- Research
- Open Access
Maximizing throughput gain via resource allocation in D2D communications
- Yucheng Wu^{1}Email author,
- Xiaocui Liu^{1},
- Xiang He^{1},
- Qiong Yu^{1} and
- Weiyang Xu^{1}
https://doi.org/10.1186/s13638-017-1007-z
© The Author(s) 2017
- Received: 21 September 2017
- Accepted: 14 December 2017
- Published: 28 December 2017
Abstract
By reusing the cellular resources, device-to-device (D2D) communication is becoming a very promising technology that greatly enhances the spectrum utilization. To harvest the benefits that D2D communications can offer, efficient resource allocation strategy is required to guarantee the demands of quality of service (QoS) for both cellular and D2D users. This paper proposes a resource allocation scheme to alleviate the performance deterioration of the D2D communications with spectrum reuse. To maximize the overall throughput gain, the proposed scheme is designed to reduce the rate loss of cellular users and improve the rate of D2D users simultaneously in a two-step manner. Specifically, it first calculates the reuse gain for a single D2D pair and a single cellular user. Next, a maximum weight bipartite matching is further proposed to select the reuse pair to maximize the overall network throughput gain. Numerical results demonstrate that the proposed resource allocation scheme can significantly improve the network throughput performance with average user rate guaranteed.
Keywords
- D2D communications
- Resource allocation
- Optimization
- Throughput gain
- Rate loss
1 Introduction
The device-to-device (D2D) communication is widely recognized as one of the key technology of the evolving 5G architecture due to the enhanced cellular spectrum utilization [1]. In the D2D scenario, the terminals can communicate directly with one another without the base station (BS) [2]. Therefore, the end-to-end latency can be decreased; also, the area spectral efficiency can be improved simultaneously. Therefore, the network is able to accommodate more users [3, 4].
It is worth noting that D2D communications rely on the reuse of cellular spectrum resources; thus, the performance of the cellular system will be subject to the interference incurred as a consequence. This key problem has drawn much attention from both the academic and industrial fields. In references, methods in [4–7] suggest to mitigate the interference that cellular users suffer by either limiting the D2D user’s transmit power or choosing the D2D users only in the interference limited area. However, the two approaches mentioned above cannot fully enhance the performance of D2D communications.
On the other hand, the motivation of works in [8–11] is to increase the network throughput. In [8], a single D2D pair is allowed to reuse a single cellular user’s resource to maximize the throughput, and also, a closed expression of the optimal power allocation is given. In [9], the overall network throughput is maximized via reusing cellular users’ resources by multiple D2D pairs where the optimization problem is solved in three steps, i.e., access control, power allocation, and channel allocation. Moreover, the literatures in [10, 11] still consider the resource allocation with the goal of maximizing the throughput while taking the throughput gain as the access control criterion. Unfortunately, none of the above studies take into account the performance loss of cellular users incurred by the spectrum reuse. In [12], the authors propose a power management scheme for an adjacent femtocell network and formulate a non-convex optimization problem in order to maximize the capacity under the power constraints. The joint uplink subchannel and power allocation in cognitive small cells using cooperative Nash bargaining game theory is investigated in [13], where the cross-tier interference mitigation, minimum outage probability requirement, imperfect CSI, and fairness are considered. In [14], the authors propose an iterative gradient user association and power allocation approach with attention to load balance constraints, energy harvesting by base stations, user quality of service requirements, energy efficiency, and cross-tier interference limits. More recently, [15] analyzes the characteristics of optimal joint power control and D2D matching strategy, based on which an energy-efficient iterative algorithm for D2D communications is proposed.
For the future evolution of cellular networks, it is significant to maintain the quality of service (QoS) of both cellular and D2D users. To this end, this paper proposes a resource allocation algorithm that maximizes the throughput gain while reducing the rate loss of cellular users and increasing the rate of D2D users at the same time. It is demonstrated that the resource allocation in this study can be modeled as a mixed integer nonlinear programming (MINLP) optimization problem. To find a tractable solution, the original MINLP problem is decomposed into two subproblems, where the optimal solutions are able to be obtained in a two-step manner without reducing the feasible domain. Specifically, the first subproblem is to obtain the maximum reuse gain when a single D2D user shares a single cellular user’s resource and determine whether it is eligible for spectrum reuse. Moreover, the second subproblem determines the best pairing between D2D and cellular users and finally maximizes the overall network throughput.
The rest of the paper is organized as follows. The system model and optimization problem description are given in Section 2. Then, in Section 3, the optimal resource allocation algorithm is investigated in detail. Numerical results are presented in Section 4 to demonstrate the performance of the proposed scheme. Finally, Section 5 concludes this paper.
2 System model and problem formulation
2.1 Introduction of system model
where K is a system-related constant, β _{ i,j } represents the multipath gain of the link between terminals i and j, which follows the exponential distribution, η _{ i,j } denotes the shadow gain of the link, following the logarithm distribution, d _{ i,j } indicates the distance of the link, and α indicates the path-loss factor. In order to distinguish different links in the system model, we adopt the following rules: D _{ m,m } indicates the D2D link m and the corresponding path gain is \(g_{D_{m,m}}\), C _{ n,B } indicates the link between cellular user n and BS and the path gain is represented as \(g_{C_{n,B}}\), D _{ m,B } denotes the link between the transmitter of D2D pair m to BS and the path gain is \(g_{D_{m,B}}\), and C _{ n,m } represents the link between the cellular user n to the receiver of the D2D pair m, whereas the path gain is expressed as \(g_{C_{n,m}}\).
2.2 Problem formulation
where P _{ n } and P _{ m } indicate the transmission power of the cellular user and D2D user, separately, and σ ^{2} denotes the variance of the additive white Gaussian noise (AWGN).
where ξ _{ m } is the SINR obtained after D2D users access the cellular resources, i.e., \(\xi _{m} = P_{m}g_{Dm,m}/\left (\sigma ^{2} + P_{n}g_{C_{n,m}}\right)\).
The target function should be converted to the maximum problem without any bias. Let λ _{1}=1 and λ _{2}=−1, so that the evaluation function is obtained. The purpose of this function is to maximize the system throughput gain. A suboptimal solution could be given to the original optimization problem, thus maximizing the system throughput gain can take into account the performance gain of the D2D user and at the same time the performance loss of the cellular user.
where D _{ A }(D _{ A }∈D) represents the subset of D2D users that can access the cellular network, ξ _{ n,min} and ξ _{ m,min} are the minimum SINR requirements for cellular users and D2D users, respectively, and ξ _{ m } represents the SINR of D2D user with interference caused by the cellular user. According to the expressions of ξ _{ n } and \(\xi _{n}^{\text {no}}\), it can be found that when ξ _{ n }≥ξ _{ n,min}, it is straightforward to derive that \(\xi _{n}^{\text {no}} \ge {\xi _{n,\min }}\), thus the constraint of \(\xi _{n}^{\text {no}} \ge {\xi _{n,\min }}\) is not required. x _{ m,n } is the identifier of the resource reuse, i.e., when the D2D user m reuses the resource of cellular user n, then x _{ m,n }=1; otherwise, x _{ m,n }=0. Since the optimization problem contains the integer variable x _{ m,n } and the objective function is nonlinear, it can be considered as a mixed integer nonlinear programming problem which is difficult to directly obtain the optimal solution. Alternatively, this optimization procedure can be decomposed into two subproblems without changing the feasible domain of the original problem. After that, the corresponding optimal solutions to subproblems are obtained separately. The next section will present the detailed description of solving the optimization problem.
3 Resource allocation for throughput gain maximization
Two subproblems are obtained from the original mixed integer nonlinear programming problem to facilitate the optimization procedure. The first subproblem is to solve the maximum reuse gain of a single D2D user when reusing a single cellular user’s resource and determine whether it is eligible to share the spectrum. The second subproblem determines the best pairings that maximize the overall network throughput gain, when multiple D2D users reuse multiple cellular users’ resources.
3.1 Joint access control and power allocation based on multiplexing gain
In order to maximize the overall network throughput gain, it is necessary to determine the subset of D2D users that can access the cellular network. First, we need to establish the optimal objective function for maximizing the throughput gain with constraints of QoS and transmit power. Then, by solving the objective function, the optimal power allocation and maximum throughput gain can be obtained. Finally, we can obtain the subset of D2D users D _{ A } by judging whether the maximum throughput gain is greater than zero.
where \(\xi _{n}^{\text {no}} = P_{n}g_{C_{n,B}}/\sigma ^{2}\).
Theorem 1
The power distribution exists at the lower boundary of the feasible solution domain, i.e., a straight line \({P_{n}}{g_{{C_{n,B}}}} = {\xi _{n,\min }}\left ({{\sigma ^{2}} + {P_{m}}{g_{{D_{m,B}}}}} \right)\).
Proof
Finally, we arrive at the conclusion f(k P _{ n },P _{ m })<f(P _{ n },P _{ m }). Thus, for any P _{ m }∈Γ, f(P _{ n },P _{ m }) is a monotonically decreasing function with respect to P _{ n }; thus, the optimal solution corresponds to the lower boundary of constraint domain Γ, i.e., \(P_{n}g_{C_{n,B}}={\xi _{n,\min }}{\sigma ^{2}} + {P_{m}}{g_{Dm,B}}\). Therefore, the power distribution exists at the lower boundary of the feasible solution domain, and the theorem is proved. □
It is necessary to point out that a constant after conversion of log2(1+ξ _{ m,min}), which does not affect the solution to the problem, can be safely removed in Eq. (13).
- 1.
When the feasible solution domain is shown as in the case of Fig. 2a, c, the range of P _{ n } is from P _{ a } to P _{ b }, where \(P_{b} = \xi _{n,\min }\left (\sigma ^{2}+g_{D_{m,B}}\right)/g_{C_{n,B}}\)
- 2.
When the feasible solution domain is shown as in the case of Fig. 2b, the range of P _{ n } is from P _{ a } to P _{ n,max}
If \(R_{n,m}^{\text {Gain}}\) is greater than zero, it comes to the conclusion that D2D user m is actually qualified to reuse the resource of cellular user n.
3.2 Multiple D2D users multiplex multiple cellular users’ resources
The solution to the above problem can be solved by the Kuhn-Munkres algorithm in [18], and the details is beyond the scope of this paper. The pseudo-code of the maximizing throughput gain via resource allocation is summarized in Algorithm 1.
4 Simulation results and discussion
where \(R_{n}^{\text {no}}\) is the rate of cellular user without interference under the same transmit power constraint.
Simulation parameters
Parameters | Value |
---|---|
Cell radio/m | 500 |
Uplink bandwidth/MHz | 20 |
RBs | 100 |
The maximum CU TX power/dBm | 24 |
The maximum D2D TX power /dBm | 24 |
D2D user SINR/dB | U [0,25] |
Cellular user SINR/dB | U [0,25] |
Number of cellular users | 100 |
Number of D2D users | 10, 20, …, 100% of CUE |
Multi-path fading λ /dB | 1 |
Shadowing μ=0 /dB | 8 |
Pathloss exponent α | 4 |
Noise power spectrum density/(dBm/Hz) | − 174 |
5 Conclusions
Aiming at reducing the performance loss caused by the reuse of cellular resources by D2D users, the concept of reuse cost is proposed to measure the rate loss of cellular users. The multi-objective optimization problem of maximizing the gain of D2D users and minimizing the loss of cellular users is established and transformed into single-objective optimization problem by constructing evaluation function. To solve the optimization problem, the original mixed integer nonlinear programming is divided into two sub-problems, and the optimal solution of the sub-problems is given. The simulation results show that the proposed algorithm can maximize the throughput gain and reduce the rate of loss of cellular users while ensuring the QoS requirements of D2D users and cellular users.
In this study, we assume the perfect CSI while the channel estimation can never be error-free in practice [19]. Therefore, the effect of imperfect CSI on the resource allocation scheme in D2D communication is worth studying further.
Declarations
Acknowledgements
The authors would like to thank Dr. Wenjiang Feng of Chongqing University for providing the code of the maximum throughput algorithm.
Funding
This work is supported by the National Natural Science Foundation of China under Grant 61201177.
Availability of data and materials
All data are fully available without restriction.
Authors’ contributions
YW, XL, and XH contributed to the main idea, designed and implemented the algorithms, and drafted the manuscript. QY and WX designed and carried out the simulation and analyzed the results. 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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