In this paper, we build a D2D-relay communications model where the D2D user is selected as a relay to forward data for the users at the edge of the networks. We aim at maximizing the achievable data rates of the cell-edge users, a resource allocation problem is formulated and an iterative power allocation algorithm is proposed. We derive the optimal closed-form power allocation expressions by the Lagrange dual method. Simulation results show that our communication scheme can achieve greater spectral efficiency than the traditional cellular-relay communication scheme.
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1 Introduction
With the rapid development of mobile services and the massive growth of smart terminals, wireless communication systems are facing enormous transmission requirements [1]. Especially for those users at the edge of the network who usually have bad coverage communications with an application server in the core network. One promising approach is to select a relay node to forward data, so as to solve the unbalanced transmission problem at the edge of cells. It is an effective scheme to further enhance the achievable data rates of the CEUs.
In recent years, as a key technology of the 5G communication network, device-to-device (D2D) communication has attracted more and more attention due to its high utilization of spectrum, high network capacity, and low end-to-end latency [2]. D2D users in close proximity can build up a direct transmission link instead of with the help of BS [3]. Applying D2D communication can greatly improve the performance of the system [4], not only reduce the burden of BS but also improve the user experience of short-range communication. Meanwhile, D2D communications can bring some co-interference into the network [5], depending on whether D2D communication reusing the frequency resources of cellular users.
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Combining D2D communication and relay technology, a new technology called D2D-relay is proposed recently. D2D relay mode is to randomly select a D2D user as a relay for data forwarding, abandoning the traditional cellular relay mode. Introducing the D2D-relay scheme into the wireless communication network will bring a lot of benefits, such as increasing the security and flexibility of the network, reducing the communication pressure, and enhancing the effective coverage of network communications.
Based on all the above analysis, to boost the achievable data rates of CEUs, this paper investigates a D2D-relay communication scenario. And the key contributions of this paper can be concluded as follows:
To solve the problem of the relative scarcity of spectrum resources, we use D2D users as a relay to forward data instead of the traditional cellular relay, which undoubtedly makes the spectrum efficiency greatly improved and guarantees transmission performance of cell-edge users.
Considering the optimal power allocation of UEs and transmission rate of the user, we formulate a mixed-integer non-linear programming (MINLP) problem to maximize the data rate of CEUs. We develop an efficient power allocation algorithm and derive the optimal closed-form solutions based on the Lagrange dual method.
Theoretical analyses and extensive simulations are provided to reveal the rationale of the proposed algorithms. Simulation results demonstrate that our D2D-relay scheme outperforms the traditional cellular-relay communication scheme.
The rest of this paper is organized as follows. We introduce the related works in Sect. 2. Section 3 presents the system model and problem formulation. The proposed algorithm is derived in Sect. 4. Simulation results are presented in Sect. 5. Finally, we conclude our paper in Sect. 6.
2 Related Work
Relay technology, as a way to improve network throughput and network coverage, has been widely studied by scholars all over the world [6‐9]. In [10], the authors study the relay control problem in a full-duplex relay network. They have developed a greedy search (GS) algorithm to enhance system performance. Moreover, some interesting works focusing on relay deployment are investigated in [11] and [12]. The authors in [11] analyze the rule of relay movement and prove that the system performance is greatly improved by reasonable relay deployment. The work [12] proposes an optimal relay deployment algorithm to maximize the coverage of the network, keeping the signal-to-interference ratio (SINR) with constrained energy efficiency. In [13], a buffered relay network is proposed. The authors jointly optimize relay selection and transmit power allocation to maximize the throughput of the network.
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Another promising technology to improve the capacity of the network is D2D communication. A lot of algorithms have been studied in this aspect [14, 15]. Yang et al. propose an interference management scheme in in-band D2D cellular networks [16]. Stackelberg game is used in [17] to eliminate the complex interference in D2D underlay networks. The authors in [18] study the spectral efficiency for multi-hop D2D communications and propose a clustering mechanism to improve the performance of the system. The works focus on optimized resources allocation problems is introduced in [19‐21]. Islam et al. [22] propose a searching algorithm for resource allocation of D2D communications. And later, by considering the QoS requirements, they propose the matching algorithm in [23] to allocate cellular resource blocks. A novel iterative algorithm [24] is proposed to maximize the energy efficiency (EE) of all the D2D pairs, meanwhile guaranteeing the QoS of cellular users. Moreover, D2D communications open opportunities for multicast networks [25], content delivery [26], and mmWave [27].
The D2D-enabled user equipment (UE) which acts as a relay between BS and other users helps transmission, named D2D-relay, is been mentioned in recent times [28, 29]. Unlike typical cellular relays, much high flexibility for networking can be found in this technology which answers the traffic by dynamic deployment and resource allocation. Zeng et al. [30] analyze the pairing problem in the D2D-relay networks. A positive association of the proposed metric and the system performance was figured out by them. Using stochastic geometry, Qu et al. [31] studies the coverage in D2D relay networks by stochastic geometry. The coverage which optimizes the overall system downlink rate is built and an algorithm is advanced for getting the best solution. Note that, there are some relevant studies in the past works, but it still has room for further exploring. D2D relays majorly concentrate on the user pairing and coverage problem. Few study on the resource allocation and transmission rate analysis, which is primarily significant on network management.
3 System Model and Problem Formulation
In this section, we introduce the system model of the network and then formulate data rate maximization and resource allocation problems.
3.1 System Model
To improve the coverage quality for cell-edge users, we need to consider the optimization problem of downward data rates in such a scenario which is shown in Fig. 1. We consider a base station (BS) which is located in the center of the cell, the set of cellular users are denoted by \(C{ = }\left\{ {1,2, \ldots ,C} \right\}\), and the set of D2D users are denoted by \(D = \left\{ {1,2, \ldots ,D} \right\}\), respectively. In this paper, we assume that the CEUs communicate with BS using either direct or relay mode. And the set of the cell-edge users are denoted by \(E{ = }\left\{ {1,2, \ldots ,E} \right\}\). When the link condition is good for communication, the CEUs perform downlink transmission from BS directly. However, when the channel condition is poor, the communications need to be supported by the relays. We assume that the Decode and Forward (DF) strategy is adopted as the protocol of relay. In relay mode, each communication period is divided into two intervals corresponding to the BS-Relay phase (cellular communication) and Relay-CEUs phase (D2D communication). Relays communicate with CEUs by reusing the uplink channel resources of cellular users which are shown in Fig. 2. In our model, to avoid further co-channel interference, we assume that one D2D pair can only reuse the resources of one cellular user, and vice versa.
Fig. 1
System model
Fig. 2
Reuse model
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3.2 Direct Mode
When a cell-edge user \(E_{i}\) directly communicating with BS, the communication link a is built (seen in Fig. 1), by using the Shannon theory, we can get the maximum data rate of the user \(E_{i}\) as
where \(P_{b}\) is the power of BS, \(H_{bi}\) is the channel gain between BS and cell-edge user \(D_{i}\). \(N_{0}\) is the Gaussian white noise.
3.3 Relay mode
However, when the cell-edge user is far from BS or the link condition is poor for direct communication, the user \(E_{i}\) may choose a D2D user \(D_{r}\) as its relay and link b is built (seen in Fig. 1). The D2D communication between the cell-edge user \(E_{i}\) and relay user \(D_{r}\) reuses the uplink channel resources of a cellular user \(C_{n}\). And similarly, the maximum achievable data rate of the user \(E_{i}\) in a relay mode can be expressed as
where \(P_{r}\) and \(P_{c}\) denote the transmit power of the relay user and cellular user, \(H_{ri}\) is the channel gain between \(D_{r}\) and \(D_{i}\), \(H_{ci}\) is the channel gain between \(C_{n}\) and \(D_{i}\). \(N_{0}\) is the Gaussian white noise, too.
3.4 Problem Formulation
In the following, we introduce the proposed optimization problem. Firstly, we define a binary variable to indicate whether the cell-edge user \(E_{i}\) chooses relay user \(D_{r}\) as its serving relay.
$$ \alpha = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{relay}}\;{\text{mode}}} \hfill \\ 0 \hfill & {{\text{direct}}\;{\text{mode}}} \hfill \\ \end{array} } \right.,\quad \forall i \in E,\;\forall r \in D $$
(3)
Our goal is to find the theoretical maximum downlink data rates of all the cell-edge users. Combining the data rates of cell edge user \(E_{i}\) in both direct mode (1) and relay mode (2), meanwhile guaranteeing the QoS of the cellular user \(C_{n}\), the optimization problem can be formulated as follow
where \(P_{\max }\) denotes the maximum transmit power of the UEs. \(R_{\min \, }\) denotes the data rate threshold of the UEs. Constrains (5)–(6) guarantee that the transmit powers of the UEs are adjusted within the desired range. Constraint (7) forces the decision variable to be binary and enforces the CEU to receive either from BS or a relay. Constraint (8) guarantees the quality of service of cellular users.
4 The Proposed Resource Allocation Scheme
4.1 Optimization Problem Transformation
When taking a D2D user \(D_{r}\) as a relay to forward data for the cell-edge user \(E_{i}\), the data transmission from BS to \(E_{i}\) consists of two phases: In the first phase, BS transmits its signals to the relay user \(D_{r}\), and the effective data rate dedicated to the \(D_{r}\) can be expressed as
where \(P_{b}\) is the power of BS, \(H_{br}\) is the channel gain between from BS to relay user. \(N_{0}\) is the Gaussian white noise.
In the second phase, the relay user \(D_{r}\) decodes the received information and then forwards it to the cell-edge user \(E_{i}\). We assume that \(E_{i}\) only receives signals in the second phase, and then we can obtain the rate of \(E_{i}\) in the access link as follow
where \(P_{r}\) and \(P_{c}\) are the powers of the relay user \(D_{r}\) and cellular user \(C_{n}\), \(H_{ri}\) is the channel gain from the relay user \(D_{r}\) to cell-edge user \(E_{i}\). \(H_{ci}\) is the channel gain from the cellular user \(C_{n}\) to cell-edge user \(E_{i}\). \(N_{0}\) is the Gaussian white noise.
Following the max-flow min-cut theory [31], the data rate of CEUs is the minimum of the two values (\(R_{br}\) and \(R_{ri}\)), expressed as follow
$$ R_{i} = \min (R_{br} ,R_{ri} ) $$
(11)
Following [32], we can get the conclusion that only when \(R_{br} = R_{ri}\),\(R_{i}\) can get its maximum value. Substituting Eq. (9) and Eq. (10) into Eq. (11), \(P_{b}\) can be expressed as
By observing problem P2, we can note that the objective function is a reduction function with respect to \(P_{c}\). Only when \(P_{c}\) gets its minimum, we can obtain the maximum of the object problem. According to the constrain (8), the minimum value of \(P_{c}\) can be calculated as
We can note that from P3, \(\alpha\) is a binary integer variable, the objective function is nonlinear due to its logarithmic form, the constraint (8) is nonlinear. So the problem P3 is a mixed-integer non-linear programming problem. To solve this problem, essential relaxation is introduced in this part. The binary variable \(\alpha\) in the objective function and the constrain (7) is relaxed to the continuous variable.
$$ \alpha \in \left[ {0,1} \right] $$
(17)
We can easily prove that optimization problem P3 is a concave maximization problem with respect to the power allocation variable \(P_{r}\). Therefore, we can use the Lagrange dual decomposition method to solve this problem. The Lagrange function can be written by
\(\lambda_{1} \ge 0\) and \(\lambda_{2} \ge 0\) are the Lagrange multipliers for the constraints (6) and (15). We can write the dual function as follow
For a given \(\alpha\), the problem is a standard optimization problem with the KKT conditions. Specifically, the partial derivative of the Lagrange \(L\left( {P,\lambda } \right)\) respect to \(P_{r}\) can be expressed as
To obtain the optimal solution, we set the partial derivative equal to 0, the optimal solution to (27) falls into two cases: 1)\(\alpha { = }0\); 2)\(\alpha { = }1\).
1) Case \(\alpha { = }0\)(direct mode).
The optimal power value for \(P_{r}\) can be derived as
Due to the differentiable of the objective function, we can use the gradient method to solve the dual primal problem. We update the dual variables as follows
where \(K\) is the iteration index. \(\sigma_{1}\) and \(\sigma_{2}\) are positive step sizes at iteration \(K\).
In Algorithm 1, we design an iterative algorithm to obtain the optimal solutions of problem P3 (as well as P1 and P2). In the beginning, we initialize the related variables (see line 1). And then, we update the Lagrange multipliers (see line 4). The power resource of relay users \(P_{r}\) is allocated in lines 5–6. After updating the Lagrange function (see line 8), we obtain the optimal \(P_{r}\) value as \(P_{r}^{*}\).
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4.3 Complexity Analysis
Our algorithm consists of two parts, direct communication mode, and relay communication mode. The computational complexity of our scheme mainly depends on the updating process of power allocation. In the direct mode, the computational complexity is O(50) for one iteration, so the complexity of the proposed scheme is O(50 N) in direct mode, where N is the iteration numbers in the direct mode. Similarly, in the relay mode, the computational complexity is O(46) for each iteration. So the complexity of the proposed scheme is O(46 M), where M is the iteration numbers in the relay mode.
5 Simulation Results
In this section, we present numerical results to compare the performances of our proposed DRPA scheme and the typical cellular relay method. For the benefit of simplicity, a single-cell scenario with scarce spectrum resources is considered. Assuming that the BS is situated at its center, D2D users and cellular users are uniformly distributed. And the communication link between the BS and CEUs is randomly chosen. The maximum communication distance is 150 m. The simulation results are presented to evaluate the performance of the DRPA scheme. The specific parameters of the simulation are shown as follows. We assume the radius of the cell is 150 m. There is one BS in the cell. The number of the CUs is 12 and the number of relays is 15. The number of CEUs is set to 11. We set the maximum transmission power \(P_{\max }\) to be 23dbm. Additive noise power \(N_{0}\) is set to -110dbm. The minimum data rate \(R_{\min }\) is set to 0.8. Moreover, the exponent of path loss is set to 3.7. And the accuracy of \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are both set to 10–5.
Figure 3 illustrates the convergence performance of our proposed DRPA scheme. It can be shown that the DRPA algorithm starts from a random initialization and converge to the optimal data rate at a very fast time (about 2 iterations). This shows that the proposed DRPA algorithm has a very fast convergence with low computational complexity.
Fig. 3
The convergence of the proposed algorithm
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To understand the interplay of the data rate of CEUs versus the distance between the BS and CEUs in direct transmission mode, the minimum data rate is defined as 1Mbps, 0.8Mbps, and 0.6Mbps. And the distance between BS and the CEUs is set from 50 to 150 m with a 10 m interval identically. From Fig. 4, we can also get that with the increase of the distance, all the date rates are monotonically decreased. The reason is that as the distance increases, the link condition gradually deteriorates and is no longer suitable for communication. Normally, we need to select a relay user for forwarding data to improve the quality of communication.
Fig. 4
The data rate of cell-edge users under different distance
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In Fig. 5, we compare direct communication (\(\alpha { = }0\)) and relay communication (\(\alpha { = 1}\)) to further illustrate the transmission performance of CEUs. In the case of the same parameters set, the data rate decreases with the distance increases in direct mode. On the contrary, in the relay mode, with the increasing of the distance, the data rate is monotonically increased. And the two modes share the same data rate at a distance of 66 m. This is coincident the relay communication is more suitable for long-distance (more than 70 m) communication.
Fig. 5
The data rate of the cell-edge user under different transmission mode
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Furthermore, Fig. 6 presents the data rate of the CEUs versus the distance between the relay and CEU with different maximum transmits power \(P_{\max }\). The distance between BS and CEUs is set from 20 to 90 m with a 10 m interval. We set \(P_{\max }\) as 20 dbm, 30 dbm, and 40 dbm. From Fig. 6, we can also observe that the data rate is decreased with the increase of the distance. This is because the fading increases when the distance increases, which has a great influence on the transmission link. So the distance between CEUs and the relay users should not be too large.
Fig. 6
The data rate of the CEUs under the different distance between the relay and CEU
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For examing the advantage of DRPA algorithm, we compare our scheme with the traditional cellular relay scheme [33] in spectrum efficiency (SE), as shown in Fig. 7. To fairly compare the two schemes, we set the distance increased from 50 to 150 m, the data rates of the CEUs increase for both schemes. And our scheme can achieve better performance than the traditional scheme. The reason is that D2D communication is adopted in the data forwarding process, which improves spectral efficiency greatly.
Fig. 7
SE versus our DRPA scheme and traditional scheme [33]
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6 Conclusions
In this paper, we improve cell-edge user coverage quality by designing a D2D-relay communication mechanism for underlay cellular networks. The problem of maximizing data rate is formulated as a non-linear mixed-integer problem. Then an effective iterative power allocation approach based on the Lagrange dual method is designed to allocate powers to the UEs. The optimal closed-form solution is derived and our proposed algorithm converges within a reasonable time. Simulation results demonstrate that our DRPA scheme significantly improves the coverage of the network and the achievable data rates of CEUs. And our scheme is superior to the traditional cellular relay scheme in improving the spectrum efficiency of the system.
Acknowledgements
This work was supported by the Guide Innovates Foundation of Northeast Petroleum University (2020YDQ-10).
Declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Competing interests
The authors have not disclosed any competing interests.
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