- Research
- Open Access
Two-way DF relaying assisted D2D communication: ergodic rate and power allocation
- Yiyang Ni^{1}Email author,
- Yuxi Wang^{1},
- Shi Jin^{2},
- Kai-Kit Wong^{3} and
- Hongbo Zhu^{4}
https://doi.org/10.1186/s13634-017-0464-1
© The Author(s) 2017
- Received: 10 January 2017
- Accepted: 18 April 2017
- Published: 30 May 2017
The Correction to this article has been published in EURASIP Journal on Advances in Signal Processing 2018 2018:2
Abstract
In this paper, we investigate the ergodic rate for a device-to-device (D2D) communication system aided by a two-way decode-and-forward (DF) relay node. We first derive closed-form expressions for the ergodic rate of the D2D link under asymmetric and symmetric cases, respectively. We subsequently discuss two special scenarios including weak interference case and high signal-to-noise ratio case. Then we derive the tight approximations for each of the considered scenarios. Assuming that each transmitter only has access to its own statistical channel state information (CSI), we further derive closed-form power allocation strategy to improve the system performance according to the analytical results of the ergodic rate. Furthermore, some insights are provided for the power allocation strategy based on the analytical results. The strategies are easy to compute and require to know only the channel statistics. Numerical results show the accuracy of the analysis results under various conditions and test the availability of the power allocation strategy.
Keywords
- Device-to-device communication
- Two-way relay
- Decode-and-forward
- Ergodic rate
- Power allocation
1 Introduction
In recent years, a seamless increase of various innovative multi-media services has kept pushing the limits of current wireless networks, urging for higher-speed communications [1, 2]. As the smart mobile devices popularize progressively, the demand for higher wireless transmission rate will grow exponentially in the next decades and a 1000 times increase in the current system capacity is required by 2020 [3, 4]. However, the fourth generation mobile communication systems which can support a rate of 1Gbit/s hardly satisfy the demand of mobile communication in the next 10 years [5]. Therefore, the fifth generation (5G) cellular network is being considered [6]. One of the key technologies for 5G systems, which has recently attracted huge attention and can greatly enhance the spectral efficiency [7–9], is device-to-device (D2D) communication.
Generally speaking, there are two main types of radio resource sharing methods used by D2D communication in a cellular network: underlay and overlay inband communication [10]. For the overlay case, D2D communication takes part of the cellular resources and leaves the other half to the cellular user. Therefore, there is no interference between cellular link and D2D link. In contrast, for the underlay case, D2D users use the same resources with the cellular user causing interference to both the cellular link and D2D link, and the base station (BS) is required to coordinate the transmit power for both the cellular and D2D users [11–13]. Compared with the conventional cellular communication, obviously, comparing to the traditional cellular communication, D2D communication can save the resources and improve the throughput greatly, due to the fact that only half of the resources are used [14].
Although lots of advantages can be taken by D2D communication, it also faces a rigorous challenge—the inter-channel interference [15]. To reduced ICI from the D2D links, interference management and coordination is important for physical-layer designs, e.g., power control and resource allocation. Great efforts to tackle the interference problem have been made in [16–18]. For traditional D2D communication systems, many power allocation strategies have presented to improve the performance of cellular link or D2D link. For example, in [12], a joint power allocation scheme was proposed which maximizes the sum-rate of D2D link and cellular link. The authors in [13] have also given an interference-aware channel allocation scheme based on Hungarian algorithm to maximize the number of permitted D2D communication pairs. In order to effectively guarantee the cellular service, Yu et al. [16] proposed a transmit power allocation algorithm while the authors in [18] presented an optimum resource allocation and power control between the cellular and D2D link to improve the performance of D2D communication.
Equally, relay-assisted communication in cellular networks has also demonstrated great potential in enhancing the system performance [19–21]. Efforts have been firstly spent on analyzing the one-way relay-assisted systems with different relay protocols including amplify-and-forward (AF), decode-and-forward (DF), and compress-and-forward (CF) protocols, e.g., [22–24]. Relaying technologies have also been proposed for two-way communications [25, 26]. The transmission schemes over two, three, or four time slots for two-way relay protocols have been investigated in [27]. Recently, the application of relay techniques in conjunction with D2D communication has increasing interest as a means of achieving further performance improvements and coverage enhancement in cellular networks. Also, the D2D communication assisted by a relay node can alleviate the interference to the cellular link as it can reduce the transmit power of the D2D users. A comprehensive resource allocation framework for the one-way DF relay-assisted D2D communication was presented in [28]. In [29], the authors presented a joint relay selection and power allocation scheme for one-way AF relayed D2D communication. Based on the outage probability performance, Wang et al. [30] presented an interference constrained precondition for the one-way DF relay aided D2D communication. It is obvious that the combination of the D2D communication and the relay-assisted communication is a very effective method to improve the performance of the next-generation cellular system. One-way relay-assisted system has been investigated in [31–33] which presented closed-form expressions for the system performance. However, it needs four time slots to realize a complete communication with one-way relay policy while only two time slots are required for the two-way relay policy. Due to its potential to enhance the spectrum efficiency, two-way relay policy has attracted a great deal of attention. An optimal power allocation algorithm was provided to minimize the outage probability of D2D users for the two-way AF relay-assisted D2D communication system [34]. However, the interference was not considered. Sun et al. [35] proposed a security-embedded interference avoidance scheme to improve the system error performance in which the D2D user served as relays to assist the two-way transmission between two cellular users. In [36], authors proposed a new scheme in which three-phase D2D communication assisted with two-way DF relay is considered. The Pareto boundary of the region of the sum rate of D2D link versus that of the cellular link was found by optimizing the transmit power at base station and cellular user, as well as, D2D users [37].
Motivated by the interest of two-way relay-assisted system, as our major contribution, we will derive closed-form expressions of the ergodic rate for the proposed relay-assisted strategy, and investigate the effects of noise, the predetermined ratio, the received power of signals including the desired signal, and the interference. Two cases in which the relaying terminal has the same (symmetric) and different (asymmetric) received power from the two terminals exchanging information are considered. We then study the performance for the weak interference case and high signal-to-noise ratio (SNR) case. The approximations of ergodic rate for these cases are derived respectively. Based on these approximations, we present closed-form power allocation strategies which involve several key system coefficients and can be easily implemented. Numerical results confirm the accuracy of the analysis results and show the tightness of our approximate results. The improvement of the ergodic rate by using the power allocation strategy also can be found from the numerical results. To the best of our knowledge, this is the first analytical result that is applicable for D2D communication with two-way DF relaying.
2 System model
3 Ergodic rate analysis
We are now ready to derive an analytical expression of (11).
3.1 Exact analysis
With the above analysis, we now investigate the closed-form expression for the ergodic rate. The case of P _{1r }≠P _{2r } is referred to as the asymmetric case. For the symmetric case, since the received power at relay node from UED_{1} is equal to that from UED_{2}, we use P _{ dr } to indicate the received power at the relay node from the D2D users. The ergodic rate of the D2D link under the two cases are derived and presented in the following theorem.
Theorem 1
Proof
See Appendix 1. □
The same result can be obtained for the case a<b. That is, the values of the expressions in (16)–(19) are always positive.
Our result in Theorem 1, in contrast, presents the exact closed-form expression which is applicable for arbitrary system parameters, and is given in closed-form expressions involving standard functions which can be easily evaluated using Matlab or Mathematics softwares. We note that this theorem presents an exact expression for the ergodic rate of the D2D communication aided by a DF relay node. In prior works, separate alternative expressions were only obtained for the traditional D2D communication scenarios without considering the different interference level in different time slots. Moreover, based on Theorem 1, we have the following observations. Since e ^{1/x } E _{1}(1/x) is a monotonically increasing function, Theorem 1 implies that P _{1r }>P _{ cr }, β P _{ r2}>P _{ b2}, P _{2r }>P _{ cr }, and (1−β)P _{ r1}>P _{ b1} should hold to transmit the message between different nodes reliably. These conditions also mean that the interferences from the BS and the cellular user play a negative role in the ergodic rate.
3.1.1 Weak interference case
In this subsection, we examine the scenario that the D2D communication occurs at the cell edge where the D2D users reuse the resources of the cellular user far away. Hence, the interference at D2D users is weak enough compared to the noise which means P _{ cr }→0, P _{ bi }→0, N _{0}/P _{ cr }→∞ and N _{0}/P _{ bi }→∞. According to these, the ergodic rate of the D2D link can be described in the following corollary.
Corollary 1
Proof
Having these results, we can easily obtain the approximations in Corollary 1. □
Corollary 1 provides approximate results of ergodic rate for the weak interference scenario. Clearly, the expressions in Corollary 1 are simpler than the ergodic rate expressions given in Theorem 1. Note that the ergodic rate only depends on the desired signal for the weak interference scenario. Since h(x) in (24) is a monotonically increasing function with x, \(R_{sum}^{WI}\) can be improved by increasing P _{ ir } and P _{ ri }. That is to say, enhancing the power of desired signals can improve the performance of D2D link when the locations of D2D users are fixed.
3.1.2 High SNR case
Here, we consider the fact that the communicating users in D2D communication systems are relatively close to each other. Here we will present new asymptotic ergodic rate expressions when the receive SNR at the D2D users goes to infinity which means P _{ ir }/N _{0}→∞ and P _{ ri }/N _{0}→∞. This will be useful in deriving the optimal power allocation for the ergodic rate at high SNR later in this section. For this case, the ergodic rate of D2D communication aided by the relay node are given in the following corollary.
Corollary 2
where λ≈0.577 is the Euler-Mascheroni constant.
Proof
□
For the case the relay has some statistical channel state information (CSI) about the system parameters, β may be chosen such that the ergodic rate is maximized. In this paper, we investigate the power allocation scheme that maximizes the ergodic rate based on the network geometry and the statistical CSI which include the second-order statistics and the interference level. For simplicity, we consider a linear network topology and assume that the relay node has only the path-loss coefficients of all the channels. We assume the transmit power at each user is P _{ T }. Since the D2D communication always occurs far from the BS and the distance between D2D users is short, we can get the approximation that d _{ b1}≈d _{ b2} which leads to P _{ b1}≈P _{ b2}≈P _{ b }.
Corollary 3
with \({g_{st}} = d_{st}^{- \alpha }(s,t = 1,2,r;s \ne t)\).
Proof
See Appendix 2. □
From the power allocation scheme in (50), we find that the power allocation coefficient is determined by the location of the relay node on the D2D link when the interference from cellular link is fixed. Instead, the interference level of the cellular link leads to difference power allocation coefficient for the fixed location of relay node. Note that the power allocation strategy in (50) uses only the second-order statistics and the interference levels from the cellular link. It means that the derived power allocation strategy can be easily implemented in practice. It is interesting that there exists some region for the optimal coefficient which equals to 0.5.
4 Numerical results
Simulation parameters
Transmit power of each user | P _{ iT }=P _{ T }(i=C,1,2,R) |
Transmit power of BS | P _{ bT }=20P _{ iT } |
Path-loss coefficients | α=4 |
Distance between D2D users | d _{12}=1 |
Noise variance | N _{0}=1 |
SNR | SNR=P _{ T }/N _{0} |
5 Conclusions
This paper proposed a new D2D communication strategy underlaying cellular networks which is aided by a relay node using two-way DF protocol. The outage probability and the ergodic rate of the new strategy were discussed for both the asymmetric and symmetric cases. For the new D2D communication strategy, we derive the closed-form expressions and their high SNR approximations for both outage probability and the ergodic rate. Based on these results, we showed that several major factors play a negative role for the system performance. Furthermore, closed-form power allocation solutions which minimize the outage probability or maximizes the ergodic rate were presented using the high SNR approximations. Analytical results were validated through numerical simulations.
6 Appendices
7 Appendix 1
7.1 Proof of Theorem 1
Here, we start from the asymmetric case. (1) The Asymmetric Case
and then combining (67) yields the desired result. (2) The Symmetric Case
Substituting (79), (80) and (87) into (78), we get (22). Then utilizing (16)–(19) and (22) yields the desired result.
8 Appendix 2
8.1 Proof of Corollary 3
Since P _{ b1}≈P _{ b2}≈P _{ b }, we have θ _{1}≈θ _{2}≈θ. In order to get the optimal β, we will consider two cases: A≤B and B≤A. (1) The A≤B Case (G _{1}≤0)
where \(R_{2r}^{HS}\) is independent of β and \(R_{r2}^{HS}\) is a strictly increasing function with respect to β. It follows that β ^{∗}=A is the optimal value.
Then, we consider the another case. 2) The B≤A Case (G _{1}≥0)
In this case, β will fall into one of the three cases, (1) β≤B, (2) B≤β≤A, and (3) A≤β. After operating the same procedure in Section (1), we can easily obtain the following results
Then the optimal β for \(R_{\max }^{B \le \beta \le A}\) is β ^{∗}=1/2.
Having the above results and combining with (98), it yields the desired result.
Notes
Declarations
Funding
This work was supported by the National Science Foundation (NSFC) for Distinguished Young Scholars of China with Grant 61625106 and the NSFC with Grant 61531011,61427801.
Authors’ contributions
HZ and SJ conceived the study. YN, YW, and SJ are designed and modelled the study. YN, SJ, and K-KW are responsible for the performance analysis. YN, YW, K-KW, and HZ are responsible for the results interpretation and manuscript writing:. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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