Ru Wang , Jia Liu , Guopeng Zhang , Shuanghong Huang , Ming Yuan

1 State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, Shaanxi, 710071, China

2 Department of Computer Science and Engineering, Huaihua University, Hunan, 418008, China

3 School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, China

4 Wireless Advanced Research Department, ZTE Corporation, Xi’an, Shaanxi, 710114, China

* The corresponding author, email: gpzhang@cumt.edu.cn

I. INTRODUCTION

With the rapid increase of smart devices and data businesses for wireless communication systems, it has become an urgent problem to improve the capacity, strengthen the quality of service (QoS) and achieve seamless coverage of cellular networks. The fourth generation(4G) wireless communication systems whose communications must be relayed by the base station (BS) have certain limitations. In [1-3],the authors investigated the performance of integrated cellular and opportunistic networks by activating direct opportunistic communications among smart mobile devices. As one of the key technologies for the fifth generation(5G) wireless communication networks [4],device-to-device (D2D) technology, which allows cellular user equipment (UE) in close proximity to communicate with each other directly, has advantages in improving network spectral efficiency, reducing transmission delay and offloading traffic for the BS [5].

Different from Bluetooth, ZigBee, WifiDirect and other short-range communication technologies, D2D communications utilize cellular spectrum bands licensed by the International Mobile Telecommunications-Ad-vanced (IMT-A). Therefore, in a D2D-enabled cellular network, the sharing of spectrum resource between D2D users and cellular users can be divided into two modes: overlay mode and underlay mode.

In this paper, the authors proposed a two-layer cellular network to allow RA-D2D link to underlay traditional cellular uplinks.

? Overlay: Divide the cellular spectrum resources into orthogonal resources by static or dynamic manners, so that the traditional cellular users and D2D users can use resources orthogonally. This resource sharing mode can avoid the interference between cellular users and D2D users effectively,but it is not conducive to the improvement of spectrum efficiency (SE). In this case,the resource allocation problem between D2D users and cellular users should be carefully optimized [6, 7].

? Underlay: D2D users reuse the spectrum re

sources which are being occupied by cellular users in a reasonable way. This resource sharing mode can improve the SE theoretically. However, there may exist serious interference between D2D users and cellular users who are sharing the same resources.In this case, reasonable mechanisms of interference management and power control are needed to limit the mutual interference into an acceptable range. For this purpose,much work has been done, such as [8, 9].

In order to improve the QoS of users in cell edge as well as enlarge the coverage of networks by one or multiple hops, a relay-aided D2D (RA-D2D) communication scheme was proposed by the Third Generation Partnership Project (3GPP). By now, most researches about D2D communications mainly aim at maximizing the throughput or spectral efficiency. The authors in [10] and [11] studied the power control of relay mode D2D communication by maximizing the D2D link’s data-rates when relay works on half-duplex (HD)and full-duplex (FD), respectively. An opportunistic mode selection and transmit power adaption were proposed in [12] by maximizing the spectral efficiency in relay-aided communications. The transmit power consumption under minimum data rate constraints in cooperative networks was minimized in [13].

With the explosion of smart devices and various applications, the energy consumption has become a non-ignorable problem in recent years. There are mainly two ways to deal with the energy problem for wireless terminals with finite battery capacity, i.e., energy saving(such as [14]) and energy harvesting (such as[15]). Different from the prevalent LTE-controlled communications in which the throughput or spectrum efficiency is mainly the target, the design of 5G wireless systems also takes the energy consumption into account in order to achieve greener wireless communications [16], and D2D technology is taken as a promising solution to reduce the energy consumption. Therefore, it has attracted more scholars to research how to build low energy consumed but high data-rate satisfied wireless networks. The energy-efficient resource allocation problem for the D2D communications overlaying LTE networks was investigated in[6]. The total energy efficiency of D2D communications when D2D links reuse the uplink time-and-frequency resources of cellular links was maximized in [17, 18]. And a tradeoff between energy efficiency and spectral efficiency for D2D communications underlaying cellular networks was found in [19]. However,the above researches about energy efficiency are all towards direct D2D communications,which can’t be used directly in RA-D2D communications. Thereby, the energy-efficient RA-D2D communications deserve further investigation.

Compared with the above works, the main contributions of this paper are summarized as follows: the paper establishes a D2D-enabled cellular network where RA-D2D communications reuse the cellular uplink resources, and proposes to address the power control problem between D2D source and D2D relay to a new angle-energy efficiency. To the best of our knowledge, this is different from the existing literature where only direct D2D link is considered.

The remainder of this paper is organized as follows. In Section II, the characteristics of the considered RA-D2D communication underlaying cellular networks are specified. In Section III, we first formulate the EE of RAD2D link into a optimization model. Then, we give an iterative method by using nonlinear fractional programming to obtain the optimal transmit powers towards our proposed model.Section IV presents some simulation results to demonstrate the effectiveness of the proposed power allocation method. Finally, this paper is concluded in Section V.

II. SYSTEM MODEL

Consider a single two-layer cellular network where D2D users and cellular users exist simultaneously. We study the case in which a D2D user transmits information to the expected destination by the aid of one relay (the relay selection mechanisms are out of the scope of this paper, and interested readers can consult [20-22] for more details). Compared with the uplink resource reuse mode, the BS will cause greater interference to D2D receivers when D2D communications reuse the cellular downlink resource. From a practical perspective, this paper studies the situation where D2D communications reuse cellular uplinks’resource by a reasonable way. Surveys have shown that most communication behaviors happen in static rather than in mobility in one resource unit. Thereby, different from [23,24] that studied the mobility performance of wireless networks, we assume the users in this paper are all in static in one resource unit.

As shown in Fig. 1, UE-C communicates with the BS by traditional cellular communication mode. And UE-S communicates with UE-D via relay UE-R by D2D communication mode, which is called as RA-D2D link in the following. The proposed system model is a frequency division duplex (FDD) network and each RA-D2D link reuses only one cellular uplink resource. Thus UE-R together with UE-D will be interfered by UE-C, and the BS will be interfered by UE-S as well as UE-R in the process of information transmission.

The power allocation methods can be divided into two categories: centralized method and distributed method [25]. In distributed method,both the D2D users and relays can not acquire CSI between them and BS, and therefore can not calculate the corresponding interference accurately. But in centralized method, CSI of all links, including the channels between UES, UE-R and BS, is assumed to be acquirable,and the interference between D2D communication and cellular communication can be calculated and coordinated accurately. Duo to the imperfect interference estimation in the distributed method, the energy efficiency of RA-D2D communication got by the centralized method is better than that got by the distributed method. Besides, it is easier for the BS to control the system and charge the users in centralized method. Therefore, the centralized method is adopted in this paper.

respectively.

Fig. 1 A two-layer cellular network

Relay protocols can be broadly divided into amplify-and-forward (AF) and decode-and-forward (DF) according to the signal processing procedure at the relay node [26]. In our proposed system model, the relay UE-R will be interfered by UE-C when it receives its expected signals sent by UE-S. The interference together with the expected signals will be amplified if the AF protocol is employed,which will result in a low received SINR at UE-D side. Therefore, we employ the DF protocol under which the relay will get rid of the interference before forwarding the received information. Assume UE-R works on HD mode, and a resource reuse cycle isTwhich can be equally divided into two for the first hop and the second hop of the RA-D2D link respectively. Then transmitting information from UE-S to UE-D via relay UE-R can be divided into two phases: in the firstUE-S transmits its signals while the relay UE-R listens; in the secondUE-R decodes the information received in the firstfirstly,and then forwards it to UE-D. Assume UE-D only receives information in the secondin every transmission cycle, and then we can get the joint received SINR at UE-D side.

The instantaneous data-rate of RA-D2D link can thus be expressed by

At the time of receiving its expected signals, the BS will receive interference caused by UE-S and UE-R due to the spectrum resource sharing with RA-D2D link. However,the interference from UE-S and UE-R happens in different time, so we can get the received SINR at the BS side by

The instantaneous data-rate of cellular link from UE-C to the BS can be expressed by

Define EE as the ratio of the data-rate to the total power consumption. Letrepresents the total power consumption, and then we can get the EE of this RA-D2D link by

The total power consumptionconsists mostly of two components, i.e., the transmit power and the circuit power. The transmit power is used for transmitting the data, and the circuit power is used for processing the data including mixing, analog-to- digital (A/D) converting and digital-to-analog (D/A)converting. If the circuit power at different users is assumed as the same and denoted bythe total power consumption of RA-D2D link can be gotten by

whereαrepresents the power amplifier efficiency, i.e.,The circuit power generates from two phases in one transmission cycle: the circuit power at both UE-S and UE-R sides in the firstand the circuit power at both UE-R and UE-D sides in the secondHowever, the transmit power at both UE-S and UE-R sides as well as the circuit power at both UE-S and UE-D sides will be only consumed in half of the transmission cycle, so there is a factor 1/2 in (7).

III. PROBLEM FORMULATION AND ANALYSIS

In our model, we give priority to UE-C, i.e.,the minimum data-rate of cellular uplink needs to be satisfied firstly. And then, we get the optimal transmit power both at UE-S and UE-R sides by maximizing the EE of the RA-D2D link. Therefore, the transmit power optimization model based on EE can be expressed by problemP1.

In the rest of this section, we solve problemP1to get the optimal solution at both UE-S and UE-R sides.

3.1 Transmit power at cellular user

By observing problemP1, we can draw a conclusion that the objective functionis a reduction function with respect toSo if we want to get the maximumneeds to be minimized, which means

Equation (9) is about not only variablebut also variablesandTo simplify the power control at UE-C side, we always take the potential maximum interference to the BS caused by UE-S or UE-D into consideration when calculating theWe can thus rewrite(9) as the following expression.

Then the optimal transmit power at UE-C side can be obtained by solving equation (10).

For the sake of simplicity in the following analyses, let

denote the channel-to-interference-plus-noise-ratio (CINR) from UE-S to UE-R and from UE-R to UE-D, respectively.

3.2 Transformation of the optimization problem

While the transmit power at UE-C side is settled, the next step is to acquire the optimal transmit powerandFrom the analyses in Section II, we can discuss problemP1from the following two cases according to

Case 1:whennamely,the objective function in problemP1can be rewritten by

Case 2: whennamely,the objective function in problemP1becomes

From the above analyses, we can easily get the following proposition:

Proposition 1: Only whencan be maximized.

P2:

However, problemP2is a nonlinear fractional programming that is difficult to be solved, but can be transformed into a nonlinear parameter programming by using the transformation method in [27]. Thereby, we construct problemP3related withP2as follows:

where the constraints resulted from problem P2 andproposition 1, andis a parameter which can be obtained by

Proposition 2: The objective functionin problemP3is quasi-concave.

Proof: By taking the first-order derivative of functionwith respect toand, respectively, we can get

And then the Hessian matrix of functioncan be gained by

Algorithm 1 An iterative algorithm for power allocation

We then first solve problemP3to obtain the temporary solutions. By replacingwithinUand taking the first-order derivative ofwith respect towe can get

And let the derivation in (22) be zero, we can obtain

Then considering the second constraint in(18), the closed-form solutioncan be acquired by

However, these are only the solutions ofP3,but not the final optimal solutions for problemP2becauseandare related about the iteration factor. To get the optimal solutions of problemP2, we need to update parameteraccording to (19) and continue getting theuntilUis equal or close to zero.

3.3 Transmit power optimization algorithm

The followingAlgorithm 1gives an iterative algorithm in order to get the optimal solutions of problemP2(as well asP1). At the beginning, we initializeascan’t be initialized as zero according to (23)) and set the permissible errorasWe can first solve the transmit power at UE-C side according to Subsection A, and then get the temporary solutionsby solvingP3. The final optimal solutionscan be obtained by using the following iterative method.

IV. SIMULATION RESULTS

This section describes numerical simulation results to demonstrate the effectiveness of the proposed algorithm. The parameters used in the simulations are shown inTable I.

The following simulation results are obtained by averaging overtopology realizations. In each topology generation, the wireless channels (including the large scale path loss and the small scale fading) are independently selected.

To testify the effectiveness of the proposed algorithm, we use EE-PA to denote the proposed EE-oriented power allocation, and SEPA to denote the SE-oriented power allocation proposed in [12]. Fig. 2 and Fig. 3 show the achieved EE and SE of RA-D2D link with different algorithms, respectively. It can be observed that the energy efficiency achieved by EE-PA is about twice that achieved by SE-PA in Fig. 2, but the spectrum efficiency achieved by EE-PA is nearly cut 40% off compared to that achieved by SE-PA in Fig. 3. This results show that our proposed algorithm is more energy efficient than the SE-PA, but this greener is at the cost of spectrum efficiency. From Fig. 2, we can also see that the maximum EE of RA-D2D link will get increased when the distance of first hop channel or the second hop channel or both these two hop channels are shorter. This result is reasonable because when the distance between two nodes gets better it will consume only a little transmit power to realize a higher data-rate, which will undoubtedly lead to the increase of the EE.

We also compare the EE achieved by EEPA algorithm of RA-D2D scheme with that ofdirect D2D scheme. The EE problem of direct D2D communications has been studied in [18,19], so we omit the analyses of direct D2D scheme here. Define the EE gain achieved by RA-D2D scheme as

Table I Parameters in the simulations

Fig. 2 The EE of RA-D2D link under different algorithms

Fig. 3 The SE of RA-D2D link under different algorithms

Fig. 4 The EE gains achieved by RA-D2D scheme

Fig. 5 The optimal transmit power at UE-S side

In the simulations, the direct distance form UE-S to UE-D is assumed to be

From Fig. 4, we can see the RA-D2D link reaches a lower EE compared with direct D2D link when the distance between UE-S and UE-D is relatively short. This reducing results from the fact that there exists circuit power consumption at UE-R side which accounts for a large proportion compared with transmit power consumption when the communication distance is short. While when the distance becomes far, the RA-D2D scheme outperforms direct D2D scheme, and the farther the distance is, the more gains it achieves. This results show that the RA-D2D scheme can make better use of energy than direct D2D link when the distance between D2D users is relatively far.

Fig. 5 and Fig. 6 give the optimal transmit power at both UE-S and UE-R side when the maximum EE is achieved under RA-D2D scheme, respectively. Taking Fig. 5 as an example, we observe that the optimal transmit power at UE-S side increases asbecomes far, but there is a slight decrement for the transmit power at UE-S side asbecomes far.The similar results can be found for transmit power at UE-R side. Considering Fig. 5 and Fig. 6 together, we can find that whenis far whileis relatively short, the optimal transmit power the optimal transmit poweris greater than the optimal transmit powerThese results also conform to the model analyses in Section. III, where

Fig. 7 shows the average iteration times forAlgorithm 1by averaging the sum of iteration times intopology realizations. We can see,for different channel distance, the iteration times are around 11, by which our proposed algorithm is proved to be effective.

V. CONCLUSIONS

In this paper, we proposed a two-layer cellular network to allow RA-D2D link to underlay traditional cellular uplinks. To optimize the transmit power at both D2D transmitter and D2D relay sides jointly, we established a optimization problem aiming at maximizing the EE of RA-D2D link while meeting the minimum data-rate requirement of cellular link. To solve the optimization problem, we proposed an effective iterative method by applying the nonlinear fractional programming. The simulation results showed that the proposed power allocation algorithm is more energy efficient than the existing works, and the proposed RAD2D scheme outperformed the direct D2D scheme when the distance between two D2D communication nodes is longer.

We investigated the energy efficiency of a single RA-D2D link in this paper. For the future work, we will further our study to a system level by jointly considering the resource allocation and energy efficiency of a whole network where D2D communications, RAD2D communications and traditional cellular communications coexist.

ACKNOWLEDGEMENTS

This work was supported by the ZTE Corp under Grant CON1412150018; and by the Natural Science Foundation of China under Grant 61572389 and 61471361.

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