[Paper Review] Outage Probability in {\eta}-{\mu}/{\eta}-{\mu} Interference-limited Scenarios

José F. Paris|arXiv (Cornell University)|Mar 2, 2011

Advanced MIMO Systems Optimization5 references3 citations

TL;DR

This paper derives exact, closed-form expressions for outage probability (OP) in η-μ/η-μ interference-limited wireless systems, where both the desired signal and cochannel interferers experience η-μ fading and noise is negligible. The key contribution is a master formula (Equation 1) that enables elementary-term OP expressions under the condition that the µ parameter of interfering signals is a positive integer, extending prior Nakagami-m results to the more general η-μ model with spatially correlated maximal ratio combining (MRC).

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 {\eta}-{\mu} fading and the background noise can be neglected. With the only assumption that the {\mu} 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 {\mu} 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.

Motivation & Objective

• To derive exact, closed-form expressions for outage probability (OP) in η-μ/η-μ interference-limited scenarios where background noise is negligible.
• To extend existing OP analysis for Nakagami-m/Nakagami-m fading to the more general η-μ fading model.
• To provide a unified analytical framework valid for both independent and spatially correlated maximal ratio combining (MRC) at the receiver.
• To establish a master formula that generalizes and complements prior results in the literature, particularly for cases with real-valued m parameters or correlated MRC.

Proposed method

• Derives a master formula (Equation 1) for the cumulative distribution function (CDF) of the ratio of sums of squared η-μ random variables (RVs), representing the signal-to-interference power ratio.
• Applies Laplace transform and residue theory to the moment generating functions (MGFs) of the sum of independent η-μ RVs for both the desired signal and interferers.
• Uses the Pochhammer symbol and generalized hypergeometric functions to express the CDF in elementary terms via residue calculus.
• Introduces a formal parameterization using sets {aℓ, αℓ} from the SOI parameters and {bj, βj} from the interferer parameters, where βj are distinct values from intermediate coefficients.
• Applies the residue theorem to compute the CDF by summing residues at poles corresponding to the distinct βj values.
• Validated through Corollary 1, which reduces the general η-μ/η-μ case to the Nakagami-m/Nakagami-m scenario by taking the limit η→0, confirming consistency with prior results.

Experimental results

Research questions

• RQ1 Can exact, closed-form expressions for outage probability be derived in η-μ/η-μ interference-limited scenarios with negligible background noise?
• RQ2 Does the derived formula generalize existing Nakagami-m/Nakagami-m results, particularly for non-integer m parameters or spatially correlated MRC?
• RQ3 What is the mathematical structure of the CDF for the ratio of sums of squared η-μ RVs when the interferer µ parameters are positive integers?
• RQ4 How does the proposed method handle spatial correlation in MRC combining for the signal of interest?
• RQ5 Can the framework be extended to mixed scenarios, such as η-μ/Rayleigh interference-limited systems?

Key findings

• A master formula (Equation 1) is derived that provides exact, closed-form expressions for the outage probability in η-μ/η-μ interference-limited systems with elementary functions.
• The derivation is valid under the condition that the µ parameter of interfering signals is a positive integer, enabling exact residue-based evaluation.
• The formula generalizes prior results for Nakagami-m/Nakagami-m fading, including [3, eq. 10.17] and [8, eq. 18], by extending them to the η-μ model.
• The method supports spatially correlated MRC for the signal of interest, enabling analysis of correlated diversity combining in non-identical fading environments.
• Corollary 1 confirms consistency with the Nakagami-m case by showing that the η-μ model reduces to Nakagami-m as η→0, with the same closed-form structure.
• Numerical results in Figures 1 and 2 validate the analytical expressions against simulations, showing perfect agreement across various η-μ and Nakagami-m parameter settings.