Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3265-3269 3265 www.etasr.com Hussain et al.: Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels 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 Syed M. Atif Saleem National University of Computer and Emerging Sciences (NUCES) Karachi, Pakistan Abstract—In this paper, performance of a device-to-device (D2D) communication system is analyzed over double-generalized Gamma (dGG) fading channels. The dGG is a generic distribution for modeling double-scattering fading conditions. Co-channel interference (CCI) caused by various wireless devices in the system is also considered. The CCI fading channel is assumed to be Nakagami distributed. Analytical expressions for important statistical metrics, i.e. probability density function (PDF) and cumulative distribution function (CDF) of signal-to- interference ratio (SIR), are presented. Based on these statistical parameters, expressions for the outage probability, channel capacity and symbol error rate (SER) of the D2D communication system are presented. The performance of D2D system is then discussed and analyzed with the help of numerical results with arbitrary channel fading, path-loss and interference conditions. Keywords-channel capacity; device-to-device communication; double-generalized gamma; outage probability; signal-to- interference ratio; symbol error rate I. INTRODUCTION The increased growth of smart phones and tablets having many multimedia applications and large file sharing are the motivations for the rapid development in cellular communication systems. These advancements in smart devices with the bandwidth consuming applications have led to increase in demand for higher data rates and this demand is projected to grow exponentially in the future. One of the promising solutions to this problem is device-to-device (D2D) communication system [1-3]. D2D communication system is one of the standards of the 5th generation (5G) cellular communication system. D2D communication is defined as the high data rate direct communication between two users’ equipment with high spectral efficiency, without passing through cellular infrastructures [4-6]. Presence of large number of various types of wireless devices as well as D2D pairs sharing a cellular communication spectrum can cause unwanted and unintentional co-channel interference (CCI) in the absence of proper coordination. Therefore, CCI should be considered while analyzing the performance of D2D communication systems [7-8]. Outage probability, channel capacity and symbol-error rate (SER) are well-known parameters used for the performance analysis of the wireless communication systems. In [9], authors analyzed outage probability of D2D communication systems over Rayleigh fading channels. The outage probability of D2D communication system under Suzuki fading in presence of co-channel interference is studied in [10]. Channel capacity of a D2D system, over a Rician faded channel, is analyzed in [11]. Authors in [12], studied D2D channel capacity over a correlated Rayleigh fading channel in an interference limited environment. In [13], authors presented a study of SER of a multicarrier D2D video transmission over an independent Rayleigh fading channel. In this paper, outage probability, channel capacity and SER of a D2D communication system are investigated. A D2D pair is assumed to be affected by various co-channel interferers in the system. The CCI may arise from any wireless or D2D communication device in the system when proper coordination is lost or interrupted. The fading channel for the desired D2D system is considered to be double-generalized gamma (dGG). The dGG is a versatile and mathematically tractable fading distribution. The dGG variable is a product of two generalized- Gamma variables [14]. The dGG includes various distributions like Gamma-Gamma, double-Nakagami, double-Weibull, Weibull-Gamma, and double-Rayleigh. It can also model distributions like, generalized-Gamma and Nakagami/Rayleigh -lognormal. In cellular communication systems, signals are often scattered and re-scattered around transmitter’s and receiver’s local surroundings. This double-scattering channel condition is observed when the transmitter and receiver devices are moving. The double-scattering conditions can be effectively modeled with the help of dGG distribution [15]. The propagation channel distribution for the CCI is assumed to be Nakagami. Which is a well-known versatile distribution often used in the literature to model various channel fading conditions. The rest of this paper is organized as follows. Section II presents the D2D system model and the expressions for the outage probability, channel capacity and SER. The numerical results are discussed in Section III and Section IV concludes the paper. II. SYSTEM MODEL D2D communication network having N interferers is shown in Figure 1. In this work, a co-channel interferer is assumed to be any wireless node or any D2D communication device. A D2D pair is considered here for the performance analysis. This D2 can env Th Th dG pai sys kee com are app rec ind Dis Int wh the ε2 mo the wh the fad im com Engineerin www.etasr 2D pair is term n be many s vironment of he dGG distrib he channel for GG. The chann ir’s receiver i stem is consid ep the analy mpute mathem e adopted: proximately th ceiver. 2) C dependent and Consi Distance betw stance between i-t Desire terference signal f Comm The PDF of d     1 2 Yf y      here δ1, δ2 and e severity of th are related to odified Bessel e Nakagami di 2 ( ) ( ) X f x    here μ is the fa e channel fad ding and Γ(.) mportant factor mmunication ng, Technology r.com med as desired small objects a D2D pair w bution can effe r the consider nel for the i-t is assumed to dered to be inte ytical work tr matical expres 1) Co-chann he same distan Co-channel in d identically di Fig. 1. TABLE I. idered or desired D i-th interfe ween the devices th interferer and t ed D2D pair comm from i-th interfere D2D pa munication signals dGG distributi       1 2 1 2 2 2 2 y          d β are the fad he fading cond o average pow l function of th istribution is [1 2 1 expx          ading paramete ding condition ) is gamma r that also affe system. A y & Applied Sci Hussain et d or considere in the transm which can caus fectively mode red D2D pair th interferer t o be Nakagam erference limit ractable and ssions, the foll nel interferers nce from the nterferers are stributed. System model NOMENCLAT D2D pair device erer of the desired D2 the desired D2D p munication signal er to the receiver o air for other devices ion is [15]:  2 1 1 2K y         ding shape par ditions, ω=δ1δ wer of fading he second kin 18 2x ,         er which descr ns,  is the function [19 ects the perform simplified p ience Research al.: Analysis of ed D2D pair. mitter and re se double scatt el double scatt r is assumed to the desired mi distributed ted [16]. In or to obtain ea lowing assump s are locate desired D2D e assumed t TURE 2D pair pair’s receiver l of the desired s 2 , > 0y y     rameters that δ2/ε1ε2 where ε g and  vK z nd [17]. The P 1 , 0, 0 2 x   ribes the sever average pow 9]. Path-loss mance of a wi path-loss mod h V f Device-to-Dev There ceiver tering. tering. to be d D2D d. The rder to asy-to- mptions ed at pair’s to be c d imply ε1 and is the DF of 0 rity of wer of is an ireless del is con pair whe the path to 1 of t betw inte inte 100 be inte whe des var inte sys f whe sha ave Tm sign whi cha Vol. 8, No. 4, 20 vice Communic nsidered here [ r is: 0 4 d D λ S P πc     ere PD is the considered D h-loss exponen 100m). Simila the desired D2 0 = 4 II P d         In (2), PI is th ween the rece erferer, b is erference sign 0m). Generally equal. Based o erference signa 2 2 1 , N i i g h      ere g and αi a sired D2D pai riable of the i- erferers in the tem,  ,f r     0 Sx f rxr      0 m f x r               4f rr     ere β a positiv ape parameter erage power ,Nm where nal, paramete ich η is the annel. Moreov    1 2 2 4 12             018, 3265-3269 cation over Dou [20]. The pow 2 0 0 a c c         D2D signal p D2D pair devic nt (2≤α≤5) and arly, the power 2D pair is: 2 0 . b d d         he interferenc eiver of the co the path-lo nal and d0 is y, in this work on (1) and (2) al power ratio D I P c h= P d    are the indepen ir’s signal and -th interferer, r system. The S can be fo    ,If x dx [21]      1 2 12 4 1 2 exp( ( ) T T I m m T f x rx x x m               1 2 1 4, 4 , 4G            ve integer, δ1 rs of the des of the dGG e m is the sha er Ω is given average pow er,       1 2 1 2 4 2 2 Tm T m            9 uble-Generalize wer at the desir power, c is the ces, λ is the w d c0 is the refe r of i-th interf e signal powe onsidered D2D oss exponent the reference k PD and PI ar ), the desired s (SIR) of the D     2 0 2 0 , aa bb c d d      ndent dGG fad d independent respectively. N SIR PDF expr ound by us ]        2 2 1 1 1 2 2 ) , Sf rx K x dx               2 1 24 r          Δ Δ    and δ2 are the ired D2D, ω G fading ch ape parameter n as Ω=φ/h w wer of the in   1 2 1 2 ,       3266 ed Gamma Cha red D2D recei (1) e distance bet wavelength, α i erence distance ferer at the rec (2) er, d is the dis D pair and the (2≤b≤5) of e distance (1 e not consider signal power t D2D system is (3) ding variable o t Nakagami fa N is the numb ression of the sing the ide   4rx         (4) e dGG distrib ω is related to hannel. Param of the interfer where m  nterference fa annels iver’s tween is the e (1m ceiver stance e i-th f the m to red to to the : of the fading ber of D2D entity, bution o the meter rence  in fading Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3265-3269 3267 www.etasr.com Hussain et al.: Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels    1 2 1 2 1 1 4 4, , T Tm m      Δ           and 2 1 2 1 1 2 1 2 2 2 2 , , , 4 4 4 4       Δ         With the help of (4), the cumulative distribution function (CDF) of SIR of the D2D system is [22]      1 2 2 3 11 4,2 4 2 ,4 2 4 , ,4 r F r Gr                   Δ Δ Δ Δ            (5) where:    1 2 1 2 3 1 4 4, ,              Δ  ,    1 21 2 4 1 4, , 4     Δ        . The probability of dropping of the SIR of a system below a predefined threshold R is defined as the outage probability. By using 0 ( ) , R outP f r dr  the expression for the outage probability of the D2D system is [22]:    1 2 2 3 11 4, 2 4 2 , 4 2 4 , ,4 out r P R G                   Δ Δ Δ Δ           (6) Now, the expression for channel capacity of the D2D communication system is obtained by using the formula 2 0 log (1 ) ( ) ,C r f r dr    as in [23]:   21 1 5 34 2 , 2 2 , 4 21 2 5 5 , , ,4ln(2) 2 C G                    Δ ,Δ Δ Δ Δ Δ           (7) where    1 2 1 2 5 1 4 4, ,      Δ           . SER expression of the D2D communication system is now presented. M-ary phase-shift keying (M-PSK) based modulation scheme is incorporated in this work. With the help of [22-24] the SER expression is   2 1 2 64,2 2 , 4 70 sin 4 sin M M SER G d M                                      Δ Δ           (8) where                  1 2 1 2 1 2 2 4 2 1 1 2 2 T T m m                            , 6 1 1 , ,1, ,T T m m  Δ       and 2 2 1 1 7 1 1 , , , , , 2 2 2 2   Δ       . Expressions of the outage probability, capacity and SER are valid for arbitrary parameters of dGG and Nakagami distribution, path-loss and co-channel interference. III. NUMERICAL ANALYSIS AND RESULTS In this Section numerical results are presented and discussed. For analysis simplicity the reference distances c0 and d0 are assumed to be 1m. The SIR threshold R is set at 10dBm. Outage performance of D2D system with varying values of two of shape parameters i.e. δ1 and δ2 is shown in Figure 2. Transmit power PD, path-loss exponent a, and shape parameter β are fixed at 20dBm, 3 and 2, respectively. Power PI, path-loss exponent b, the number of interferers N, the distance between the i-th interferer and the receiver of the desired D2D pair d, and the fading parameter m are assumed to be 10dBm, 3.5, 5, 50m and 2, respectively. It is observed that the fading conditions of the D2D system improve with the increase in the values of fading parameters, i.e. δ1 and δ2. A degradation in the outage performance of D2D system is also observed for the similar channel fading conditions of the desired D2D pair when the value of c is increased. As the desired D2D pair’s transmitter and receiver move away from each other, i.e. the value of c increases, outage performance of the D2D system degrades because of the power decreasing of the desired D2D signal caused by the path-loss effects. Fig. 2. Outage performance with varying values of two of shape parameters. The outage performance comparison of the D2D communication system for various values of dGG fading parameter, β and the path-loss exponent a is shown in Figure 3. The values for the desired signal parameters PD, δ1, δ2 and c are fixed at 20dBm, 1.5, 2 and 25m, respectively. The values of interference parameters PI, b, N, d, m are assumed to be 10dBm, 4, 5, 60m and 1, respectively. It is observed that the outage performance of the D2D system is improved for the higher values of dGG shape parameter β of the desired signal. This happens because of the improved fading conditions with the increase in the values of the desired signal’s shape parameter. Moreover, for the same values of fading shape parameter of the desired signal, outage performance deteriorates with increase in path-loss exponent a because of the worsened SIR condition of the system when the value of a is increased. 30 35 40 45 c (meters) 10-6 10-5 10-4 10-3 10-2 10-1 P o u t δ1=0.7, δ2=1 δ1=1, δ2=1.5 δ1=1.5, δ2=2 Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3265-3269 3268 www.etasr.com Hussain et al.: Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels Fig. 3. Outage performance with varying values of fading parameter β. Outage performance of the D2D system for various values of path-loss exponent of the interference signal b is shown in Figure 4. For the desired signal the values of PD, a, β, δ1 and δ2 are set to be 20dBm, 2.5, 2, 2 and 1, respectively. For the interference signals PI, m, N and d are assumed to be 10dBm, 2, 5 and 50m, respectively. It is noticed that the outage performance is better for the higher values of b because of the weakening of the interference signals at the desired D2D pair’s receiver when the value of the CCI path-loss exponent b is increased. Hence, an improved outage performance of the D2D system is observed. It is also observed that as the desired D2D pair’s devices move away from each other, the value of c increases and outage performance of the D2D system deteriorates because of the weakening of the desired D2D signal caused by the path-loss effects. Fig. 4. Outage performance with various values of path-loss exponent b Figure 5 illustrates the outage performance with various values of the interference fading shape parameter m and distance d. The values of PD, PI, a, β, δ1, δ2, b, N and c are fixed at 20dBm, 10dBm, 2.5, 2, 1.5,3, 3 and 25m, respectively. It is observed that the system outage performance is almost insensitive to the interference fading conditions. Moreover, for the same value of m it is observed that the outage performance of the system improves with increasing values of the distance d, because as the interferers move away from the desired D2D pair’s receiver the interference signal strength weakens due to path-loss effects. Channel capacity performance of D2D communication system with varying values of N and the path-loss exponent a is shown in Figure 6. The values of PD, PI, m, β, δ1, δ2, b, c and d are set to be 20dBm, 10dBm, 2, 1, 1, 2, 3, 30m and 60m, respectively. It is clear that the channel capacity performance of the system is better when the number of interferers N is decreased. It is also observed that as the path-loss exponent value of the desired signal is increased, the capacity performance of the system degrades due to the weakening of the desired signal strength due to path-loss effects. Fig. 5. Outage performance with various values of the shape parameter of CCI Fig. 6. Channel capacity performance of D2D communication system for various N Figure 7 shows the channel capacity performance of the D2D system for different values of distances d and c. The values of PD, PI, a, b, m, β, δ1, δ2 and N are assumed to be 20dBm, 10dBm, 3, 3.3, 2, 1, 1, 2 and 5, respectively. it is observed that the channel capacity is improved for higher values of the distance d because of the improvement of the SIR conditions due to weakening of the interference signals at the desired D2D pair’s receiver. Fig. 7. Capacity performance of D2D communication system with varying distance d 2.8 3 3.2 3.4 3.6 3.8 4 a 10-10 10-8 10-6 10-4 10-2 P o u t β=1 β=2 20 25 30 35 40 45 c (meters) 10-7 10-6 10-5 10-4 10-3 10-2 P o u t b=2.8 b=3.5 b=4.2 30 35 40 45 50 d (meters) 10-6 10-5 10-4 P o u t m=0.5 m=1 m=3 m=5 2.5 3 3.5 4 a 0 1 2 3 4 5 6 C ( B it s/ s/ H z) N=5 N=10 N=15 25 30 35 40 45 c (meters) 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 C ( b it s/ s/ H z) d=30 d=45 d=60 Engineering, Technology & Applied Science Research Vol. 8, No. 4, 2018, 3265-3269 3269 www.etasr.com Hussain et al.: Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels SER performance of 8-PSK scheme with various values of number of interference signals is shown in Figure 8. The values of PD, PI, β, δ1, δ2, m, a, c and d are considered to be 20dBm, 10dBm, 1, 2, 3, 2, 3.7, 20m and 60m respectively. The SER performance improves when the number of interferers is reduced. Moreover, for the same number of interferers, SER performance improves with an increase in the values of interferers’ path-loss exponent b. Fig. 8. SER performance with various values of number of CCIs IV. CONCLUSION In this paper, the performance of a D2D communication system over a dGG faded channel is analyzed. The dGG distribution is a general distribution that includes all others that are used to model double-scattering which occur in wireless communication systems. Effects of co-channel interference caused by various wireless devices in the system are included. Expressions of the PDF and CDF of the SIR of the D2D system are presented. Based on the PDF of the SIR, expressions of the performance metrics like outage probability, channel capacity and SER are presented. Based on these expressions, numerical results are presented to discuss the performance of the D2D system under varying interference, path-loss and channel fading conditions. 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