arXiv subjects

Paschalis C. Sofotasios

Publications and source records attributed to Paschalis C. Sofotasios.

52 records · Page 3Linked to original sources

arXiv2015

Error Rate and Power Allocation Analysis of Regenerative Networks under Generalized Fading Conditions

Cooperative communication has been shown to provide significant increase of transmission reliability and network capacity while expanding coverage in cellular networks. The present work is devoted to the investigation of the end-to-end performance and power allocation of a maximum-ratio-combining based regenerative multi-relay cooperative network over non-homogeneous scattering environment, which is the case in realistic wireless communication scenarios. Novel analytic expressions are derived for the end-to-end symbol-error-rate of both $M-$ary Phase-Shift Keying and $M-$ary Quadrature Amplitude Modulation over independent and non-identically distributed generalized fading channels. The offered results are expressed in closed-form involving the Lauricella function and can be readily evaluated with the aid of a proposed computational algorithm. Simple expressions are also derived for the corresponding symbol-error-rate at asymptotically high signal-to-noise ratios. The derived expressions are corroborated with respective results from computer simulations and are subsequently employed in formulating a power optimization problem that enhances the system performance under total power constraints within the multi-relay cooperative system. Furthermore, it is shown that optimum power allocation provides substantial performance gains over equal power allocation, particularly, when the source-relay and relay-destination paths are highly unbalanced.

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arXiv2015

Exact Error Analysis and Energy-Efficiency Optimization of Regenerative Relay Systems with Spatial Correlation

Energy efficiency and its optimization constitute critical tasks in the design of low-power wireless networks. The present work is devoted to the error rate analysis and energy-efficiency optimization of regenerative cooperative networks in the presence of multipath fading under spatial correlation. To this end, exact and asymptotic analytic expressions are firstly derived for the symbol-error-rate of $M{-}$ary quadrature amplitude and $M{-}$ary phase shift keying modulations assuming a dual-hop decode-and-forward relay system, spatially correlated Nakagami${-}m$ multipath fading and maximum ratio combining. The derived expressions are subsequently employed in quantifying the energy consumption of the considered system, incorporating both transmit energy and the energy consumed by the transceiver circuits, as well as in deriving the optimal power allocation formulation for minimizing energy consumption under certain quality-of-service requirements. A relatively harsh path-loss model, that also accounts for realistic device-to-device communications, is adopted in numerical evaluations and various useful insights are provided for the design of future low-energy wireless networks deployments. Indicatively, it is shown that depending on the degree of spatial correlation, severity of fading, transmission distance, relay location and power allocation strategy, target performance can be achieved with large overall energy reduction compared to direct transmission reference.

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arXiv2015

On the $η-μ$/gamma and the $λ-μ$/gamma Composite Distributions

This work is devoted to the formulation and derivation of the $η{-}μ{/}$gamma and $λ{-}μ{/}$gamma distributions which correspond to physical fading models. These distributions are composite and are based on the $η-μ$ and $λ-μ$ generalized multipath models, respectively, and the gamma shadowing model. Novel analytic expressions are derived for the corresponding envelope probability density functions. Importantly, the proposed models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects which is achieved thanks to the remarkable flexibility offered by their parameters that render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is additionally justified by the fact that they include as special cases the widely known fading models such as Hoyt/gamma, Nakagami-m/gamma and Rayleigh/gamma. As a result, they can be meaningfully utilized in various analytical studies related to the performance evaluation of digital communications over composite multipath/shadowing fading channels.

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arXiv2015

Solutions to the Incomplete Toronto Function and Incomplete Lipschitz-Hankel Integrals

This paper provides novel analytic expressions for the incomplete Toronto function, $T_{B}(m,n,r)$, and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function of the first kind, $Ie_{m,n}(a,z)$. These expressions are expressed in closed-form and are valid for the case that $n$ is an odd multiple of $1/2$, i.e. $n \pm 0.5\in\mathbb{N}$. Capitalizing on these, tight upper and lower bounds are subsequently proposed for both $T_{B}(m,n,r)$ function and $Ie_{m,n}(a,z)$ integrals. Importantly, all new representations are expressed in closed-form whilst the proposed bounds are shown to be rather tight. To this effect, they can be effectively exploited in various analytical studies related to wireless communication theory. Indicative applications include, among others, the performance evaluation of digital communications over fading channels and the information-theoretic analysis of multiple-input multiple-output systems.

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arXiv2015

Tight Approximations for the Two Dimensional Gaussian $Q-$function

The aim of this work is the derivation of two approximated expressions for the two dimensional Gaussian Q-function, $Q(x,y;ρ)$. These expressions are highly accurate and are expressed in closed-form. Furthermore, their algebraic representation is relatively simple and therefore, convenient to handle both analytically and numerically. This feature is particularly useful for two reasons: firstly because it renders the derived expressions useful mathematical tools that can be utilized in numerous analytic performance evaluation studies in digital communications under fading; secondly because the two dimensional Gaussian Q-function is neither tabulated nor a built-in function in popular mathematical software packages such as $Maple$, $Mathematica$ and $Matlab$.

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arXiv2015

On the $κ$-$μ$/Gamma Generalized Multipath/ Shadowing Fading Distribution

This work is devoted to the formulation and derivation of the $κ-μ$/gamma distribution which corresponds to A physical fading model. This distribution is composite and is based on the well known $κ-μ$ generalized multipath model and the gamma shadowing model. A special case of the derived model constitutes the $κ-μ$ Extreme/gamma model which accounts for severe multipath and shadowing effects. These models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects. This is achieved thanks to the remarkable flexibility of their named parameters which render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is additionally justified by the fact that they include as special cases the widely known composite fading models such as Rice/gamma, Nakagami-m/gamma and Rayleigh/gamma. Novel analytic expressions are derived for the envelope and power probability density function of these distributions which are expressed in a relatively simple algebraic form which is convenient to handle both analytically and numerically. As a result, they can be meaningfully utilized in the derivation of numerous vital measures in investigations related to the analytic performance evaluation of digital communications over composite multipath/shadowing fading channels.

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arXiv2015

Sensing of Unknown Signals over Weibull Fading Conditions

Energy detection is a widely used method of spectrum sensing in cognitive radio and Radio Detection And Ranging (RADAR) systems. This paper is devoted to the analytical evaluation of the performance of an energy detector over Weibull fading channels. This is a flexible fading model that has been shown capable of providing accurate characterization of multipath fading in, e.g., typical cellular radio frequency range of 800${/}$900 MHz. A novel analytic expression for the corresponding average probability of detection is derived in a simple algebraic representation which renders it convenient to handle both analytically and numerically. As expected, the performance of the detector is highly dependent upon the severity of fading as even small variation of the fading parameters affect significantly the value of the average probability of detection. This appears to be particularly the case in severe fading conditions. The offered results are useful in evaluating the effect of multipath fading in energy detection-based cognitive radio communication systems and therefore they can be used in quantifying the associated trade-offs between sensing performance and energy efficiency in cognitive radio networks.

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arXiv2015

A Generalized Non-Linear Composite Fading Model

This work is devoted to the formulation and derivation of the $α{-}κ{-}μ{/}$gamma distribution which corresponds to a physical fading model. The proposed distribution is composite and is constituted by the $α{-}κ{-}μ$ non-linear generalized multipath model and the gamma shadowing model. It also constitute the basis for deriving the $α{-}κ{-}μ$ \textit{Extreme}${/}$gamma model which accounts for non-linear severe multipath and shadowing effects and also includes the more widely known $α{-}μ$ and $κ{-}μ$ models which includes as special cases the Rice, Weibull, Nakagami-$m$ and Rayleigh distributions. The derived models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects. This is achieved thanks to the remarkable flexibility of their named parameters which have been shown to render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is also evident by the fact that they include as special cases the widely known composite fading models such as the recently reported $κ{-}μ{/}$gamma model and the novel $α{-}μ{/}$gamma model. Novel analytic expressions are derived for the corresponding probability density function of these distributions which are expressed in a convenient algebraic form and can be efficiently utilized in the derivation of numerous vital measures in investigations related to the analytic performance evaluation of digital communications over composite multipath${/}$shadowing fading channels.

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arXiv2015

Novel Expressions for the Rice $Ie{-}$Function and the Incomplete Lipschitz-Hankel Integrals

This paper presents novel analytic expressions for the Rice $Ie{-}$function, $Ie(k,x)$, and the incomplete Lipschitz-Hankel Integrals (ILHIs) of the modified Bessel function of the first kind, $Ie_{m,n}(a,z)$. Firstly, an exact infinite series and an accurate polynomial approximation are derived for the $Ie(k ,x)$ function which are valid for all values of $k$. Secondly, an exact closed-form expression is derived for the $Ie_{m,n}(a,z)$ integrals for the case that $n$ is an odd multiple of $1/2$ and subsequently an infinite series and a tight polynomial approximation which are valid for all values of $m$ and $n$. Analytic upper bounds are also derived for the corresponding truncation errors of the derived series'. Importantly, these bounds are expressed in closed-form and are particularly tight while they straightforwardly indicate that a remarkable accuracy is obtained by truncating each series after a small number of terms. Furthermore, the offered expressions have a convenient algebraic representation which renders them easy to handle both analytically and numerically. As a result, they can be considered as useful mathematical tools that can be efficiently utilized in applications related to the analytical performance evaluation of classical and modern digital communication systems over fading environments, among others.

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arXiv2015

Closed-Form Bounds for the Rice $Ie$-Function

This work is devoted in the derivation of novel upper and lower bounds for the Rice $Ie$-function. These bounds are expressed in closed-form and are shown to be quite tight. This is particularly evident by the fact that for a certain range of parameter values, the derived lower bound virtually behaves as a remarkably accurate approximation. As a result, the offered expressions can be considered useful mathematical tools that can be efficiently employed in various analytical studies related to natural sciences and engineering. To this effect, they can be sufficiently applied in the area of digital communications over fading channels for the derivation of explicit representations for vital performance measures such as bit and symbol error probability, among others.

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arXiv2015

Useful Results for Computing the Nuttall${-}Q$ and Incomplete Toronto Special Functions

This work is devoted to the derivation of novel analytic results for special functions which are particularly useful in wireless communication theory. Capitalizing on recently reported series representations for the Nuttall $Q{-}$function and the incomplete Toronto function, we derive closed-form upper bounds for the corresponding truncation error of these series as well as closed-form upper bounds that under certain cases become accurate approximations. The derived expressions are tight and their algebraic representation is rather convenient to handle analytically and numerically. Given that the Nuttall${-}Q$ and incomplete Toronto functions are not built-in in popular mathematical software packages, the proposed results are particularly useful in computing these functions when employed in applications relating to natural sciences and engineering, such as wireless communication over fading channels.

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arXiv2015

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

This work 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, the incomplete Toronto function, the Rice $Ie$-function and the incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and the Humbert, $Φ_{1}$, function as well as for specific cases of the Kamp${\it \acute{e}}$ de F${\it \acute{e}}$riet function. These functions can be considered 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 multi-antenna systems. As an example, new closed-form expressions are derived for the outage probability over non-linear 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 the corresponding optimum cut-off signal-to-noise ratio for single-and multi-antenna communication systems over Rician fading channels. The accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results.

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arXiv2015

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.

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arXiv2015

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.

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arXiv2011

Closed-Form Bounds to the Rice and Incomplete Toronto Functions and Incomplete Lipschitz-Hankel Integrals

This article provides novel analytical results for the Rice function, the incomplete Toronto function and the incomplete Lipschitz-Hankel Integrals. Firstly, upper and lower bounds are derived for the Rice function, $Ie(k,x)$. Secondly, explicit expressions are derived for the incomplete Toronto function, $T_{B}(m,n,r)$, and the incomplete Lipschitz-Hankel Integrals of the modified Bessel function of the first kind, $Ie_{μ,n}(a,z)$, for the case that $n$ is an odd multiple of 0.5 and $m \geq n$. By exploiting these expressions, tight upper and lower bounds are subsequently proposed for both $T_{B}(m,n,r)$ function and $Ie_{μ,n}(a,z)$ integrals. Importantly, all new representations are expressed in closed-form whilst the proposed bounds are shown to be rather tight. Based on these features, it is evident that the offered results can be utilized effectively in analytical studies related to wireless communications. Indicative applications include, among others, the performance evaluation of digital communications over fading channels and the information-theoretic analysis of multiple-input multiple-output systems.

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arXiv2011

A Comparative Study of Relaying Schemes with Decode-and-Forward over Nakagami-m Fading Channels

Utilizing relaying techniques to improve performance of wireless systems is a promising avenue. However, it is crucial to understand what type of relaying schemes should be used for achieving different performance objectives under realistic fading conditions. In this paper, we present a general framework for modelling and evaluating the performance of relaying schemes based on the decode-and-forward (DF) protocol over independent and not necessarily identically distributed (INID) Nakagami-m fading channels. In particular, we present closed-form expressions for the statistics of the instantaneous output signal-to-noise ratio of four significant relaying schemes with DF; two based on repetitive transmission and the other two based on relay selection (RS). These expressions are then used to obtain closed-form expressions for the outage probability and the average symbol error probability for several modulations of all considered relaying schemes over INID Nakagami-m fading. Importantly, it is shown that when the channel state information for RS is perfect, RS-based transmission schemes always outperform repetitive ones. Furthermore, when the direct link between the source and the destination nodes is sufficiently strong, relaying may not result in any gains and in this case it should be switched-off.

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