Energy Detection of Gaussian Signals Subject to Impulsive Noise in Generalized Fading Channels

Abstract

Novel, simple, and accurately approximated expressions for the probability of detection of Gaussian signals in $\eta -\mu$, $\kappa -\mu$, and $\alpha -\mu$ fading channels at the output of an energy detector subject to impulsive noise (Bernoulli-Gaussian model) are presented. The generalized Gauss-Laguerre quadrature is used to approximate the probability of detection as a finite sum. Monte Carlo simulations corroborate the accuracy of the approximations. The results are further extended to cooperative detection with hard decision combining information.

Appendix A

The generalized Gauss-Laguerre quadrature [7] states that, for any real number $\beta > -1$,

$$\begin{aligned} \int \limits _{0}^{\infty }t^{\beta }e^{-t}{f}(t)\;\mathrm {d}t \approx \sum _{n=1}^{M}v_n{f}(r_n), \end{aligned}$$

(18)

in which $r_n$ is the n-th root of the generalized Laguerre polynomial of order M, i.e. $L_{M}^{\beta }$, and the weight $v_n$ is given as

$$\begin{aligned} v_n = \dfrac{r_n\varGamma (M + \beta + 1)}{M!(M+1)^2\left[ {L}_{M+1}^{\beta }(r_n)\right] ^2}. \end{aligned}$$

(19)