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The need for the distribution of combination of random variables (RVs) arises in many areas of sciences and engineering. In this paper, closed-form approximations for the distribution of squared sum of products of independent Nakagami-m RVs are derived. Three different approaches (central limit theorem, Edgeworth expansion, and a one-term gamma approximation) are considered. The Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises statistics are used as a quantitative metrics to compare the derived distribution forms with the empirical distribution obtained from a simulation study. Furthermore, an application for the derived distributions in wireless communication field is presented. As a result, it is shown that the most accurate and simplest closed-form expression is the one obtained by a one-term gamma approximation. [ABSTRACT FROM AUTHOR]

In this paper, the performance of the dual-hop radio frequency/free space optical (RF/FSO) system based on the amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes is analyzed. The RF link is modeled by Nakagami-m distribution for the multipath fading channel which is a generalized distribution. The FSO link is characterized by Fisher-Snedecor (F ) fading distribution that is valid for all atmospheric turbulence conditions. Operating the intensity modulation direct detection scheme, the unified expression of the cumulative distribution function (CDF) is employed for the instantaneous end-to-end received signal-to-noise ratio (SNR). By utilizing its CDF, a novel mathematical framework to drive the exact closed-form expressions of the outage probability (OP) and the average bit error rate (ABER) with different modulation schemes are calculated for the considered system involving Meijer-G functions. Additionally, to get a deeper understanding, asymptotic expressions for the OP and ABER are also obtained in terms of basic elementary functions. Further, the analytical results collaborate with simulation results which validate the use of the derived expressions. The results revealed that increases in the severity of atmospheric turbulence profoundly degrade the system performance. Furthermore, comparisons between dual-hop RF/FSO systems, hybrid RF/FSO systems, and single FSO systems are presented. [ABSTRACT FROM AUTHOR]

Mobile communications systems are affected by what is known as fading, which is a well-known problem largely studied for decades. The direct consequence of fading is the complete loss of signal (or a large decrease of the received power). Rayleigh fading is a reasonable model for wireless channels although, Nakagami-m distribution seems better suited to fitting experimental data. In this paper we obtain the Nakagami-m distribution as a composite (mixture) of the Rayleigh distribution, a result which as far as we know it has not been shown in the literature. This representation of the Nakagami-m distribution facilitates computations of the average BER (Bit Error Rate) for DPSK (Differential Phase Shift Keying) and MSK (Minimum-Shift Keying) modulations for this distribution and higher moments of them, which is of great applicability to modeling wireless fading channels. Furthermore, a simple, not depending on any special function, apart of the Gamma function, bivariate version of the Nakagami-m distribution is also proposed as a special case of the multivariate version which is also presented. The proposed composite distribution is simulated through the standard procedure of summation of phasors, and results for the new closed-form measures for the MSK modulation are also shown. From that it is clear that the alternative formulation of the Nakagami-m distribution allows for easier modeling of fading fading-shadowing wireless channels through the new explicit second order statistics metrics. is well suited for modelling fading-shadowing wireless channels. [ABSTRACT FROM AUTHOR]

Nonorthogonal multiple access (NOMA) is used to superpose multifarious user signals for concurrent transmission, enhancing spectral efficiency. Additionally, wireless energy sources neighbouring the NOMA sender are utilized for enhanced energy efficiency. Practically, nonlinear energy harvesting (nlEH) circuits reflect faithfully characteristics of components implementing these circuits. In addition, reflected intelligent surface (RIS) is helpful with a role of the relay to maintain communication from the NOMA sender to the far NOMA recipient. However, challenges in RIS-aided NOMA with nlEH (RISaNOMAwEH) include channel state error (CSE) and fading severity. These factors directly impact harvested energy and communication reliability. As such, this paper analyzes their influences on the RISaNOMAwEH through three pivotal metrics (total throughput, outage probability, energy efficiency) under practical considerations like the nlEH, the CSE, and relatively-general fading (Nakagami-m). Demonstrative results reveal that the CSE, the fading severity m, and the quantity of the reflectors of the RIS drastically impact these metrics whereas the nlEH slightly influences them. Remarkably, the RISaNOMAwEH can conduct the prevention of complete outage through proper adoption of required spectral efficiency (R), time splitting factor (η) , and power splitting coefficient. Moreover, optimum metrics are achieved with the optimal configuration of parameters (R , η) . Furthermore, the proposed scheme dramatically outperforms a benchmark scheme (RIS-aided orthogonal multiple access (OMA) with nlEH) in various parameter configurations, highlighting the benefits of NOMA over OMA. [ABSTRACT FROM AUTHOR]

A reconfigurable intelligent surface (RIS)-aided wireless communication system is considered in this paper, where the transmitter sends data to the receiver via a direct link and the RIS. The phases of the reflecting elements of the RIS are selected considering the phases of all the fading channels to maximize the performance of the system. Series-form expressions for the probability density function (p.d.f.) and cumulative distribution function (c.d.f.) are derived for the composite channel of the communication system by considering the RIS channels to follow independent Nakagami-m distributions and the envelope of the direct channel to follow a Rayleigh distribution. Furthermore, the expressions for the statistics of the composite channel in terms of its p.d.f. and c.d.f. are also derived by considering the approximation of the central limit theorem (CLT) and the square of the channel envelope without the direct channel to approximately follow a Gamma distribution. Utilizing the derived statistics, the performance of the RIS-assisted system is studied by deriving series-form expressions for the symbol error probability (SEP) and outage probability. Numerical results are presented to corroborate the analytical framework. It is observed that a decreasing number of reflecting elements of the RIS and an increasing shape parameter of the fading channels increase the randomness of the overall channel of the RIS-assisted wireless system. Moreover, the inefficacy of both the approximate statistics is demonstrated via simulation studies of the p.d.f., c.d.f., SEP, and outage probability.

The advent of the next generation of wireless communication (NextGen) demands substantial investments and collaborative research for the fundamental need of wireless communications. Therefore, cooperative communication plays a vital role in overcoming challenges such as reliability, throughput, and outage trade-offs. We propose a two-transmission phase spectrum-sharing protocol, employing cooperative decode-and-forward relaying to grant spectrum access for both primary and secondary users. The system consists of a primary sender (PS), primary recipient (PR), secondary sender (SS), and secondary recipient (SR), linked as PS-SS, PS-PR, PS-SR, SS-SR, and SS-PR. In the first transmission phase, PS broadcasts the primary signal, received by PR, SS, and SR. SS regenerates the primary signal after successful reception, combining it linearly with the secondary signal, and allocating power fractions $\epsilon $ and ( $1 - \epsilon $ ) to the primary and secondary signals. SS then broadcasts the combined signal in the second transmission phase. Analysis reveals a threshold for optimal performance when SS is within range of PS. Beyond this threshold, the outage performance for the primary user equals or exceeds the case without spectrum sharing. The outage performance for the secondary system is also quantified. The performance of both the primary and secondary users is assessed by deriving a closed-form expression for the outage probability using the Nakagami-m distribution. The effectiveness of the scheme is affirmed through analytical and simulation results.

This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily identically distributed (i.n.i.d.) Nakagami-m random variables (RVs) in terms of Meijer’s G-function. Additionally, exact series representations are also derived for the sum of double-Nakagami RVs, providing useful insights on the trade-off between accuracy and computational cost. Simple asymptotic analytical expressions are provided to gain further insight into the derived formula, and the achievable diversity order is obtained. The suggested statistical properties are proved to be a highly useful tool for modeling parallel cascaded Nakagami-m fading channels. The application of these new results is illustrated by deriving exact expressions and simple tight upper bounds for the outage probability (OP) and average symbol error rate (ASER) of several binary and multilevel modulation signals in intelligent reflecting surfaces (IRSs)-assisted communication systems operating over Nakagami-m fading channels. It is demonstrated that the new asymptotic expression is highly accurate and can be extended to encompass a wider range of scenarios. To validate the theoretical frameworks and formulations, Monte-Carlo simulation results are presented. Additionally, supplementary simulations are provided to compare the derived results with two common types of approximations available in the literature, namely the central limit theorem (CLT) and gamma distribution.

Reconfigurable intelligent surfaces (RISs) are acknowledged as one of the key technologies for the next-generation communication systems due to their low cost, high-energy efficiency, and the ability to intelligently control the wireless propagation environment. In this paper, we present a hybrid active–passive reconfigurable intelligent surface (HAPR) for cooperative transmission system, where HAPR can intelligently change its operating mode according to the channel environment, eliminating the "multiplicative fading" effect of traditional passive RIS (P-RIS) and higher power consumption of active RIS (A-RIS), and combining the advantages of both to effectively improve the system performance. First, we investigate the ideal reflection coefficient of RIS reflecting elements (REs) under the condition of a limited power budget. Using the compound Simpson formula, the closed-form approximation expression for the system outage probability (OP) has been derived. Finally, Monte Carlo simulation is used to confirm the accuracy of the expression. The simulation results demonstrate that HAPR has a better performance than both A-RIS and P-RIS, which can achieve a lower OP. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of non-ideal environmental factors, including hardware impairments, random user distributions, and imperfect channel conditions, on the performance of distributed reconfigurable intelligent surface (RIS)-assisted air–ground fusion networks. Using an unmanned aerial vehicle (UAV) as an aerial base station, performance metrics such as the outage probability, ergodic rate, and energy efficiency are analyzed with Nakagami-m fading channels. To highlight the superiority of RIS-assisted air–ground networks, comparisons are made with point-to-point links, amplify-and-forward (AF) relay scenarios, conventional centralized RIS deployment, and fusion networks without hardware impairments. Monte Carlo simulations are employed to validate theoretical analyses, demonstrating that in non-ideal environmental conditions, distributed RIS-assisted air–ground fusion networks outperform benchmark scenarios. This model offers some insights into the improvement of wireless communication networks in emerging smart cities.

Reconfigurable intelligent surfaces (RISs) are acknowledged as one of the key technologies for the next-generation communication systems due to their low cost, high-energy efficiency, and the ability to intelligently control the wireless propagation environment. In this paper, we present a hybrid active–passive reconfigurable intelligent surface (HAPR) for cooperative transmission system, where HAPR can intelligently change its operating mode according to the channel environment, eliminating the “multiplicative fading” effect of traditional passive RIS (P-RIS) and higher power consumption of active RIS (A-RIS), and combining the advantages of both to effectively improve the system performance. First, we investigate the ideal reflection coefficient of RIS reflecting elements (REs) under the condition of a limited power budget. Using the compound Simpson formula, the closed-form approximation expression for the system outage probability (OP) has been derived. Finally, Monte Carlo simulation is used to confirm the accuracy of the expression. The simulation results demonstrate that HAPR has a better performance than both A-RIS and P-RIS, which can achieve a lower OP.

Unnamed aerial vehicles (UAVs) are of great importance on various platforms because of its rapid and easy deployment. In order to get an insight of UAV aided communication systems, an accurate channel model of UAV channels is needed. We propose a general channel model for UAV link based on alpha-beta model, which is extensively used in the literature. Specifically, we derive the normalized expression of probability density function (PDF), cumulative distribution function (CDF), and moments of the proposed model. Shadowing component is assumed to follow log-normal distribution and multipath component is characterized with the help of Nakagami-m distribution. The outage probability of a UAV based communication system is also obtained by using CDF expression. [ABSTRACT FROM AUTHOR]

Underlay device-to-device (D2D) communication network is becoming a promising solution for the fifth generation (5G) and beyond wireless technology. It exploits the proximity of the D2D pairs and improves the overall network’s latency, capacity, and spectral efficiency by sharing/reusing the existing cellular resources. However, due to the frequency-sharing/reusing, the security of the device users (DUs) and the cellular users (CUs) becomes vulnerable. This paper presents a novel physical-layer security (PLS) scheme for the underlay multiple-input multiple-output (MIMO) D2D communications in the presence of multiple eavesdroppers. The proposed new PLS scheme can significantly reduce the information leakage for both CUs and DUs by adopting a null steering scheme at the transmitter. A signal alignment technique is also employed to eradicate the stringent requirement of a larger number of transmitter antennas than that of the receiver antennas. A generalized nonlinear optimization problem has been formulated to improve the PLS performance for MIMO-D2D communications. A closed-form and generalized analytical expression of the secrecy outage probability for CUs and DUs is derived over the imperfect Nakagami- $m$ and Norton fading channels. Theoretical and simulation results of our proposed new PLS scheme have shown significant improvement in the secrecy capacity and secrecy outage probability for both CUs and DUs in comparison with the existing methods. [ABSTRACT FROM AUTHOR]