Relay-Assisted D2D Communication over Extended η-μ Fading Channels

In this paper, two cases of Device-to-Device (D2D) communication over a recently introduced extended η-μ fading channel are analyzed. Case A considers a direct D2D communication. While in case B, amplify-and-forward relay-assisted D2D communication is discussed. The effects of cochannel interference at the relay and D2D destination are also included. To combat fading, selection combiningand maximal ratio combining-based diversity schemes are also incorporated at the receiver. Power harvesting based on power splitting technique is also engulfed. Expressions of success and outage probabilities are derived with the help of characteristic function approach. Success and outage probability expressions are functions of path loss, distance between various devices and channel parameters. Based on these expressions, numerical results are presented and discussed.

communication. In [15], author examined Wyner's wiretap composite multipath/shadowing fading channel model and presented physical layer security secrecy performance. The analysis for average secrecy capacity in heavy shadowing is presented.
The main contributions of this paper are as follows: a newly proposed extended η-μ distribution [16] is considered for the outage probability and success probability performance analyses of the D2D communication system in an interference limited scenario. Two cases are considered in this paper. In case A, a direct D2D communication is analyzed. While in case B, amplify-and-forward relayassisted communication is presented. The cochannel interference (CCI) signals are considered at the relay and the D2D receiver. CCI and D2D channels are considered to be independent and nonidentically distributed. The path loss conditions are included in the expressions. Power splitting-(PS-) based power harvesting technique is also considered. Selection combining (SC) and maximal ratio combining (MRC) diversity schemes are being used to tackle the effects of fading. To the best of our knowledge, no published work has considered the newly proposed extended η-μ faded channels for the relay-assisted D2D communication system with CCI signals, pathloss, diversity reception, and power harvesting. The extended η-μ distribution is a flexible, generalized, and more realistic fading model that includes fading distribution like, classic η-μ and the Nakagami and Hoyt as special cases [16]. The rest of the paper is organized as follows. The section named System Model presents the considered system and expressions of outage probability and success probability. In the Numerical Analysis, numerical results are presented and discussed. Finally, this paper is concluded in last the section.

System Model
Device-to-device (D2D) communication schemes with direct and amplify-and-forward (AF) relay-assisted are shown in Figures 1(I) and 1(II), respectively. In Table 1, parameters of Figures 1(I) and 1(II) are defined. There are M cochannel interferers at the relay and N cochannel interferers at the D2D receiver. Cochannel interference (CCI) is assumed to be independent and nonidentically distributed. Two types of D2D communication cases are considered here. In case A, D2D signal is directly received by the D2D receiver from the source. In case B, the D2D signal from the source is received by the relay. There are M CCI signals at the relay. The relay then amplifies and forwards the D2D and CCI signals to the D2D receiver.
The extended η-μ fading channel is assumed for all the signals in the system. The probability density function (PDF) of envelope Ʀ of extended η-μ is [16] where 1 F 1 ð:Þ is the confluent hypergeometric function [17] and μ is the total number of clusters. Also, ξ = 1 + η/1 + p and r −2 is the total mean power. Extended η-μ fading model follows two formats. Based on Format 1, η is the ratio of inphase and quadrature power components and, in Format 2, η is the normalized power's difference of in-phase and quadrature components. In Format 1, p is the ratio of the number of multipath clusters and, in Format 2, it represents the normalized difference of the number of multipath clusters.
The fading of the relay D2D receiver path is assumed to be negligible; however, the signal is affected by path loss. Mobile wireless communication systems can have strong direct line-of-sight (LoS) component. Under such conditions, there will be negligible fading. Therefore, we have considered negligible fading conditions between relay and the receiver. The D2D ssreceiver employs an L-branch selection combining (SC) or maximal ratio combining-(MRC-) based diversity scheme to combat fading effects of the channel.

Case A.
For case A, the received signal in the l-th branch of D2D receiver is where s 0 ðtÞ is the desired signal and s n ðtÞ is the n-th CCI signal. E½js 0 ðtÞj 2 = 1 and E½js n ðtÞj 2 = 1, n = 1, 2, 3, ⋯, N: The D2D receiver employs a L-branch SCbased diversity scheme. The signal-to-interference noise power ratio (SINR) at the l-th branch of D2D receiver is where S l is the D2D signal power in the l-th branch of the D2D receiver, h l is the independent extended η-μ fading variable in the l-th branch, and S I is the total power of CCI at the D2D receiver. The receiver incorporates a power splitting (PS) scheme, based on which, a fraction of the received signal is provided for the desired data retrieval and the rest is used by the power harvester [18]. The fraction ð0 ≤ β ≤ 1Þ, known as the power splitting ratio, controls the amount of received signal used by the power harvester. σ 2 is the variance of the additive white Gaussian noise (AWGN) introduced by the power harvesting circuit. P is the power of the D2D signal and u is the path-loss exponent for the D2D signal from source to relay. P I,n is the power of the nth CCI signal at the D2D receiver and c n is the path-loss exponent of the n-th CCI signal. The outage probability P out is defined as the probability when the SINR of the system falls below a threshold value R.
where Pr ð:Þ is the probability and S MAX = max where Ω l = E½h l and Ω n = E½α n are average powers and μ l and μ n are the total number of clusters of the l-th branch D2D and n-th CCI signals, respectively. Based on Format 1, η l and η n are the ratios of in-phase and quadrature power components and, in Format 2, η l and η n are the normalized powers' difference of in-phase and quadrature components in the l-th branch D2D signal and of n-th CCI signal, respectively. In Format 1, p l and p n are the ratio of the number of multipath clusters and, in Format 2, they represent the normalized difference of the number of multipath clusters of the l-th branch D2D and n-th CCI signals, respectively. Also, The outage probability can be obtained by using the formula ϕ θ l is given in (3). Im ð:Þ is the imaginary part. For an independent and identically distributed (IID) case, the CF of the decision variable is The outage probability can be obtained by using the identity shown below, ϕ θ is given in (4). Success probability is the probability for which the SINR of the received signal exceeds a predefined threshold R. For our case the success probability is For an IID situation,

Mobile Information Systems
Total average power harvested, P H,SC , by the receiver will be 2.1.2. MRC Scheme. For an L-branch maximal ratio combining-(MRC-) based diversity scheme, the SINR is where S MRC is the D2D signal power for the MRC case. Outage probability for this case will be P out = Pr The outage probability will be where ϕ φ l is given in (6). The CF of the decision variable for IID case is Outage probability can be found by using the expression The success probability for MRC scheme is where ϕ φ l is given in (6). Success probability for IID case of MRC scheme is where ϕ φ is given in (7). Total average power harvested, P H,MRC , by the receiver will be By considering the maximum distance between D2D transmitter-receiver to be Q meters, the transmitterreceiver distance k can have a random value in range ð0 ≤ k ≤ QÞ meters. The distance k follows a linear distribution. The PDF of k can be written as [19] Under such conditions, the outage probability will be Similarly, the success probability will be 2.2. Case B. For case B, the received signal at the relay is where s m ðtÞ is the m-th CCI signal. E½js m ðtÞj 2 = 1, m = 1, 2 , 3, ⋯, M: The received signal in the l-th branch of D2D receiver is 2.2.1. SC Scheme. The D2D signal is first received by the relay which then amplifies and forwards it to the D2D receiver. The D2D receiver employs a L-branch SC-based diversity scheme.

Mobile Information Systems
The SINR at the l-th branch of D2D receiver is where is the is the power of the m-th CCI signal at the relay, v m is the pathloss exponent of the m-th CCI at the relay, γ m is an independent extended η-μ fading variable of the m-th CCI and, a and b are path-loss exponents. G is the relay's amplification factor given as [20] where P 2 is the relay amplifying power, Ω = E½h and Ω m = E½γ m are average powers of D2D and m-th CCI signals at the relay, respectively. The CF of the decision variable θ l = RS I − S l is where μ m is the total number of clusters of the m-th CCI signal at the relay. Based on Format 1 of the extended η-μ, η m is the ratio of in-phase and quadrature power components, and in Format 2, η m is the normalized powers' difference of in-phase and quadrature components of m-th CCI signal.
In extended η-μ Format 1, p m is the ratio of the number of multipath clusters and, in Format 2, it represents the normalized difference of the number of multipath clusters of the m-th CCI signal at the relay. Also, ξ m = 1 + η m /1 + p m , The outage probability will be For an IID case, where Success probability is ϕ θ l is given in (27). For an IID situation success probability is where ϕ θ is given in (30). Total average power harvested, P H,RSC , for this case is where Outage probability for the case is P out = Pr ðRS I > S MRC Þ. The CF of the decision variable Ψ l = RS I − S MRC is The outage probability is

Mobile Information Systems
For an IID case, ϕ Ψ in above expression will be The success probability is where ϕ Ψ l is given in (10). For an IID scenario, success probability is where ϕ Ψ is given in (11). Total average power harvested P H,RMRC is For the relay-based MRC system, by considering the maximum distance between relay-receiver to be A meters. The relay-receiver distance, y can have a random value in the range ð0 ≤ y ≤ AÞ meters. The PDF of y can be written as f Y y ð Þ = 2y A 2 , 0 < y < A: ð41Þ

Distance between m-th cochannel interferer and relay in case B z m
Distance between n-th cochannel interferer and D2D receiver g n

Mobile Information Systems
The outage probability will be Similarly, the success probability will be The double integral in the outage and success probability expressions can be solved with the help of MATLAB.

Results and Analysis
The numerical results based on the analysis of System Model are presented in this section. Expressions presented in System Model are valid for arbitrary values. Here, numerical analysis is presented for various assumed values of the parameters. Table 2 shows the parameters whose values are fixed. In Figures 2 and 3, outage performance comparisons with varying path-loss exponents for the relay-based systems are presented. The performance is also compared when the total distance between the D2D source and receiver is varied. For the relay-based system, the total distance between the D2D source and receiver is considered to be x + y. , it is clear that as the total distance between D2D devices is increased, the outage performance of the system degrades for all scenarios. In Figure 2, SC-based diversity is considered. From the figure, it is clear that the relay-based system performs well as compared to the system without relay. However, as the path-loss exponent is increased from the relay to D2D receiver, the outage performance for the relay-based system degrades. Also, when there is no SC scheme, performance degrades. In Figure 3, MRC-based diversity is considered. By comparing Figures 2 and 3, it is clear that MRC-based systems outperform SC-based systems with and without relay cases.
In Figure 4, outage performance with varying total number of clusters for the relay-based system is presented. MRC diversity is considered: β =0. . From the figure, it is observed that as the number of total clusters are decreased, the performance of the relay-based system degrades and underperforms the nonrelay-based system for the distance of 20 m to 30 m; however, the gap is reduced as the distance between D2D source and receiver is increased.
In Figure 5, outage performance with varying ratio of inphase and quadrature power components for the relay-based system is presented. MRC diversity is considered: β =0.   observed that as the ratio of in-phase and quadrature power components is increased, the performance of the relaybased system degrades. In Figure 6, outage performance with varying ratio of the number of multipath clusters p l for the relay-based system is presented. MRC diversity is considered: β =0. In Figure 7, outage performance with varying total number of clusters for the cochannel interferers at the relay and

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Mobile Information Systems In Figure 8, outage performance with varying the ratio of the number of multipath clusters for the cochannel interferers at the relay and receiver is presented. MRC diversity is considered: β =0. 3 [2,4], μ l = [2,3,5], and μ m = [2,3]. From the figure, it is obvious that the outage performance is unaffected by any variation in the ratio of the number of multipath clusters for the cochannel interferers at relay and D2D receiver. In Figure 9, outage performance with varying power splitting (PS) ratio is presented. MRC diversity with relay is considered. And, x =25 m, b =3, c n = [3, 2. it is clear that the success performance of the system degrades as the PS ratio is increased. In Figure 11, outage with varying power splitting (PS) ratio is presented and variable maximum relay-receiver distance, i.e., A is considered.  Figure 11, it is clear that the outage performance of the system degrades as the maximum distance between relay-receiver and PS ratio is increased. In Figure 12 , it is clear that as the transmit power of the D2D signal is increased, outage performance of the system is improved. However, by increasing the path-loss exponent of the relay-receiver path, the outage performance degrades.

Conclusions
Outage and success performances of relay-assisted D2D communication systems over recently introduced extended η-μ fading channel are studied. Effects of CCI on the performances are also presented. Outage and success probability expressions are presented based on a characteristic function-(CF-) based approach. These expressions are functions of interference conditions, channel fading, and path-loss parameters of the system. Selection combining-(SC-) and maximal ratio combining-(MRC-) based diversity schemes are also considered in the system to counter fading. Power splitting-(PS-) based power harvesting technique is also incorporated in this work. Amplify-and-forward (AF) relay-assisted scheme is compared with D2D-(without relay) based system. It is observed that relay-based systems show better performance than the systems without relay. Variations in the extended η-μ fading conditions of the CCI system show negligible effects on the performance of the system. It is also observed that SC incorporated relaybased system shows best performance in terms of power harvesting. Also, the success probability performance of the system degrades, as the PS ratio is increased.

Data Availability
No data were used to support this study.