Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels

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-tointerference 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-tointerference ratio; symbol error rate

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

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cation over Dou [20]. The pow D2D signal p D2D pair devic nt (2≤α≤5) and arly, the power 2D pair is: he interferenc eiver of the co the path-lo nal and d 0 is y, in this work on (1) and (2)   ) , With the help of (4), the cumulative distribution function (CDF) of SIR of the D2D system is [22]       , , 4 where: The probability of dropping of the SIR of a system below a predefined threshold R is defined as the outage probability. By Now, the expression for channel capacity of the D2D communication system is obtained by using the formula 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][23][24] 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 c 0 and d 0 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. δ 1 and δ 2 is shown in Figure 2. Transmit power P D , path-loss exponent a, and shape parameter β are fixed at 20dBm, 3 and 2, respectively. Power P I , 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. δ 1 and δ 2 . 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. 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 P D , δ 1 , δ 2 and c are fixed at 20dBm, 1.5, 2 and 25m, respectively. The values of interference parameters P I , 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.  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 P D , a, β, δ 1 and δ 2 are set to be 20dBm, 2.5, 2, 2 and 1, respectively. For the interference signals P I , 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. 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 P D , P I , a, β, δ 1 , δ 2 , 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.

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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 P D , P I , m, β, δ 1 , δ 2 , 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. 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 P D , P I , a, b, m, β, δ 1 , δ 2 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.  Figure 8. The values of P D , P I , β, δ 1 , δ 2 , 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.

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. It is observed that the path-loss significantly affects the performance of the D2D communication system. Moreover, co-channel interference, regardless of being affected by the channel fading and path-loss conditions, manages to affect the performance of the D2D system.