Analytic solutions to a Marcum Q-function-based integral and application in energy detection of unknown signals over multipath fading channels

This work presents analytic solutions for a useful integral in wireless communications, which involves the Marcum $Q{-}$function in combination with an exponential function and arbitrary power terms. The derived expressions have a rather simple algebraic representation which renders them convenient both analytically and computationally. Furthermore, they can be useful in wireless communications and particularly in the context of cognitive radio communications and radar systems, where this integral is often encountered. To this end, we derive novel expressions for the probability of detection in energy detection based spectrum sensing over $\eta{-}\mu$ fading channels. These expressions are given in closed-form and are subsequently employed in analyzing the effects of generalised multipath fading conditions in cognitive radio systems. As expected, it is shown that the detector is highly dependent upon the severity of fading conditions as even slight variation of the fading parameters affect the corresponding performance significantly.Comment: Latest/Preprint Versio

Solutions to Integrals Involving the Marcum Q-Function and Applications

Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals. The offered expressions are both convenient and versatile, which is particularly useful in applications relating to natural sciences and engineering, including wireless cpmmunications and signal processing. To this end, they are employed in the derivation of the channel capacity for fixed rate and channel inversion in the case of correlated multipath fading and switched diversity.Comment: 15 Pages, 2 Figure

Energy Detection of Unknown Signals over Cascaded Fading Channels

Energy detection is a favorable mechanism in several applications relating to the identification of deterministic unknown signals such as in radar systems and cognitive radio communications. The present work quantifies the detrimental effects of cascaded multipath fading on energy detection and investigates the corresponding performance capability. A novel analytic solution is firstly derived for a generic integral that involves a product of the Meijer $G-$function, the Marcum $Q-$function and arbitrary power terms. This solution is subsequently employed in the derivation of an exact closed-form expression for the average probability of detection of unknown signals over $N$*Rayleigh channels. The offered results are also extended to the case of square-law selection, which is a relatively simple and effective diversity method. It is shown that the detection performance is considerably degraded by the number of cascaded channels and that these effects can be effectively mitigated by a non-substantial increase of diversity branches.Comment: 12 page

Area under ROC curve of energy detection over generalized fading channels

A fast and reliable detection scheme is essential in several wireless applications such as radar and cognitive radio systems. Energy detection is such a method as it does not require a priori information of the received signal while it exhibits low implementation complexity and costs. Since the detection capability of ED is largely affected by the effects of multipath fading, this paper is devoted to a thorough analysis of energy detection based spectrum sensing over generalized fading conditions. To this end, analytical expressions are firstly derived using the area under the receiver operating characteristic curve (AUC) under additive white Gaussian noise. This analysis is subsequently extended to the case of generalized fading conditions characterized by k - μ and η - μ fading distributions. The offered results are novel and are employed in analyzing the corresponding performance. It is shown that fading phenomena result to detrimental effects on the performance of spectrum sensing since the deviation between severe and non-severe conditions is rather substantial

A Comprehensive Framework for Spectrum Sensing in Non-Linear and Generalized Fading Conditions

We derive a comprehensive analytical framework for the ED over generalized, extreme, and non-linear fading conditions which addresses the topic completely. This is carried out for both conventional and diversity receptions and it is based on the area under the ROC curve (AUC), which is an efficient performance measure that is widely used in physical sciences and engineering. This differentiates the considered methodology from the aforementioned routine approaches and additionally provides generic results on the arbitrary derivatives of the MGF of useful generalized processes. The asymptotic behavior of the derived expressions is also analyzed providing direct and concrete insights on the role and effect of the involved parameters on the ED performance. The offered analytic results are subsequently employed in quantifying the performance of ED over various types of fading conditions, which exhibits that ED performance is significantly degraded by even slight variations of the severity of fading. To this end, it is shown that the detrimental effects of fading can be effectively mitigated with the aid of square-law combining and switch-and-stay combining methods, as a low number of diversity branches can ensure sufficient and holistic performance improvement even in severe fading conditions