Microsoft Word - 19-2291_s Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3405 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel Analysis of D2D Communication System Over κ-µ Shadowed Fading Channel Zakir Hussain National University of Computer and Emerging Sciences (NUCES), Karachi, Pakistan Asim ur Rehman Khan National University of Computer and Emerging Sciences (NUCES), Karachi, Pakistan Haider Mehdi National University of Computer and Emerging Sciences (NUCES), Karachi, Pakistan S. M. Atif Saleem National University of Computer and Emerging Sciences (NUCES), Karachi, Pakistan Abstract—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 I. 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]: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 1 1 1 1 , , z m Z m m z e z f z F m mm µ κ µµ µ µ µ κ µ κ κ µ µκµ µκ + − − Ω  + + = ×   + ΩΓ Ω +   where 1F1(.) 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 Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3406 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel 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. Fig. 1. D2D system layout Considered D2D device n th interference Distance between desired D2D devices x Distance between n th interference and the desired D2D pair’s receiver yn Desired D2D communication signal n th Interference signal A. MRC Scheme The signal-to-interference power ratio (SIR) at the output of M branches MRC combiner is: 2 0 1, 2 0, , 1 n n u M d lu ld MRC vN I n I n nv n n x P h S x S y P y β − = − =      =        ∑ ∑ (1) In (1), Pd is the power of the D2D signal, x is the distance between D2D devices, u is the path-loss exponent ( )2 5u≤ ≤ for the D2D signal, x0 is the reference distance and hl 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 PI,n which is located at a distance yn from the D2D receiver, y0,n is the reference distance, vn is the path-loss exponent of the n th co-channel interferer and βn 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 Pout is defined as the probability that the instantaneous SIR of the system drops below threshold R. The outage probability is: ( ), ,Prout MRC I d MRCP RS S= > (2) where Pr(.) denotes the probability. Using the expression given in (2), a decision variable ϕ is defined as: ,I d MRC RS Sϕ = − (3) For an acceptable quality of a desired D2D received signal, the value of φ has to be negative. Otherwise, outage will occur. Mathematically, Outage Acceptable transmission 0 0 ϕ >  ≤ (4) 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: ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 n n n n l l l l m N nn m n n n m M ll m l l l W jA C X j T jA B Z j µ ϕ µ µ µ ω φ ω ω ω ω − = − =  −  = ×  − −   +    − +  ∏ ∏ (5) where: ( )1 , n nm n n n n n n n n m A m µ µ κ µ κ  − +    =     Ω +    ( )1 , n n n n n W C µ κ+ = Ω n n n n n n m X W mµ κ   =   +  , ( ) ( ) 2 0, , n n v n n I n v n y C RP y − = , ( )1 l l m l l l l l l l l m A m µ µ κ µ κ  − +    =     Ω +    , ( ) 1l l l l l T B µ κ+ = Ω , l l l l l l m Z T mµ κ   =   +  , 2 0 u l d u x B P x − = , [ ]n nE βΩ = and [ ]l lE hΩ = . Based on (4) and (5), the outage probability of the D2D communication system can be obtained by using the formula: 0 1 1 2 out Im( ( )) P d ϕϕ ω ω π ω ∞ = + ∫ 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), ( )1 1tan tann n n n n n m m X W ω ω θ µ− −     = − −        and ( ) 1 1tan tanl l l l l l m m T Z ω ω ψ µ − −     = − −        . The success probability is defined as the probability for which the SIR of a system excides a fixed threshold R. PS of MRC based D2D communication system is given in (7). Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3407 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 22 2 1 , 1 10 2 2 2 22 2 sin 1 1 1 2 n n l l n n l l N m m n lM N n l nn l S SC m m l n n l n l W TA A P d C B X Z µ µ µ µ θ ψ ω ω ω π ω ω ω − − ∞ = = =        +   + +       = − + ×     − −        + +         ∑ ∏ ∏∫ (6) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 22 2 1 1 , 1 10 2 2 2 22 2 sin 1 1 2 n n l l n n l l N M m m n lN M n l n ln l S MRC m m n ln l n l W TA A P d C B X Z µ µ µ µ θ ψ ω ω ω π ω ω ω ∞ = = = = − −      +  + +      = −      − −       + +       ∑ ∑ ∏ ∏∫ (7) B. Selection Combining For the D2D communication system with SC diversity technique, the SIR of the l th diversity branch is: 2 0 , 2 0, , 1 n n u d lu d SC l vN I n I n nv n n x P h S x S y P y β − − − =      =         ∑ (8) The outage probability for a SC diversity based D2D communication system is: ( ), ,Prout SC I d SC MAXP RS S −= > (9) where ( ), , 1, , maxd SC MAX d SC l l M S S− − = = … . A decision variable Θ is defined as: Outage Acceptable Transmission 0 0 > Θ  ≤ (10) 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. ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 22 2 1 , 1 10 2 2 2 22 2 sin 1 1 2 n n l l n n l l N m m n lM N n l nn l out SC m m l n n l n l W TA A P d C B X Z µ µ µ µ θ ψ ω ω ω π ω ω ω − − ∞ = = =        +   + +       = + ×     − −        + +         ∑ ∏ ∏∫ (11) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 22 2 1 , 1 10 2 2 2 22 2 sin 1 1 1 2 n n l l n n l l N m m n lM N n l nn l S SC m m l n n l n l W TA A P d C B X Z µ µ µ µ θ ψ ω ω ω π ω ω ω − − ∞ = = =        +   + +       = − + ×     − −        + +         ∑ ∏ ∏∫ (12) III. NUMERICAL RESULTS In this section, numerical results are discussed based on the expressions presented above. The reference distances x0, yn,0 are considered to be 1m. Outage threshold R is fixed at 10dBm. In Figure 2, the number of diversity branches M is considered to be 3 for both SC and MRC. The values of signal power of the desired D2D signal Pd, path-loss exponent u, shadowing parameter ml, parameters µl and κl are assumed to be 20dBm, 3.2, {4, 1, 2}, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For CCI signals, the values of signal power PI,n, path-loss exponents vn, distances between interferers and the receiver of D2D pair yn, shadowing parameters mn, parameters µn, and κn, and number of interferers N are considered to be {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7} and 5, respectively. It can be observed that MRC outperforms SC. Furthermore, as the desired D2D devices move away from each other outage performance degrades. It is due to increase in path-loss effects. Fig. 2. Outage performance comparison of MRC and SC scheme Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3408 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel Figure 3 shows the outage performance with MRC diversity based D2D communication system for various M. The values of Pd and u are assumed to be 20dBm and 3.3, respectively. The values of ml, µl and κl for M=2 are set to be {4, 1}, {1, 2}, {2.7, 3.7}, for M=3 the values of ml, µl and κl are {4, 1, 2}, {1, 2, 3}, {2.7, 3.7, 1.7} and for M=4 the values of ml, µl and κl are {4, 1, 2, 2}, {1, 2, 3, 2}, {2.7, 3.7, 1.7, 1}, respectively. For the interference signals, parameters PI,n, vn, yn, N, mn, µn and κn are fixed at {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. From the figure, it can be observed that by increasing the number of diversity branches, the outage performance of the system improves. Fig. 3. Outage performance with varying number of diversity branches Outage performance with varying fading parameter values of the D2D signal µl is shown in Figure 4. MRC diversity scheme is considered. The values of Pd, u, M, ml and κl are fixed at 20dBm, 3.4, 3, {3, 1, 2} and {2.7, 3.7, 1.7}, respectively. For the interference signals, parameters PI,n, vn, yn, N, mn, µn and κn are considered to be {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. It can be observed that as the values of fading parameter µl are increased, the outage performance of D2D system is improved. Fig. 4. Outage performance with various values of µl of the D2D signal Outage performance with varying shadowing parameter values of the interference signal mn is shown in Figure 5. MRC diversity scheme is considered. The values of Pd, u, M, ml, µl and κl are fixed at 20dBm, 3.4, 3, {3, 1, 2}, {3, 4, 5} and {2.7, 3.7, 1.7}, respectively. For CCI signals, values of PI,n, vn, yn, N, µn and κn are assumed to be {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. It is observed that slight change in the outage performance of the system occurs when the interference shadowing conditions are changed. Therefore, outage performance is mostly insensitive to the variations of CCI shadowing conditions. Fig. 5. Outage performance with various values of interference shadowing parameters. Outage performance with varying values of interference signal µn is shown in Figure 6. MRC diversity scheme is incorporated. The values of x, u, M, ml, µl and κl are fixed at 20m, 3.3, 3, {4, 1, 2}, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For the interference signals, parameters PI,n, vn, yn, N, mn and κn the values are fixed at {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {3, 2, 1, 4, 4}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. The value of R is 10dBm. From the figure, it is observed that the outage performance of the D2D system is largely insensitive to the varying values of interference parameter µn. Fig. 6. Outage performance with various values of µn of CCI P o u t P o u t 17 18 19 20 21 22 Pd (dBm) 10 -8 10 -7 10 -6 10 -5 10 -4 P o u t µn=[1, 2, 3, 1, 3] µn=[2, 3, 4, 2, 5] µn=[3, 4, 5, 3, 6] µn=[4, 5, 6, 4, 7] Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3409 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel Outage performance with varying path-loss exponent values of D2D signal u is shown in Figure 7. SC diversity scheme is incorporated. The values of x, M, ml, µl and κl are fixed at 25m, 3, {4, 1, 2}, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For CCI signals, parameters PI,n, vn, yn, N, mn, µn and κn the are assumed to be {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. It is clear from the figure that outage performance degrades as the path-loss exponent values of the D2D signal is increased. It is due to degradation of the SIR due to path-loss effects. Outage performance with varying shadowing parameter values of the D2D signal ml is shown in Figure 8. MRC diversity scheme is considered. The values of Pd, u, M, µl and κl are fixed at 20dBm, 3.2, 3, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For CCI signals, values of PI,n, vn, yn, N, µn and κn are assumed to be {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. It is observed that the outage performance of D2D communication system improves with increasing values of the shadowing parameter of D2D signal ml. It is because of improved shadowing conditions of D2D signal’s channel with increase in values of shadowing parameter ml. Fig. 7. Outage performance with various path-loss exponent values of D2D signal Fig. 8. Outage performance with varying values of shadowing parameter of D2D signal. Success probability performance of D2D communication system varying path-loss exponent values of interference signal vn is shown in Figure 9. SC diversity scheme is considered. The values of Pd, u, M, ml, µl and κl are fixed at 20dBm, 3.9, 3, {1, 2, 3}, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For the interference signals, parameters PI,n, yn, N, mn, µn and κn are fixed at {19.59, 19.03, 18.14, 19.35, 19.3}, {3, 3.2, 3.4, 3, 2.5}, {20, 30, 25, 15, 30} meters, 5, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.7, 2.7, 2.7, 2.7}, respectively. It is observed that for higher path-loss exponent values of interference signals success the probability of the D2D system is high. It is due to weakening of the CCI signals at the receiver of the desired D2D pair. This is because of path-loss effects. The success probability performance with varying distances yn is shown in Figure 10. MRC diversity scheme is assumed. The values of x, u, M, ml, µl and κl are fixed at 30m, 3.3, 3, {4, 1, 2}, {1, 2, 3} and {2.7, 3.7, 1.7}, respectively. For interference signals, parameters PI,n, vn, N, mn, µn and κn are fixed at {19.59, 19.03, 18.14, 19.35, 19.3}, {2.5, 2.7, 3, 3.3, 2.8}, 5, {3, 2, 1, 4, 4}, {1, 2, 2, 1, 3}, {2.7, 3.5, 4.1, 3.2, 3.6}, respectively. It is clear that as the interferers move away from the desired D2D receiver, success probability performance of the system improves. It is because as the interferers move away from the D2D receiver, interference signals weaken at the D2D receiver side. It is due to path-loss effects. Fig. 9. Success probability performance with various path-loss exponent values of interference signal Fig. 10. Success probability performance with varying distances yn 20 20.5 21 21.5 22 22.5 23 Pd (dBm) 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 P o u t u=3.0 u=3.3 u=3.6 20 22 24 26 28 30 x (meters) 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 P o u t ml=[4, 1, 2] ml=[5, 2, 3] ml=[6, 3, 4] P s 13 14 15 16 17 18 Pd (dBm) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P s yn=[18, 30, 25, 15, 20] yn=[20, 35, 30, 20, 25] Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3405-3410 3410 www.etasr.com Hussain et al.: Analysis of D2D Communication System over κ-µ Shadowed Fading Channel 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. REFERENCES [1] H. H. Esmat, M. M. Elmesalawy, I. I. Ibrahim, “Adaptive Resource Sharing Algorithm for Device-to-Device Communications Underlaying Cellular Networks”, IEEE Communications Letters, Vol. 20, No. 3, pp. 530-533, 2016 [2] Y. J. Chun, S. L. Cotton, H. S. Dhillon, A. Ghrayeb, M. O. Hasna, “A Stochastic Geometric Analysis of Device-to-Device Communications Operating Over Generalized Fading Channels”, IEEE Transactions on Wireless Communications, Vol. 16, No. 7, pp. 4151-4165, 2017 [3] W. Song, Y. Zhao, W. Zhuang, “Stable Device Pairing for Collaborative Data Dissemination With Device-to-Device Communications”, IEEE Internet of Things Journal, Vol. 5, No. 2, pp. 1251-1264, 2018 [4] K. Yang, S. Martin, C. Xing, J. Wu, R. Fan, “Energy-Efficient Power Control for Device-to-Device Communications”, IEEE Journal on Selected Areas in Communications, Vol. 34, No. 12, pp. 3208-3220, 2016 [5] N. Vo, T. Q. Duong, H. D. Tuan, A. Kortun, “Optimal Video Streaming in Dense 5G Networks With D2D Communications”, IEEE Access, Vol. 6, pp. 209-223, 2018 [6] K. S. Ali, H. ElSawy, M. Alouini, “Modeling Cellular Networks With Full-Duplex D2D Communication: A Stochastic Geometry Approach”, IEEE Transactions on Communications, Vol. 64, No. 10, pp. 4409-4424, 2016 [7] L. Wang, H. Tang, H. Wu, G. L. Stuber, “Resource Allocation for D2D Communications Underlay in Rayleigh Fading Channels”, IEEE Transactions on Vehicular Technology, Vol. 66, No. 2, pp. 1159-1170, 2017 [8] M. Peng, Y. Li, T. Q. S. Quek, C. Wang, “Device-to-Device Underlaid Cellular Networks under Rician Fading Channels”, IEEE Transactions on Wireless Communications, Vol. 13, No. 8, pp. 4247-4259, 2014 [9] D. Marshall, S. Durrani, J. Guo, N. Yang, “Performance comparison of device-to-device mode selection schemes”, IEEE 26th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications, Hong Kong, China, August 30 – September 2, 2015 [10] S. L. Cotton, “Human Body Shadowing in Cellular Device-to-Device Communications: Channel Modeling Using the Shadowed κ-µ Fading Model”, IEEE Journal on Selected Areas in Communications, Vol. 33, No. 1, pp. 111-119, 2015 [11] J. F. Paris, “Statistical Characterization of κ-µ Shadowed Fading”, IEEE Transactions on Vehicular Technology, Vol. 63, No. 2, pp. 518-526, 2014 [12] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed, Academic Press, 2007 [13] A. Goldsmith, Wireless Communications, Cambridge University Press, 2005