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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.

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.

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.

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]

For outdoor millimeter-wave mobile radio systems, the main service area is expected to be in line-of-sight (LOS) and semi-line-of-sight (SLOS) environments. The modeling of propagation in a mixed LOS/SLOS environment is thus important in system design. For modeling propagation in an SLOS environment, the application of the Loo model developed for land mobile satellite service with roadside shadowing is promising because this model reflects the physical mechanism of radio propagation. However, the model is inconvenient in practice because its calculation involves numerical integration over an infinite range. In this article, we approximate the Loo distribution using three basic distributions, namely the Nakagami-Rice distribution (or Rician distribution), Nakagami-m distribution, and lognormal distribution. Based on the evaluation results, we propose the use of the Nakagami-m distribution in place of the Loo distribution. We demonstrate the conversion of Loo distribution parameters to Nakagami-m distribution parameters. Finally, we examine a multistate model that expresses environments composed of LOS, SLOS, and non-LOS conditions. [ABSTRACT FROM AUTHOR]

Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closedform approximation to the sum of not necessarily identically distributed Nakagami-m random variables. The necessary parameters of the approximate solution are estimated by using the well-known expectation maximization algorithm with a Nakagami-m mixture model. The proposed approximation finds applicability in obtaining important performance metrics of communications systems where sums of variates arise. More specifically, we apply the proposed method to derive a closed-form expression for average bit error probability (ABEP) of multibranch equal-gain combining receivers. The presented models are general and can be applied to any modulation scheme. Furthermore, simplified asymptotic closed-form expressions for the ABEP have been derived to examine the achievable diversity and coding gains. Finally, the performance of the proposed approach is verified by comparing itself against both the exact evaluation and the previous results in the literature.

Wireless communications and power line communications (PLC) are essential components for smart grid communications. This paper analyses the performance of a dual-hop wireless-power line mixed communication setup employing a decode-and-forward relay in terms of analytical average bit error rate (BER), outage probability, and average channel capacity. The Nakagami-m distribution captures the wireless channel fading; whereas the PLC channel gain is characterized by the Log-normal distribution. The additive PLC channel noise is assumed to be Bernoulli-Gaussian distributed. Approximate closed-form expression of the average BER and exact closed-form expression of the outage probability are derived for the considered system. Further, we obtain an approximate closed-form expression of the capacity of the wireless-power line mixed system in terms of the Meijer-G function. It is observed that the system performance deteriorates as the impulsive noise index and the arrival probability of the impulsive component of the PLC additive noise increase.

In this paper, we leverage concepts from stochastic geometry to investigate the downlink performance of a vertical heterogeneous network (VHetNet) comprising aerial base stations (ABSs) and terrestrial base stations (TBSs). We model the ABSs as a 2D Poisson point process (PPP) deployed at a particular altitude while the TBSs are modelled as a 2D PPP deployed on the ground. The proposed analytical framework adopts an appropriate air-to-ground (A2G) channel model that incorporates line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. We begin the main technical part of the analysis by deriving analytical expressions for the distribution of the distances between a typical user and the closest LoS ABS, NLoS ABS, and TBS. After that, we derive expressions for the probabilities that a typical user is associated with a NLoS ABS, LoS ABS, or TBS. Under the assumption that A2G and terrestrial channels experience Nakagami- $m$ fading with different $m$ parameters, we derive an expression for the Laplace transform of interference power. Furthermore, we derive exact and approximate analytical expressions for the coverage probability and achievable rate. We show that these approximations match the simulations with negligible errors for small SINR thresholds and $m$ parameters of Nakagami- $m$ fading. [ABSTRACT FROM AUTHOR]

The Nakagami-m distribution plays an important role in problems related to communication engineering. This distribution can also be used for modeling reliability data as its hazard rate (mean residual life) function presents increasing (decreasing) or bathtub (unimodal) shapes. In this study, a Bayesian inference considering objective priors for the Nakagami-m distribution parameters is presented. We propose a theorem with sufficient and necessary conditions so that a general class of posteriors are proper. The impropriety of these posteriors can be observed by the behavior of the objective priors. This theorem is applied to different objective priors such as Jeffreys’ rule, Jeffreys prior, maximal data information prior, and reference priors. Simulation studies were conducted to investigate the performance of the Bayes estimators. Finally, our methodology is illustrated using two real lifetime datasets showing that the Nakagami-m distribution can be used to describe lifetime data. [ABSTRACT FROM PUBLISHER]

Power line communication (PLC) utilizes power lines for the purpose of electronic data transmission. Differential binary phase shift keying (DBPSK) is a popular modulation scheme proposed in the PLC standards like G3, PRIME, and IEEE P1901.2. This letter provides the performance evaluation of a PLC system assuming DBPSK modulation under the combined effect of Nakagami-$m$ background noise and impulsive noise. We utilize a simple, yet accurate approximation available in literature to derive the probability density function of the sum of two Nakagami-$m$ random variables. Closed-form expressions of the analytical average bit error rate and the outage probability of the system are derived. Validity of the derived analytical expressions is closely verified by simulated results. [ABSTRACT FROM PUBLISHER]

Power line communication (PLC) is the use of power lines for the purpose of electronic data transmission. The presence of additive noise, namely, background noise and impulsive noise, significantly affects the performance of a PLC system. While the background noise is modeled by Nakagami- $m$ distribution, the impulsive noise is modeled using Middleton class A distribution. In this letter, we study the performance of a PLC system under the combined effect of Nakagami- $m$ background noise and Middleton class A impulsive noise assuming binary phase shift keying signaling. The probability density function of decision variable under the influence of additive noise (sum of background noise and impulsive noise) is derived. We also derive an analytical expression for the average bit error rate of the considered PLC system. The analytical expressions are validated by close matching to the simulation results. The analysis presented in this letter closely predicts the behavior of the PLC system under the combined effect of background and impulsive noises. [ABSTRACT FROM PUBLISHER]

Power line communication (PLC) utilizes power lines for transmission of power as well as data transmission. It is an emerging field of communication for the home area network of smart grid. The performance of a PLC system is significantly affected by the additive and multiplicative power line noises; the additive noises are of two types, namely background noise and impulsive noise. Whereas, the multiplicative PLC noise leads to fading in the received signal strength. This paper provides the performance analysis of a PLC system over Rayleigh fading channel under Nakagami- $m$ distributed additive background noise assuming binary phase shift keying modulation scheme. The probability density function of the decision variable is derived. We obtain a numerically computable expression of the analytical average bit error rate of the considered system. The closed-form expression of the outage probability of the PLC system is also computed. Simulation results closely verify the validity of the derived analytical expressions. [ABSTRACT FROM PUBLISHER]

The optimality of nondynamic DF relaying over a general three-node Nakagami fading channel in terms of the diversity-multiplexing tradeoff (DMT) is established. In particular, when the fading of the relay-source link is less severe than that of the relay-destination link, both orthogonal and nonorthogonal DF protocols are shown to be DMT-optimal over certain ranges of the multiplexing gains. It is also shown that when the multiplexing gains are sufficiently high, the DMT of the DF protocols is completely independent of the statistical properties of the relay-destination link. [ABSTRACT FROM AUTHOR]

The performance of switch-and-examine diversity (SED) over L arbitrarily correlated and not necessarily identically distributed Nakagami-m fading channels is studied. Analytical expressions for the distribution of the SED output signal-to-noise ratio (SNR) are obtained for the constant correlation model. For the most general case of arbitrary correlation, by assuming half-integer or integer values for the fading parameterm, analytical expressions for the distribution of the output SNR with L ≤ 3 are derived. Moreover, for L>3, analytical approximations for the output SNR are presented. The derived expressions are used to study the outage and average symbol error probability of SED receivers. Performance results obtained by numerical evaluation and verified by means of computer simulations show that the performance of the receivers under consideration is degraded with increasing branch correlation. Nevertheless, SED receivers outperform uncorrelated switch-and-stay diversity receivers, even when they operate under high branch correlation. [ABSTRACT FROM AUTHOR]

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami-m fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter in on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-m and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MLMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds. [ABSTRACT FROM AUTHOR]

This paper presents the multiple-input multiple-output (MIMO) channel capacity over the Nakagami-m fading channel. The joint eigenvalue density function of W = HH†, where H is the channel matrix, is derived in closed form for H (2 x 2) and any integer values of m, as well as for H (2 x 3) with m = 2 and m = 3. The marginal eigenvalue distribution of W is also derived in a closed-form expression. All the results are validated by numerical Monte Carlo simulations and are in excellent agreement. [ABSTRACT FROM AUTHOR]

This paper presents two general fading distributions, the κ-μ distribution and the η-μ distribution, for which fading models are proposed. These distributions are fully characterized in terms of measurable physical parameters. The κ-μ distribution includes the Rice (Nakagami-n), the Nakagami-m, the Rayleigh, and the One-Sided Gaussian distributions as special cases. The η-μ distribution includes the Hoyt (Nakagami-q), the Nakagami-m, the Rayleigh, and the One-Sided Gaussian distributions as special cases. Field measurement campaigns were used to validate these distributions. It was observed that their fit to experimental data outperformed that provided by the widely known fading distributions, such as the Rayleigh, Rice, and Nakagami-m. In particular, the κ-μ distribution is better suited for line-of-sight applications, whereas the η-μ distribution gives better results for non-line-of-sight applications. [ABSTRACT FROM AUTHOR]

This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution—the α-μ distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated α-μ variates are obtained, and they are directly related to the physical fading parameters. [ABSTRACT FROM AUTHOR]

Body worn wireless sensors for monitoring health information is a promising new application. In developing these sensors, a communication channel model is essential. However, there are currently few measurements or models describing propagation around the body. To address this problem, we have measured electromagnetic waves near the torso and derived relevant statistics. We find that components diffracting around the body are well modeled using correlated log normal variables, and a Nakagami-m distribution can be used to incorporate the influence of arm motions. We have implement this model and evaluated it in terms of important communication metrics. This paper describes body area propagation statistics and proposes a suitable computer model implementation. [ABSTRACT FROM PUBLISHER]

This letter studies the diversity advantage of single and multiuser systems utilizing multiple-input multiple-output (MIMO) antennas for known channels at the transmitter and receiver(s) by investigating the overall distribution of the resulting channel. For the single-user case, the resultant channel is taken as the largest singular value of the MIMO channel whereas for the multiuser scenario, the resultant channel is obtained by a recently proposed joint-channel diagonalization. The channel distribution is studied using hypothesis testing with the hypothesis that the distribution follows a Nakagami-m distribution with given parameters. It is concluded from the chi-square goodness-of-fit test that the distribution of the resultant channel for single or multiuser MIMO channel is well matched with a Nakagami-m distribution. [ABSTRACT FROM PUBLISHER]