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Outage Probability in η-μ/η-μ Interference-limited Scenarios

Jose F. Paris

Abstract

In this paper exact closed-form expressions are derived for the outage probability (OP) in scenarios where both the signal of interest (SOI) and the interfering signals experience η-μ fading and the background noise can be neglected. With the only assumption that the μ parameter is a positive integer number for the interfering signals, the derived expressions are given in elementary terms for maximal ratio combining (MRC) with independent branches. The analysis is also valid when the μ parameters of the pre-combining SOI power envelopes are positive integer or half-integer numbers and the SOI is formed at the receiver from spatially correlated MRC.

Outage Probability in η-μ/η-μ Interference-limited Scenarios

Abstract

In this paper exact closed-form expressions are derived for the outage probability (OP) in scenarios where both the signal of interest (SOI) and the interfering signals experience η-μ fading and the background noise can be neglected. With the only assumption that the μ parameter is a positive integer number for the interfering signals, the derived expressions are given in elementary terms for maximal ratio combining (MRC) with independent branches. The analysis is also valid when the μ parameters of the pre-combining SOI power envelopes are positive integer or half-integer numbers and the SOI is formed at the receiver from spatially correlated MRC.

Paper Structure

This paper contains 11 sections, 2 theorems, 25 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Distribution of the Quotient of Sums of Squared $\eta$-$\mu$ RVs
  3. Outage Probability Analysis
  4. Interference-limited scenarios with independent MRC
  5. Type I, $\eta$-$\mu$/$\eta$-$\mu$ interference-limited scenario
  6. Type II, $\eta$-$\mu$/Nakagami-$m$ interference-limited scenario
  7. Extension to spatially correlated MRC
  8. Numerical Results
  9. Conclusions
  10. Proof of Lemma I
  11. Proof of Corollary I

Key Result

Lemma 1

Let $\{X_n\}_{n=1}^N$ and $\{Y_k\}_{k=1}^K$ be $N+K$ mutually independent squared $\eta$-$\mu$ RVs with sets of parameters, defined according to format 1, given by $\mathcal{S}_X\equiv\{\Omega_{X_n},\eta_{X_n},\mu_{X_n}\}_{n=1}^N$ and $\mathcal{S}_Y\equiv\{\Omega_{Y_k},\eta_{Y_k},\mu_{Y_k}\}_{k=1}^K Along this paper it is assumed that $\prod\limits_{k = a}^b {s_k }=1$ when $b<a$. where $(c)_{\ell}

Figures (3)

  • Figure 1: Type I OP expression (\ref{['eq:OP1']}) versus average SIR $\Omega$ for different values of $\mu$, where $\mathcal{S}_X\equiv\{\Omega_{X_n},\eta_{X_n},\mu_{X_n}\}_{n=1}^3=\{\{\Omega,2.6,\mu\},\{0.8\Omega,3.4,\mu\},\{0.7\Omega,1.7,\mu\}\}$, $\mathcal{S}_Y\equiv\{\Omega_{Y_k},\eta_{Y_k},\mu_{Y_k}\}_{k=1}^3=\{\{1,3.3,2\},\{1,3.3,2\},\{0.5,1.7,1\}\}$ and $\zeta_o=10$.
  • Figure 2: Type II OP expression (\ref{['eq:OP2']}) versus average SIR $\Omega$ for different values of $m$, where $\mathcal{S}_X\equiv\{\Omega_{X_n},\eta_{X_n},\mu_{X_n}\}_{n=1}^2 =\{\{2\Omega,1,0.5\},\{0.7\Omega,0.6,2\}\}$, $\mathcal{G}_Y\equiv\{\Omega_{Y_k},m_{Y_k}\}_{k=1}^4=\{\{1,m\},\{1,m\},\{0.5,m\},\{0.2,m\}\}$ and $\zeta_o=10$.
  • Figure 3: Singularity structure of the integration kernel $\Xi(p)$ and integration paths involved in the proof of Lemma 1.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Corollary 1
  • proof