Development of analytical model for energy detectors with SC and MRC diversity over Inverse‐Gamma fading

Abstract

Summary An ever‐escalating demand for wireless applications has caused great concern for the proper exploitation of the accessible radio spectrum. Cognitive radio materializes as an auspicious remedy to the present‐day crisis of spectral congestion, by detecting the licensed primary user (PU). This is accomplished with the assistance of the spectrum sensing technique, which provides an indication of the presence of PU over the spectrum. Energy detection is one of the prevailing spectrum sensing techniques due to its low implementation complexity. In the present work, the performance of an energy detector (ED) over Inverse‐Gamma (I‐Gamma) fading distribution is examined. Initially, a closed‐form expression of the probability density function for I‐Gamma distribution with maximal ratio combining diversity reception is derived. Following it, an investigation of an ED‐based cognitive radio device is carried out in the form of the average probability of detection (PD) and average area under the receiver operating characteristic curve (AUC). In addition, we also present a performance analysis of an ED with selection combining diversity. Optimization of the detection threshold is also executed alongside the low signal‐to‐noise ratio analysis. In the end, the resulting expression of the PD is exploited to examine the functioning of cooperative spectrum sensing within the erroneous environment. The validation of derived mathematical forms has been confirmed by comparing it with the Monte‐Carlo simulation and exact numerical results.

Analytical framework for the performance of energy detectors over α‐μ fading model with MRC diversity

“…Employing multiple SUs for spectrum detection is a more reasonable approach due to possibility of all SUs making a wrong decision becomes very less. In literature, 4,19 it has been confirmed that the mutual sharing of statistics helps in the enhancement of functioning of the ED.…”

“…This is achieved by reducing the total error rate (TER), denoted as . The optimum value of λ is attained by minimizing the TER 19 and can be expressed as , and for fixed J , the optimum the value of n , and as declared in Chauhan et al, 8 the n opt is given as where where is the ceiling function.…”

“…The optimum value of λ is attained by minimizing the TER 19 and can be expressed as λ opt ¼ argmin Q e ð Þ, and for fixed J, the optimum the value of n, and as declared in Chauhan et al, 8 the n opt is given as…”

“…14,15 In the past, various authors have acknowledged the study of the ED-based CR devices in their works like, Sofotasios et al 16 presented the performance analysis of spectrum sensing with ED over the Weibull fading model, while in Upaddhyay et al, 17 the analysis is extended to consider more realistic composite Weibull/Inverse-Gamma fading distribution. Verma et al 18 carried out analysis over the inverse-Gaussian fading model with SC diversity, whereas in Maurya et al, 19 the inverse-gamma fading model is employed to study the performance of ED with SC and MRC diversity. Yacoub et al 20,21 have proposed three new fading models, α-μ, κ-μ, and η-μ, respectively, to estimate the impact nonlinearity and non-homogeneity of the propagation environment under line-of-sight (LOS) and non-line-of-sight (NLOS) situations.…”