relay selection and power allocation. The results quantify the diversity gain as $d=2m$ in the basic setup and as $d=NM$ in the generalized topology, enabling precise outage predictions and resource planning in NCC-enabled networks over Nakagami-$m$ channels.

Abstract

In this paper, we develop an accurate closed-form analytic expression of the outage probability for each source-destination (S-D) pair in the two S-D pairs two relays wireless network, where cooperative network coding is applied over Nakagami-$m$ fading channels. For different values of the shape parameter $m$, our analytic relation is validated with Monte-Carlo simulations of the outage probability using the overall equivalent signal-to-noise ratio (SNR) within each source-destination pair. The outage probability is also provided for the extended versions of the network consisting of multiple relays and multiple S-D pairs. Furthermore, we investigate the role of varying the fading factor ($m$ values) on different links in the end-to-end outage probability performance, which yields interesting results that may be crucial for relay selection and power allocation procedures. Moreover, we derive the diversity order for the generalized extended version of cooperative network coded wireless networks.

Outage Probability in Network Coding Based Cooperative Wireless Networks over Nakagami-m Fading Channels

TL;DR

This work addresses the outage performance of network-coded cooperative wireless networks operating under Nakagami- fading. It develops exact closed-form outage expressions for a two S-D pair, two-relay topology and extends the results to general S-D pairs and relays by deriving a product-form end-to-end outage probability and a corresponding diversity order. The authors validate the analytic expressions with Monte-Carlo simulations using the equivalent end-to-end SNR and analyze how the fading parameter on individual links shapes performance, revealing practical implications for relay selection and power allocation. The results quantify the diversity gain as in the basic setup and as in the generalized topology, enabling precise outage predictions and resource planning in NCC-enabled networks over Nakagami- channels.

Abstract

In this paper, we develop an accurate closed-form analytic expression of the outage probability for each source-destination (S-D) pair in the two S-D pairs two relays wireless network, where cooperative network coding is applied over Nakagami- fading channels. For different values of the shape parameter , our analytic relation is validated with Monte-Carlo simulations of the outage probability using the overall equivalent signal-to-noise ratio (SNR) within each source-destination pair. The outage probability is also provided for the extended versions of the network consisting of multiple relays and multiple S-D pairs. Furthermore, we investigate the role of varying the fading factor ( values) on different links in the end-to-end outage probability performance, which yields interesting results that may be crucial for relay selection and power allocation procedures. Moreover, we derive the diversity order for the generalized extended version of cooperative network coded wireless networks.
Paper Structure (5 sections, 2 theorems, 33 equations, 6 figures)

This paper contains 5 sections, 2 theorems, 33 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Outage Analysis
  4. Simulation Results
  5. Conclusion

Key Result

Theorem 1

(Extended multiple S-D pairs multiple relays network) In an extended version of the network constituted of $N$ source-destination pairs and two relays with $i.i.d.$ Nakagami-$m$ fading channel links and the same value of fading factor $m$, the outage probability expression is given by Moreover, if we have $M$ ($M>2$) relays $R_1, R_2,...,R_M$ in series instead of two ($R_1$ being always the one i

Figures (6)

  • Figure 1: Considered system: Two S-D pairs two relays wireless network
  • Figure 2: Extended topology of the wireless network with $M$ relays and $N$ source-destination pairs
  • Figure 3: Decreasing analytic outage probability of (\ref{['16']}) tightly with MC simulated BER for increasing values of $m$ (0.5, 1, 2) and $R_t\approx 1.1~bps/Hz$.
  • Figure 4: Precise match of simulated with analytic decreasing outage probabilities with increasing values of $m$ ($0.5, 1, 2, 4$).
  • Figure 5: Outage probability of expression (\ref{['15']}) for $m = 2$ or $m = 4$ on the links and $R_t = 1~bps/Hz$.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2