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

Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory

This paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall Q-function, incomplete Toronto function, Rice Ie-function, and incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and Humbert, Φ1, function as well as for specific cases of the Kampé de Fériet function. These functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems, such as cognitive radio, cooperative, and free-space optical communications as well as radar, diversity, and multiantenna systems. As an example, new closed-form expressions are derived for the outage probability over nonlinear generalized fading channels, namely, α-η-μ, α-λ-μ, and α-κ-μ as well as for specific cases of the η-μ and λ-μ fading channels. Furthermore, simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal-to-noise ratio for single-antenna and multiantenna communication systems over Rician fading channels. The accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results

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

Energy detection based spectrum sensing over enriched multipath fading channels

Energy detection has been for long constituting the most popular sensing method in RADAR and cognitive radio systems. The present paper investigates the sensing behaviour of an energy detector over Hoyt fading channels, which have been extensively shown to provide rather accurate characterization of enriched multipath fading conditions. To this end, a simple series representation and an exact closed-form expression are firstly derived for the corresponding average probability of detection for the conventional single-channel communication scenario. These expressions are subsequently employed in deriving novel analytic results for the case of both collaborative detection and square-law selection diversity reception. The derived expressions have a relatively tractable algebraic representation which renders them convenient to handle both analytically and numerically. As a result, they can be utilized in quantifying the effect of fading in energy detection based spectrum sensing and in the determination of the trade-offs between sensing performance and energy efficiency in cognitive radio communications. Based on this, it is shown that the performance of the energy detector depends highly on the severity of fading as even slight variations of the fading conditions affect the value of the average probability of detection. It is also clearly shown that the detection performance improves substantially as the number of branches or collaborating users increase. This improvement is substantial in both moderate and severe fading conditions and can practically provide full compensation for the latter cases

Energy Detection Based Spectrum Sensing Over k-μ and k-μ Extreme Fading Channels

Energy detection (ED) is a simple and popular method of spectrum sensing in cognitive radio systems. It is also widely known that the performance of sensing techniques is largely affected when users experience fading effects. This paper investigates the performance of an energy detector over generalized κ-μ and κ- μ extreme fading channels, which have been shown to provide remarkably accurate fading characterization. Novel analytic expressions are firstly derived for the corresponding average probability of detection for the case of single-user detection. These results are subsequently extended to the case of square-law selection (SLS) diversity and for collaborative detection scenarios. As expected, the performance of the detector is highly dependent upon the severity of fading since even small variations of the fading conditions affect significantly the value of the average probability of detection. Furthermore, the performance of the detector improves substantially as the number of branches or collaborating users increase in both severe and moderate fading conditions, whereas it is shown that the κ- μ extreme model is capable of accounting for fading variations even at low signal-to-noise values. The offered results are particularly useful in assessing the effect of fading in ED-based cognitive radio communication systems; therefore, they can be used in quantifying the associated tradeoffs between sensing performance and energy efficiency in cognitive radio networks.

Multi-RAT Aggregation Through Spectrum Reallocation for Future Wireless Networks

Next generation wireless networks are becoming the main focus of the industry by putting efforts to launch beyond 4G (i.e. 5G) communication systems by 2020. Towards the 5G-system vision, the efficient spectrum aggregation by integrating multiple radio access technologies (multi-RAT) is one of the enablers to achieve the highest data rates. To this end, a multi-RAT aggregation is envisioned that can be provided using the spectrum reallocation technique. Spectrum reallocation among multi-RATs can provide spectrum opportunities for aggregation and, thus, the overall spectrum utilization and network capacity increase. Maintaining an optimum quality of experience (QoE) for users of different RATs in such an extremely complex network environment can be facilitated by such a multi-RAT aggregation (spectrum aggregation from different RATs), through spectrum reallocation. To this end, both network and functional architectures are specified and spectrum assignment solutions are proposed in this article. The goal is to efficiently increase the data rates supporting a required QoE for all users

Is backscatter link stronger than direct link in reconfigurable intelligent surface-assisted system?

This letter considers integrating a backscatter link with a reconfigurable intelligent surface to enhance backscatter communication while assisting the direct communication. We derive the probability that the backscatter channel dominates in the composite channel. This probability is a useful performance measure to determine the number of reflectors. Since the exact probability lacks a closed-form solution, we develop two approximations by modeling the gain of the backscatter link with a Gaussian or Gamma distribution. We found that these approximations match well with the exact value. Importantly, with a well-designed number of reflectors, the channel gain of the backscatter link may be always stronger than that of the direct one

The κ-μ/IG composite statistical distribution in RF and FSO wireless channels

The aim of this work is the proposition of the κ-μ/Inverse Gaussian distribution which corresponds to a physical fading model. This is a composite distribution which is based on the κ-μ multipath model and the recently proposed Inverse Gaussian shadowing model. The former is a generalised model which includes as special cases the widely known Nakagamim, Rayleigh, Rice and one sided Gaussian distributions and accounts particularly for Non-Line-of-Sight communications. The latter is a convenient model which was recently shown to characterize shadowing effect more accurately than the widely used gamma distribution. As a result, the proposed composite model provides an overall efficient characterisation of multipath and shadowing effects which typically occur simultaneously. The offered modelling accuracy is achieved thanks to the remarkable flexibility of its parameters which is verified by the fact that the model is capable of providing good fittings to measurement data from realistic communication scenarios. Novel analytic expressions are derived for the probability density function (pdf) and the moments of the κ-μ/Inverse Gaussian composite fading model which includes as special cases the Nakagami-m/Inverse Gaussian, Rayleigh/Inverse Gaussian and Rice/Inverse Gaussian composite fading distributions. The offered expressions can be readily utilized in the derivation of vital performance measures in radio and free-space-optical communications over multipath/shadowing and medium-to-strong atmospheric turbulence, respectively. In this context, a closed-form expression is derived for the Amount of Fading over κ-μ/IG fading channels

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 η - μ 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