Analysis of D 2 D Communication System Over κ-μ Shadowed Fading Channel

Outage performance of a device-to-device (D2D) communication system in the presence of co-channel interference (CCI) is analyzed in this paper. Channels for the D2D and CCI signals are assumed to be κ-μ shadowed faded. Maximal ratio combining (MRC) and selection combining (SC) techniques are considered to combat fading conditions. Characteristic function (CF) expression of the D2D system in the presence of CCI is presented. Outage probability and success probability expressions are presented for the MRC and SC schemes. These outage probability and success probability expressions are functions of various CCI, path-loss and channel fading parameters. With the help of numerical results, effects of CCI on the performance of D2D communication system under different channel fading and path-loss conditions are discussed. Keywords-co-channel interference; D2D communication; κ-μ shadowed distribution; maximal ratio combining; selection combining; outage probability


INTRODUCTION
The continuous development of technology and ever increasing number of connected devices has boosted the requirement of high data rates for efficient communication.Device-to-device (D2D) communication system has emerged as a promising solution for this problem.D2D communication system is one of the most important standards of the 5 th generation (5G) cellular communication system that permits the communication of nearby devices directly bypassing the base station (BS) [1].D2D communication system can improve data rate and bandwidth efficiency.It can also offload the base station, and it is power efficient communication for the user equipment [2][3].Many D2D communication devices coexisting with other wireless devices are competing for limited bandwidth recourses, which may lead to the co-channel interference (CCI) problem.Therefore, the effects of CCI must be taken into account while analyzing the performance of D2D communication systems [4][5].The aim of this paper is to analyze the outage and success probabilities of a D2D communication system in an interference limited scenario.Outage performance of a full duplex D2D system over a Rayleigh fading channel is studied in [6].Authors in [7], studied outage performance of D2D communication system over a Rayleigh fading channel in the presence of interference.Success probability performance of D2D communication system over Rician fading channel is studied and analyzed in [8].In [9], authors analyzed the success probability performance of D2D communication system over a Rayleigh fading channel.
The main objective of this work is to analyze the outage and success probabilities of a D2D communication system affected by several co-channel interferers over a κ-µ shadowed fading channel.The interference signals are assumed to originate from any wireless device in the system with which proper coordination is either lost or interrupted.The κ-µ shadowed fading channel is considered for both desired D2D and CCI signals.The κ-µ shadowed fading distribution is a versatile model with a mathematically tractable form [10].The κ-µ shadowed fading distribution can model Rayleigh, Rician, one-side Gaussian, and Rician shadowed fading distributions.Maximal ratio combining (MRC) and selection combining (SC) techniques are incorporated to tackle the fading conditions.Outage probability and success probability expressions based on the characteristic function (CF) expressions for the MRC and SC cases are presented.These outage probability and success probability expressions are functions of various channel fading, shadowing, path-loss and interference conditions.

II. SYSTEM MODEL
The D2D communication model consists of a pair of D2D enabled devices communicating with each other directly.The system model is shown in Figure 1.There are N co-channel interferers in the system.The D2D and CCI signals are assumed to be independent and non-identically distributed.The CCI sources are considered to be situated at different distances from the receiver of the D2D pair.The κ-µ shadowed fading channel is assumed for both desired D2D and CCI signals.The probability density function (PDF) of κ-µ shadowed fading distribution is [11]:  where 1 F 1 (.) is the confluent hypergeometric function of first kind [12].The signal modeled by κ-µ shadowed fading distribution is considered to contain clusters of multipath signals.Each cluster has a dominant component and that component can fluctuate randomly due to shadowing.µ denotes the number of clusters, κ is the ratio of sum of powers of dominant components to the sum of powers of all the scattered components, m is the shadowing parameter and Ω is related to the average power.A simplified path-loss model is also considered [13].MRC and SC based diversity techniques with M branches are incorporated to combat fading conditions.

A. MRC Scheme
The signal-to-interference power ratio (SIR) at the output of M branches MRC combiner is: In (1), P d is the power of the D2D signal, x is the distance between D2D devices, u is the path-loss exponent ( ) for the D2D signal, x 0 is the reference distance and h l is an independent κ-µ shadowed fading variable in the l th diversity branch.Similarly, the power of the n th co-channel interferer is P I,n which is located at a distance y n from the D2D receiver, y 0,n is the reference distance, v n is the path-loss exponent of the n th co-channel interferer and β n is an independent κ-µ shadowed fading variable of the n th co-channel interferer.The performance of a wireless communication system is assessed by computing the outage probability.The outage probability P out is defined as the probability that the instantaneous SIR of the system drops below threshold R. The outage probability is: where Pr(.) denotes the probability.Using the expression given in (2), a decision variable ϕ is defined as: For an acceptable quality of a desired D2D received signal, the value of φ has to be negative.Otherwise, outage will occur.Mathematically, To get the expression of the outage probability, a characteristic function (CF) based approach is considered here.
With the help of [11], the CF of the decision variable ϕ is: ) where: ( ) Based on (4) and ( 5), the outage probability of the D2D communication system can be obtained by using the formula: where Im(.) is the imaginary part of the CF of the decision variable φ.The outage probability of MRC based D2D communication system is given in (6).In (6), ( ) . The success probability is defined as the probability for which the SIR of a system excides a fixed threshold R. P S of MRC based D2D communication system is given in (7).

B. Selection Combining
For the D2D communication system with SC diversity technique, the SIR of the l th diversity branch is: The outage probability for a SC diversity based D2D communication system is: Pr where ( ) Based on ( 9) and ( 10), the outage probability and success probability expressions of SC diversity based D2D communication system are given in (11) and ( 12) respectively.

IV. CONCLUSIONS
Outage and success probabilities of a D2D communication system over κ-µ shadowed faded channels have been analyzed.Effects of CCI on the performances were also considered.MRC and SC based diversity techniques are considered to mitigate fading conditions.The D2D and CCI signals are assumed to be independent and non-identically distributed.The interferers are assumed to be present at different distances from the receiver of the considered D2D pair.Outage probability and success probability expressions are presented based on a CF based approach.These outage probability and success probability expressions are functions of interference, channel fading and shadowing, and path-loss parameters.From the numerical results, it was observed that the fading, shadowing, path-loss and CCI affect the performance of the D2D system.It was also observed that D2D communication system performance is largely insensitive to the channel conditions of the interferers.

Fig. 2 .
Fig. 2.Outage performance comparison of MRC and SC scheme

Fig. 4 .
Fig. 4. Outage performance with various values of µl of the D2D signal

Fig. 5 .
Fig. 5.Outage performance with various values of interference shadowing parameters.

Fig. 6 .
Fig.6.Outage performance with various values of µn of CCI

Fig. 9 .
Fig. 9. Success probability performance with various path-loss exponent values of interference signal