Performance Analysis of Device to Device Communications Overlaying/Underlaying Cellular Network
Subject Areas : GeneralHossein Ghavami 1 , Shahriar Shirvani Moghaddam 2
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Keywords: Device to Device Communications, Overlay, Underlay, Outage probability, Throughput,
Abstract :
Minimizing the outage probability and maximizing throughput are two important aspects in device to device (D2D) communications, which are greatly related to each other. In this paper, first, the exact formulas of the outage probability for D2D communications underlaying or overlaying cellular network are derived which jointly experience Additive White Gaussian Noise (AWGN) and Rayleigh multipath fading. Then, simulation results of the exact formulas and previously respected approximate formulas are compared in MATLAB for both underlay and overlay scenarios. It is shown that the approximate formula in underlay scenario is a good estimate for exact one while approximate formula for overlaying scenario is a good approximation when the average distance between the transmit/receive nodes of D2D pair is less than half of the maximum distance between these nodes or variance of multipath fading is greater than 1.5. In addition, the probability density functions of Signal to Interference plus Noise Ratio (SINR) for underlay and overlay scenarios are found. Moreover, a new scenario is proposed which jointly considers overlay and underlay scenarios. Furthermore, exact and approximate formulas for outage probability and throughput of D2D users in the proposed scenario are derived. Finally, these formulas are compared to underlay and overlay scenarios in three special cases, low, moderate and high traffic loads
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[3] D. Feng, L. Lu, Y. Yuan-Wu, G.Li, G. Feng, and S. Li, "Device to device communications underlaying cellular networks," IEEE Transactions on Communications, vol. 61, no. 8, pp. 3541–51, 2013.
[4] P. Sartori, H. Bagheri, V. Desai, B. Classon, A. Soong, M. Al-Shalash, et al., "Design of a D2D overlay for next generation LTE," In: 80th IEEE Vehicular Technology Conference (VTC Fall), Vancouver, Canada, pp. 1-5, 2014.
[5] M. Hasan, E. Hossain, and D. I. Kim, "Resource allocation under channel uncertainties for relay-aided device-to-device communication underlaying LTE-A cellular networks," IEEE Transactions on Wireless Communications, vol. 13, no. 4, pp. 2322 - 2338, 2014 .
[6] J. Liu, N. Kato, J. Ma, and N. Kadowaki, "Device-to-device communication in LTE-advanced networks: A survey," IEEE Communications Surveys and Tutorials, vol. 17, no. 4, pp. 1923-1940, 2015.
[7] H. Min, W. Seo, J. Lee, S. Park, and D. Hong, "Reliability improvement using receive mode selection in the device-to-device uplink period underlaying cellular networks," IEEE Transactions on Wireless Communications, vol. 10, no. 2, pp. 413-418, 2011.
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[10] H. Wang and X. Chu, "Distance-constrained resource-sharing criteria for device-to-device communications underlaying cellular networks," IET Electronics Letters., vol. 48, no. 9, pp. 528-530, Apr. 2012.
[11] Han, Q. Cui, C. Yang, and X. Tao, "Bipartite matching approach to optimal resource allocation in device to device underlaying cellular network," IET Electronics Letters, vol. 50, no. 3, pp. 212-214, 2014.
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Iranian Journal of Information Technology & Communication | No.33-34, Vol.9, Fall & Winter 2018 |
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Performance Analysis of Device to Device Communications Overlaying/Underlaying Cellular Network
* Hossein Ghavami ** Shahriar Shirvani Moghaddam
* Digital Communications Signal Processing (DCSP) Research Lab., Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
** Faculty of Electrical Engineering, Shahid Rajaee Teacher Training University (SRTTU), 16788-15811, Tehran, Iran
Abstract
Minimizing the outage probability and maximizing throughput are two important aspects in device to device (D2D) communications, which are greatly related to each other. In this paper, first, the exact formulas of the outage probability for D2D communications underlaying or overlaying cellular network are derived which jointly experience Additive White Gaussian Noise (AWGN) and Rayleigh multipath fading. Then, simulation results of the exact formulas and previously respected approximate formulas are compared in MATLAB for both underlay and overlay scenarios. It is shown that the approximate formula in underlay scenario is a good estimate for exact one while approximate formula for overlaying scenario is a good approximation when the average distance between the transmit/receive nodes of D2D pair is less than half of the maximum distance between these nodes or variance of multipath fading is greater than 1.5. In addition, the probability density functions of Signal to Interference plus Noise Ratio (SINR) for underlay and overlay scenarios are found. Moreover, a new scenario is proposed which jointly considers overlay and underlay scenarios. Furthermore, exact and approximate formulas for outage probability and throughput of D2D users in the proposed scenario are derived. Finally, these formulas are compared to underlay and overlay scenarios in three special cases, low, moderate and high traffic loads.
Keywords: Device to Device Communications; Overlay; Underlay; Outage probability; Throughput.
1. Introduction
Device to Device (D2D) communications is considered as a key solution for spectrum scarcity in the 3rd Generation Partnership Project (3GPP), Long Term Evolution (LTE) [1]. In a cellular communications system, the user equipment (UE) need to use an interface such as cellular Base Station (BS) or Relay Station (RS) to be connected to another UE. Unlike cellular users, in direct D2D communications, two nearby users communicate with each other without sending their data to BS or RS [2]. D2D communications improves network capacity and this type of communications is a keyway in 5G for achieving higher data rates, which is in the spotlight of researchers [3].
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In general, D2D communications can increase physical layer security, enhance connecting probability, improve cell coverage, decrease transmission delay, and reduce the burden on base station [2, 7].
One of the research topics considered in the D2D communications outage and maximizing throughput in order to efficient resource allocation for cellular users. In the other words, the aim is to minimize the outage probability "The probability that the received Signal to Interference plus Noise Ratio (SINR) is less than the threshold" [8] and to maximize throughput "a nonlinear objective function on SINR".
Previous studies [4, 8-12] presented only the approximate equations for outage probability in underlay and overlay scenarios, but exact equations have not been reported in these studies.
In this paper, the exact formulas for both outage probability and throughput in underlay and overlay scenarios are extracted in the case of Additive White Gaussian Noise (AWGN) and multipath Rayleigh fading channel. In addition, as a comparative study, numerical results of the new acquired exact formulas for underlay and overlay scenarios and previously reported approximate formulas are compared with simulation results in MATLAB. Finally, a new scenario is proposed which considers jointly overlay and underlay scenarios.
This paper is structured as follows. In Section 2, system model for D2D communications underlaying and overlaying cellular network is illustrated. In Section 3, exact and approximate formulas of outage probability for both underlay and overlay scenarios are obtained. In Section 4, first numerical analysis of scenarios 1 and 2 is presented which let us to compare the analytical (exact and approximate formulas) and simulation results. The overlay/underlay scenario is proposed in Section 5. In this section, exact and approximate formulas for outage probability and throughput are presented. Second numerical analysis is reported in Section 6. Finally, Section 7 concludes this paper.
2. System model
As shown in Figure 1, an omni-directional base station is located in the center of a cell radius of 1000m. This one-cell model is including M cellular users and N D2D pairs uniformly distributed throughout the cell. It is assumed that small-scale fading is in accordance with a Rayleigh distribution and a Line Of Sight (L.O.S) path loss model is considered for radio channels between cellular user and D2D pair and transmit/receive nodes of D2D pair. Moreover, each D2D pair allowed to use one idle radio resource in overlay and reuse just one radio resource in underlay manner.
Fig. 1. System model for D2D communications in a cellular system
2.1. Overlaying Scenario
In overlay scenario, radio resources of both D2D pairs and cellular users are orthogonal. It means that cellular users and D2D pairs does not interfere with each other. Hence, the received signal at the receive node of a D2D pair is as (1):
(1) |
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Since overlaying scenario is interference-free, SINR equals to Signal to Noise Ratio (SNR). It means that SINR is as (2) [9]:
(2) |
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2.2. Underlaying Scenario
In this scenario, resources of D2D pairs are not orthogonal to the cellular user resources, which means that cellular users make interference on D2D users and vice versa. Hence, the received signal at the receive node of a D2D pair is as (3) [10]:
(3) |
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SINR on the i-th D2D pair, which reuses the radio resource of the j-th cellular user, is as (4) [8, 11]:
(4) |
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where 
is the signal transmitted from the transmit node of the i-th D2D pair, 
and 
are the transmit powers of the cellular user and D2D pair, respectively. 
is the distance between the transmit and receive nodes of a D2D pair. 
is the distance of the i-th D2D pair from j-th cellular user. 
and 
are in accordance with Rayleigh fading channels for the i-th D2D pair and j-th cellular user. 
is the path loss exponent factor.
In formulas (2), (4) we have
(5) |
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(6) |
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where respectively are the powers in the receive node of D2D pair received from the transmitters of D2D pair and cellular user.
Considering the power spectral density of noise, N0/2 and receiver bandwidth BW, the noise power is as (7)
(7) |
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3. Outage Probability for Underlaying and Overlaying Scenarios
3.1. Underlay scenario
According to formula (4), we have
(8) |
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So that
(9) |
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(10) |
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where and are Rayleigh faded channel responses with variance of 
. According to this fact that the statistical distribution of channel power gain is exponential and based on [13 (Equation 5-18)], we have the probability density functions (pdfs) of 
and 
, respectively as (11) and (12).
(11) |
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(12) |
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In order to find the exact formula, it is assumed that noise (
) is a zero-mean Gaussian random variable with variance of 
. By considering
(13) |
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the probability density function of 
is
(14) |
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By supposing
(15) |
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and considering [13 (Equation 6-45)], we have
(16) |
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SINR which is needed to be modeled for finding the outage probability and throughput, is as the form
(17) |
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Applying [13 (Equation 6-59)], we can find the probability density function of SINR as
(18) |
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According to (19), exact formula of outage probability for underlay scenario is as (20).
(19) |
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(20) |
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In approximate equation [4, 12], it is assumed that 
is constant. Hence, considering [13 (Equation 5-18)], we have
(21) |
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and consequently according to [13 (Equation 6-59)], we have
(22) |
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Finally, according to [4, 12] and Equation (19), approximate formula of outage probability for underlay scenario is as (23):
(23) |
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3.2. Overlay scenario
According to Equation (2), we have
(24) |
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So that
(25) |
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where is Rayleigh distributions with variance of. It is clear that the statistical distribution of channel gain is exponential, and based on [13 (Equation 5-18)], we have
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as the probability density function of . In order to find the exact formula, it is assumed that noise () is a zero-mean Gaussian random variable with variance of . By considering
(27) |
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the probability density function of Y is
(28) |
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Applying [13 (Equation 6-59)], we can find the probability density function of SINR as
(29) |
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According to Equation (19), the exact formula of outage probability for overlay scenario is as (30).
