[Paper Review] Performance of Cognitive Radio Systems over $\kappa-\mu$ Shadowed with Integer $\mu$ and Fisher-Snedecor $\mathcal{F}$ Fading Channels

Hussien Al‐Hmood|arXiv (Cornell University)|Jul 25, 2018

Cognitive Radio Networks and Spectrum Sensing13 references3 citations

TL;DR

This paper proposes exact, closed-form expressions for the PDF and CDF of the signal-to-noise ratio (SNR) in κ−μ shadowed and Fisher-Snedecor ℱ fading channels under integer fading parameters, enabling precise performance analysis of cognitive radio systems. It derives exact analytical expressions for energy detection metrics (average detection probability and AUC) and effective rate, validated through simulations and comparisons with conventional models.

ABSTRACT

In this paper, we analyze the performance of cognitive radio (CR) systems over different composite generalized multipath /shadowed fading scenarios. The \k{appa}-{\mu} shadowed and Fisher-Snedecor F fading channels which are proposed as a simple and high accurate distributions in comparison with generalized-K (KG) and Nakagami-m shadowed conditions are used in this analysis. For the \k{appa}-{\mu} shadowed, a novel simple exact closed-form analytic expression for the probability density function (PDF) and the cumulative distribution function (CDF) are introduced by assuming the fading parameters are integer numbers. To this end, the detection performance metrics, namely, the average detection probability and the average area under the receiver operating characteristics curve (AUC) which are used in the analysis of energy detection and the effective rate and the effective rate are derived. To validate the results of this work, comparisons between the simulated and numerical results as well as with various conventional channel models and scenarios are given.

Motivation & Objective

• To develop simple, exact closed-form expressions for the SNR PDF and CDF in κ−μ shadowed fading under integer fading parameters.
• To analyze energy detection performance metrics—average detection probability and AUC—over κ−μ shadowed and Fisher-Snedecor ℱ fading channels.
• To derive exact expressions for the effective rate in cognitive radio systems over these generalized fading models.
• To validate analytical results through Monte Carlo simulations and comparisons with conventional fading models.

Proposed method

• Derives a closed-form PDF for κ−μ shadowed fading by assuming integer values for κ and μ, using convolution of Gamma-distributed MGFs and binomial expansion.
• Employs inverse Laplace transforms and properties of the lower incomplete Gamma function to express the SNR PDF in terms of power and exponential functions.
• Applies the derived PDFs to compute key energy detection metrics: average detection probability and average AUC, using integral expressions involving the CDF.
• Uses the Meijer G-function and hypergeometric function identities to evaluate the effective rate integral in closed form for both fading models.
• Validates results via Monte Carlo simulations with 10^5 iterations, comparing numerical and simulated curves.
• Introduces a novel analytical framework for Fisher-Snedecor ℱ fading in cognitive radio systems, a model not previously used for ED or effective rate analysis.

Experimental results

Research questions

• RQ1 Can exact, closed-form expressions for the SNR PDF and CDF be derived in κ−μ shadowed fading when κ and μ are integers?
• RQ2 How do the average detection probability and AUC of energy detection vary over κ−μ shadowed and Fisher-Snedecor ℱ fading channels under integer parameters?
• RQ3 What is the exact analytical expression for the effective rate in cognitive radio systems over these generalized fading models?
• RQ4 How do the fading parameters (κ, μ, ƒ, ƒb) influence detection performance and effective rate in these scenarios?
• RQ5 How accurate are the derived analytical expressions compared to Monte Carlo simulations and conventional fading models?

Key findings

• The PDF of κ−μ shadowed fading is derived in exact closed form using integer κ and μ, expressed via binomial coefficients and incomplete Gamma functions.
• The average detection probability and AUC for energy detection are derived in exact closed form for both κ−μ shadowed and Fisher-Snedecor ℱ fading channels.
• The effective rate is derived in closed form for both fading models, with the Fisher-Snedecor ℱ case expressed using the hypergeometric function 2F1.
• Simulations confirm perfect agreement between numerical results and Monte Carlo simulations, validating the analytical derivations.
• Performance improves with increasing κ (dominant wave power) and μ (number of multipath clusters), and with higher ƒ or ƒb (reduced shadowing severity).
• The proposed models outperform conventional fading models in accuracy, especially in scenarios with strong line-of-sight and moderate-to-strong shadowing.