A Novel Social Aware Reverse Relay Selection Scheme for Underlaying Multi- Hop D2D Communications

Abstract

Device-to-Device (D2D) communication has received increasing attention and been studied extensively thanks to its advantages in improving spectral efficiency and energy efficiency of cellular networks. This paper proposes a novel relay selection algorithm for multi-hop full-duplex D2D communications underlaying cellular networks. By selecting the relay of each hop in a reverse manner, the proposed algorithm reduces the heavy signaling overhead that traditional relay selection algorithms introduce. In addition, the social domain information of mobile terminals is taken into consideration and its influence on the performance of D2D communications studied, which is found significant enough not to be overlooked. Moreover, simulations show that the proposed algorithm, in absence of social relationship information, improves data throughput by around 70% and 7% and energy efficiency by 64% and 6%, compared with two benchmark algorithms, when D2D distance is 260 meters. In a more practical implementation considering social relationship information, although the proposed algorithm naturally achieves less throughput, it substantially increases the energy efficiency than the benchmarks.

1. Introduction

Recent years have seen an upsurge of smart wireless terminals and the explosive increase of mobile subscribers thanks to the rapid development of Internet industry and the adoption of advanced mobile communication technologies [1]. Providing services to so many users increases the network load and worsens many known network issues such as scarce yet under-utilized spectrum resources. Researchers have therefore proposed Device-to-Device (D2D) communications that allows two nearby devices to directly communicate without the intervention from the base station (BS) [2]. Direct data exchange between two adjacent mobile devices underlaying conventional cellular network can improve spectrum usage and transmission latency [3]. Moreover, the D2D technology provides high-speed data transmission that operates with or without the existence of a BS [4].

D2D communications can be classified into inband and outband operation modes, based on the spectrum band exploitation [5]. The former, where D2D links are allowed to reuse the licensed cellular spectrum, can significantly improve spectrum utilization, helping mitigate the spectrum shortage problem. Moreover, it demonstrates potentials to improve data throughput, energy efficiency, delay, and user fairness [6]. Thanks to the various advantages, inband D2D has been chosen by the global standardization body 3GPP (the 3rd Generation Partnership Project) as one of the key technologies for 5G systems and beyond. It thereafter has rapidly attracted increasing research interests globally in further developing D2D technologies in various aspects.

However, it is also discovered that direct D2D communication can suffer from problems such as short communication distance, high device power consumption, and sometimes severe interference to/from cellular networks. To tackle these problems, relay devices can be used to enable longer D2D distance to form multi-hop D2D communications. Different devices acting as relays can lead to considerably varying performances of D2D links because of different relay distance, channel quality, etc. Therefore, the selection of relays is one of the key challenges in D2D relay communications [7].

The relays were assumed half-duplex in the early studies of D2D relay selection to avoid self and other user interference. It intrinsically limits D2D link performances. Full-duplex improves the spectral efficiency of overall system [8], however, introduces so-called self-interference [9]. Various advanced interference mitigation/cancellation techniques [10] [11] are available to significantly mitigate such interference. Using frequency division duplex (FDD) mode for relays can also alleviate this problem.

When modelling practical mobile communications, researchers are made aware that the device selected as a relay may not be entirely willing to help the D2D device forward data. This means that the device with good channel quality may refuse to use its full or partial transmit power for the relay link. The willingness of the device/user can be modeled by social interaction information between users and therefore is referred to as social factor. Its role and impacts on the multi-hop D2D communications have not been thoroughly studied in literature.

The rest of this paper is organized as follows. In Section 2, some related works are surveyed and summarized. The system model is constructed in Section 3, which covers both physical and social domains. Section 4 introduces a social-aware relay selection algorithm. Section 5 verifies the performance of the proposed algorithm, and the conclusions are drawn in Section 6.

2. Related Work

Different from previous researchers who choose single relay selection criterion, Xia et al. [12] studied two-hop D2D communications and proposes a relay selection strategy that can be based on either the relay’s CSI (Channel State Information) or distance, depending on the radio link quality. Moreover, Ma et al. [13] propose a relay selection algorithm for full-duplex relay based D2D networks. It demonstrates better power efficiency of mobile devices compared to half-duplex devices.

The above-mentioned works assume the algorithms be executed in the BS, wherein excessive signaling is generated. Therefore, researchers have studied relay selection algorithms that do not require the participation of the BS. For instance, a timer-based relay selection method proposed in [14] can determine the best relay in a distributed manner. Its performance is close to that of the centralized optimal method. A device-centric relay selection scheme is proposed in [15], which obtains the common neighboring devices of D2D devices and selects relays based on various parameters, such as SINR, link capacity, residual energy, buffer space, and reliability. However, these distributed schemes only work in the ideal situations because the information assumed accessible to D2D devices may not be practically available to the terminals in real-life systems.

D2D performance could be enhanced by extending from two-hop to multi-hop relay to achieve larger D2D communication range. In [16], a D2D multi-hop routing algorithm based on the Dijkstra's algorithm is proposed and compared with the exhaustive search algorithm. In [17], an adaptive interference-aware multi-hop path selection algorithm is proposed, where the D2D path consists of "escape", "migrate" and "return" parts. This algorithm considerably enhances the overall network capacity with only a fractional capacity loss of overlaying cellular network. Unlike previous works that focus on relay selection algorithms, Wen et al. [18] analyze the upper bound of achievable D2D link throughput of a multi-hop D2D system assuming half-duplex relays in time-division duplex mode.

The above-mentioned works demonstrate that relay-assisted transmission can effectively improve the performance of D2D networks. However, they all imply that the relay device is willing to help forward data, which may not be the case in real-life. Researchers therefore introduce the social domain of the devices into the D2D studies. It is reported that this can more accurately and sometimes more effectively address technical issues and improve system performances [19].

Hu et al. [20] propose a social-aware relay selection algorithm where the selfish and trusty relationship between users is considered. The strength (strong or weak) of the social relationship between users is modelled by analyzing their historical information of location check-in and access to interest communities. The strength of the social relationship is used as an important input to determine the most suitable relay. Considering that most relevant works only consider social information of the transmitter and the relay, Wang et al. [21] propose a relay selection scheme that is based on the social relationship between the transmitter and relays and between the receiver and relays. Furthermore, D2D relay selection with social information is studied in IoT (Internet of Things) networks. For instance, Chen et al. [22] propose a relay selection algorithm incorporating trust probability of D2D connections derived from a ranking-based trust model. This algorithm works in a distributed manner and its performance is close to that of the exhaustive relay search.

In summary, most studies on relay selection in multi-hop D2D communications so far are based on half-duplex relay and lack considerations of the algorithm complexity and its impacts on execution and implementation. To solve the issue, distributed D2D schemes are proposed but assume that all the required information is available to the terminals. Furthermore, the impacts of social domain information on the system performance are not sufficiently studied particularly in multi-hop full-duplex based D2D communications. Therefore, in this paper, a novel relay selection algorithm is proposed for multi-hop full-duplex D2D communications underlaying cellular networks. The aim is to improve system performance and to guarantee link stability. The algorithm considers the willingness of relay devices and purposely select the relays in a reverse order.

The main contributions of this paper are summarized as follows:

(1) A reverse relay selection algorithm is proposed for multi-hop full-duplex D2D communications underlaying cellular networks, where the relays are selected from last relay link backwards to the first link. Such design allows the algorithm to be executed in a semi-distributed mode and significantly reduces the role of BS hence resulting in less signalling overload.

(2) The social relationship between users is taken into account. The social relationship is based on a model derived from real-life data between the candidate relays and the D2D source and destination.

(3) When designing the cellular user channel reuse scheme, two special considerations are taken to assure the quality of service (QoS) of cellular users not degraded. Firstly, a protection area is introduced wherein a cellular user will not share its channel with D2D devices. Secondly, the channel-sharing cellular users are distant enough from D2D devices to minimize interference between them.

(4) The proposed algorithm is thoroughly analyzed and its performances are simulated and compared against two benchmark algorithms. It shows that the system throughput and power efficiency considerably outperform the benchmark algorithms.

3. System Model

The system model considered in this paper is shown in Fig. 1. The system consists of a BS located at the center of the cell, a number of active cellular equipment (CE) communicating with BS, some idle equipment (IE), source (S) and destination (D) of the D2D communication, and a number of relays (R) that are selected from IEs to form a multi-hop link to forward data from S to D. It is assumed that all devices are equipped with two antennas. We consider only the uplink communication of the cellular, where the uplink channels of all CEs are orthogonal to each other. The red lines indicate the uplink channels from CEs to BS. The solid black lines indicate channels from S to D via relays. The dotted black line indicates that there might be more relays over S to D path which are not shown in the figure.

Fig. 1. System model for multi-hop D2D communications coexisted with cellular network

To improve spectral efficiency, multi-hop D2D inband operation mode is assumed where D2D devices reuse CEs’ uplink channels. This means that the D2D links will interfere the CEs’ uplinks at the BS. It is designed so due to the fact that in cellular networks, uplink channel is generally underutilized due to less data to transmit and the BS is a central node and can eliminate the other user interference more effectively than the CEs.

3.1 Channel Model

It is assumed that all wireless channels between two nodes are line-of-sight, therefore, the slow fading is not considered. The channel model consists of a distance-based path loss model and independent and identically distributed Rayleigh fading channels. Therefore, the received signal power of node y from transmitter node x is:

P^y_x = P_xh^y_x(d^y_x)^-α       (1)

h^y_x=|h₀|²       (2)

where P_x denotes the transmit power of node x, h^y_x denotes the channel coefficient from x to y, d^y_x denotes the distance between x and y, α denotes the path loss exponent, and h₀ follows the complex Gaussian distribution with zero mean and unit variance.

3.2 Social Relationship Model

In practical D2D communications, the users of selected relays may not be willing to act as a relay for others or contribute part of its battery power to forward others' data because the power resource of the devices is limited. On the other hand, two people are more likely to help each other if they are close in real life. Taking into account these two factors, we introduce social relationships into the relay selection algorithm.

In real life, two people who are more closely related contact each other more frequently with longer communication time (such as phone calls and social media interactions), and vice versa. Please note that this is based on statistical data and there exists cases where strong social links do not represent good relationship. In this paper, the frequency and duration of online contacts between users are used to measure the strength of their social relationships, as shown below:

\(\begin{aligned}u_{i, j}=\left(\frac{T_{i, j}}{\sum T_{i, k}}+\frac{D_{i, j}}{\sum D_{i, k}}\right) / 2\end{aligned}\)       (3)

where u_i,j denotes the strength of social relationship between user j and user i and it is in the range of [0,1]. T_i,j and D_i,j denote the contact frequency and the total contact duration between them, respectively, ∑T_i,k and ∑D_i,k denote the sum of contact frequency and the sum of contact duration between user i and all other users, respectively.

According to the study of real-life social media data in [23], most users have strong social relationships with only a few other users, which can be rather accurately modeled by the pareto distribution. In this study, the pareto distribution is employed to model the strength of social relationships of (relay, S) and (relay, D) that are consequently applied to cap the relay’s transmit power.

Using u_S,j and u_D,j to denote the strength of the social relationship between device j and S, D, respectively. When device j is selected as a relay, its transmit power’s upper bound is then adjusted to:

P_j'=max{u_S,j,u_D,j}∙P_max       (4)

where P_max indicates the maximum transmit power of the IE.

4. Relay Selection Algorithm

We consider the scenario where S initiates a data transfer to D by D2D communication. However, they are too distant that the communication can only be successfully established with the help of multiple relays selected from IEs. Hence, how to select relays from IEs is the key issue to solve. In this work, we propose a three-phased reverse relay selection algorithm as described below. Please note that in the D2D communications with or without relays, there exists an important step which is device discovery. This process enables a device to sense neighboring devices as D2D destination or relays. It is assumed that device discovery is performed and is not within the scope of the proposed algorithm.

4.1 Phase-1: Determine the Candidate Relays

The ideal relays can be selected by exhaustively examining all IEs in the cell. However, this leads to excessive complexity of the algorithm and is unsuitable for practical implementation. Inspired by the research works of relay selection and routing strategies in multi-hop cognitive wireless networks [24] and cognitive relay networks [25], and to keep the algorithm complexity low, we propose a cluster-based relay determination scheme, in which only IEs in certain regions (clusters) are considered as candidate relays.

Assuming that the distance between S and D is d^D_S and M-1 relays are needed (i.e. M hops, M≥3). Each relay will be selected from IEs located in its cluster. The locations of the clusters are determined by the direct line between S and D. Please note that the sizes of the clusters are dependent on the device discovery process and can be pre-defined by the BS as parameters. Without losing generality, in this paper, the distance between clusters is set as pre-defined fixed value L. Each cluster is assumed to be a r-radiused circular area centered on the S to D direct line. The distance between the first cluster center and S is set to r. The distance between the centers of the following two clusters is set to L (L≥2r), and the distance between D and the center of the last cluster is denoted by l. When L/2<l≤L, the last cluster radius is set to r, as shown in Fig. 2. When 0<l≤L/2, as the distance between last relay and D become quite small, the link between them may well deviate from the S, D direction and degrade the performance of the D2D link, we adjust the last cluster’s radius to r/2, and the distance between its center and the penultimate cluster therefore becomes L-r/2, as shown in Fig. 3.

Fig. 2. Design of clusters in normal case

Fig. 3. Design of clusters in special case

4.2 Phase-2: Determine the CEs for Channel Reuse

To improve the throughput of D2D communication, all relays are assumed to be full-duplex equipment. To avoid inter-hop interference, each hop reuses the uplink channel of different CEs. This means that the relays operate in FDD mode with full-duplex relays.

As shown in Fig. 4, we refer TX_m and RX_m as the transmitter and receiver of the m-th hop of the D2D communication, respectively, and C_m as the CE whose uplink channel is reused at this hop. To ensure CE’s link quality, the SINR (Signal to Interference plus Noise Ratio) of C_m’s signal received by the BS needs to be greater than the threshold, i.e.:

Fig. 4. Interference in the m-th hop D2D communication

\(\begin{aligned}\operatorname{SINR}_{C_{m}}^{\mathrm{BS}}=\frac{P_{C_{m}}\left(d_{C_{m}}^{\mathrm{BS}}\right)^{-\alpha} h_{C_{m}}^{\mathrm{BS}}}{P_{T X_{m}}\left(d_{T X_{m}}^{\mathrm{BS}}\right)^{-\alpha} h_{T X_{m}}^{\mathrm{BS}}+N_{0}} \geq r_{t h}\end{aligned}\)       (5)

where P_Cm denotes the transmit power of C_m (for all CEs, P_Cm is set to its maximum value P_C), P_TXm denotes the transmit power of TX_m, d^BS_Cm, h^BS_Cm denote the distance and channel coefficient between C_m and BS, respectively, d^BS_TXm, h^BS_TXm denote the distance and channel coefficient between TX_m and BS, respectively, r_th denotes the SINR threshold for CEs in the uplink, and N₀ denotes the power of background noise following Gaussian distribution N(0, N₀). Therefore,

\(\begin{aligned}P_{T X_{m}} \leq \frac{\frac{P_{C_{m}}\left(d_{C_{m}}^{\mathrm{BS}}\right)^{-\alpha} \mathrm{h}_{\mathrm{Cm}}^{\mathrm{BS}}}{r_{t h}}-N_{0}}{\left(d_{T X_{m}}^{\mathrm{BS}}\right)^{-\alpha} h_{T X_{m}}^{\mathrm{BS}}}\end{aligned}\)       (6)

Taking

\(\begin{aligned}P_{T X_{m}}=\frac{\frac{P_{C_{m}}\left(d_{C_{m}}^{\mathrm{BS}}\right)^{-\alpha} h_{C_{m}}^{\mathrm{BS}}}{r_{t h}}-N_{0}}{\left(d_{T X_{m}}^{\mathrm{BS}}\right)^{-\alpha} h_{T X_{m}}^{\mathrm{BS}}}\end{aligned}\)       (7)

where one can observe that P_TXm increases with the decrease of d^BS_Cm. The SINR of the signal received by RX_m from TX_m is:

\(\begin{aligned}\operatorname{SINR}_{T X_{m}}^{R X_{m}}=\frac{P_{T X_{m}}\left(d_{T X_{m}}^{R X_{m}}\right)^{-\alpha} h_{T X_{m}}^{R X_{m}}}{P_{C_{m}}\left(d_{C_{m}}^{R X_{m}}\right)^{-\alpha} h_{C_{m}}^{R X_{m}}+N_{0}}\end{aligned}\)       (8)

where dRXmTXm, hRXmTXm denote the distance and channel coefficient between TXm and RXm, respectively, and dRXmCm, hRXmCm denote the distance and channel coefficient between Cm and RXm, respectively. It is observed that SINRRXmTXm increases with increased PTXm and dRXmCm. Since the allowable throughput of this hop is based on SINRRXmTXm, one can increase PTXm, i.e., decreasing dBSCm, or increase dRXmCm to increase this hop’s throughput. At the same time, a short distance between TXm and BS (dBSTXm) will lead to excessive interference to Cm’s uplink. Therefore, it is suggested to set a circular protection area with radius Ar around the BS wherein D2D communications are not allowed.

Thereafter, the C_m can be selected as shown in Fig. 5. We first draw a straight line from the center of m-th cluster (where RX_m is located) to BS, extend it further and draw a circle inner tangent to the protection area with its center on the extension line and radius being r/2. Within this circle, the CE with maximum received signal power at BS is selected as C_m. This design can achieve a good trade-off between CE uplink quality and D2D hop’s throughput. Please note that, in the last hop, RX_m is D and its location is interpreted as the relay cluster center.

Fig. 5. D2D only allowed outside the protection area

4.3 Phase-3: Determine the Multi-hop Relays

The multi-hop D2D communication involves, in each hop, selecting a CE for channel sharing and a relay from IEs located in the cluster. Relay selection process centrally placed in and managed by BS will generate excessive computation load and large signaling overhead. Therefore, in this paper, a semi-centralized relay selection algorithm is proposed where BS only needs to collect relevant information such as essential channel coefficients and node locations and the relay selection is managed by the D2D devices involved.

It is assumed that the channel coefficient h^x_y is known to node x by node y transmitting a pre-defined and fixed powered sequence. When node x uses the same frequency channel to transmit, due to the channel reciprocity, h^x_y will be known to node y. And we also assume all channel state information is known at the BS.

Assuming that the D2D communication between S and D is M hops, uplink frequency channels of M CEs are shared, denoted as F = {f₁, f₂, …, f_M}, and the corresponding CEs are C = {C₁, C₂, …, C_M}. In addition, M-1 relays are to be selected from M-1 relay clusters. Assuming N IEs in each normal cluster and N/4 IEs in small cluster, the set of IEs in the m-th cluster is referred to as IE_m={IE_1,m, …, IE_n,m, …, IE_K,m}, m=1, …, M-1, K = N for normal sized clusters and K = N/4 for last small cluster. Define P'_n,m as the transmit power of IE_n,m calculated by (4) considering social relations and a set P'={P'_1,1, …, P'_n,m, …, P'_K,M-1} can be formed. Similarly, define P''_n,m as the maximum transmit power of IE_n,m calculated by (7) considering interference and a set P''={P''_1,1, …, P''_n,m, …, P''_K,M-1} is formed.

The proposed relay selection algorithm thereafter is named as SAA (Social Aware Algorithm) and its details are presented in Algorithm 1.

Algorithm 1 SAA

Input: system setup including the locations of BS, CEs, IEs, S and D, frequency channel used by all the CEs in the uplink.

Output: All the relay IEs are selected, and all the reused frequency channels are decided. The S starts D2D communication via all the relays to D.

Step 1: S and D send D2D communication requests to the BS;

Step 2: BS determines the locations of S and D, the location of each relay cluster, as well as the location of IEs therein, according to Phase-1;

Step 3: BS determines C according to Phase-2 and records F; calculates P' and P'' and takes P = min{P', P''}; and collects channel coefficients from C₁ to IEs in IE₁ and from C₂ to IEs in IE₂ that will be used in Step 8;

Step 4: BS sends to D all location information, channel coefficients, P, and F.

Step 5: D sends received data to IEs in IE_M-1 on channel f_M (in this process IEs in IE_M-1 obtain the channel coefficients to/from D) and sets its receiver frequency to f_M;

Step 6: Assuming sending a fix power signal on f_M, each IE in IE_M-1 calculate D’s received signal power. A timer is set inversely proportional to the received signal power for each IE and all timers set off at the same time. The IE whose timer times out first is selected as the relay R_M-1 and other IEs are notified of this message by R_M-1. The R_M-1 sends the received data to IEs in IE_M-2 on f_M-1 and sets its transmit and receive channels to f_M and f_M-1, respectively;

m=M-2;

Repeat

Step 7: The IEs in IE_m calculate the received signal power, assuming sending a fix power signal to R_m+1 on f_m+1. A timer is set inversely proportional to the received signal power for each IE and all timers set off at the same time. The IE whose timer times out first is selected as the relay R_m and other IEs are notified of this message by R_m. The R_m sends the received data to IE_m-1 on channel f_m+1 and sets its transmit and receive channels to f_m+1 and f_m, respectively, afterwards;

m=m-1;

until m=1

Step 8: From the channel coefficients collected in Step 3, the IEs in IE₁ calculate the SINRs to R₂ and send them together with received data to S. S calculates the SINR to the IEs in IE₁. For each IE in IE₁, the smaller value of received SINRs of the first hop and second hop is chosen and compared with other IEs and the IE with highest value is selected as R₁. R₁ adjusts the transmit and receive channels accordingly.

Step 9: S calculates its transmission power according to (7), sets the transmit channel to f₁ and starts D2D communication.

It is noted that the proposed algorithm selects the relay of each hop from D to S, in a reverse fashion. That means the SAA algorithm decides the last relay first and other relays are selected one by one in a reverse order till to the first relay.

The reason of taking this approach is that the IEs can use received signal to obtain the channel coefficients to/from next relay or D. Therefore, by taking advantage of the channel reciprocity, the proposed algorithm relies on the IEs to make relay selection decision without BS involvement. Hence, it is a semi-centralized algorithm and significantly reduces the computation and signalling load at BS.

The computational complexity analysis of SAA: Giving the distance between S and D is d^D_S and the radius of each cluster is r, and the number of IEs in each cluster is n. the time complexity of Phase-1 is 𝑂(⌊d^D_S⌋n + ⌊d^D_S⌋ + n), and the time complexity of Phase-2 is 𝑂(⌊d^D_S⌋), the time complexity of Phase-3 is 𝑂(⌊d^D_S⌋n + ⌊d^D_S⌋ + n). Eventually, the time complexity of SAA algorithm can be obtained as 𝑂(⌊d^D_S⌋n + ⌊d^D_S⌋ + n). This time complexity is linear to the viables and therefore reasonable.

After determining the multi-hop links based on the above algorithm, the throughput of each hop can be calculated. Assuming that the spectrum bandwidth of the CE is B, the throughput of the first hop is:

\(\begin{aligned}\Omega_{1}=B \cdot \log _{2}\left(1+\frac{P_{\mathrm{S}}\left(d_{\mathrm{S}}^{R_{I}}\right)^{-\alpha} h_{\mathrm{S}}^{R_{I}}}{P_{C_{l}}\left(d_{C_{1}}^{R_{I}}\right)^{-\alpha} h_{C_{I}}^{R_{I}}+N_{0}}\right)\end{aligned}\)       (9)

The throughput of the m-th hop is:

\(\begin{aligned}\Omega_{m}=B \cdot \log _{2}\left(1+\frac{P_{R_{m-1}}\left(d_{R_{m-l}}^{R_{m}}\right)^{-\alpha} h_{R_{m-1}^{R_{m}}}}{P_{C_{m}}\left(d_{C_{m}}^{R_{m}}\right)^{-\alpha} h_{C_{m}}^{R_{m}}+N_{0}}\right), m=2, \ldots, M-1\end{aligned}\)       (10)

And the throughput of the last hop is:

\(\begin{aligned}\Omega_{M}=B \cdot \log _{2}\left(1+\frac{P_{R_{M-1}}\left(d_{R_{M-1}}^{\mathrm{D}}\right)^{-\alpha} h_{R_{M-1}}^{\mathrm{D}}}{P_{C_{M}}\left(d_{C_{M}}^{\mathrm{D}}\right)^{-\alpha} h_{C_{M}}^{\mathrm{D}}+N_{0}}\right)\end{aligned}\)       (11)

The throughput of the multi-hop D2D link (DT) is limited by the hop with minimum throughput as below:

DT= min{Ω₁, …, Ω_m, …, Ω_M}       (12)

Since relays must consume additional power for receiving and relaying data, it is also very important to study the energy efficiency of D2D link (DEE), which is defined as below:

\(\begin{aligned}\mathrm{DEE}=\frac{\mathrm{DT}}{P_{\mathrm{S}}+\sum_{m=1}^{M-1} P_{R_{m}}}\end{aligned}\)       (13)

Regarding the spectrum efficiency, the SAA algorithm enables D2D links to reuse the cellular users’ uplink frequency channels, while guaranteeing cellular users SIR, hence their data throughput. Therefore, over the total spectrum bandwidth, additional data throughput of DT resulted from D2D can be supported. The overall system spectrum efficiency hence is enhanced by D2D communications.

5. Numerical Results and Performance Analysis

In this section, due to the complex nature of the problem and the algorithm designed to solve the problem, the system level simulation is used to achieve the solutions. The performance of proposed algorithm is evaluated through extensive Monte Carlo system level simulations. To investigate the impacts of social domain information on the D2D performance, we investigate the algorithm with and without social information, respectively:

SAA (Social Aware Algorithm): the proposed algorithm with social information considered;

SUAA (Social Un-Aware Algorithm): the proposed algorithm without social information (taking P = P'' in Step 3).

Two most recently developed and most referenced algorithms are selected as benchmarks for performance comparison, which, are the most suitable given the similar use cases and assumptions made by authors.

MLS (Max Link Selection): SNR-based relay selection from the first to the last hop [26].

HTPRS (Highest Transmit Power Relay Selection): relay selection based on transmit power from the first to the last hop [27].

After analysis, it is noted that the above two benchmark algorithms, when applied to the system mode, have the same computational complexity as SAA.

The simulations consider an omni-directional single-cell with radius of 500 meters, wherein D2D pairs and CEs are randomly and uniformly located. The D2D link distance normally in practical systems shall be much smaller than the cell radius and it is reflected in the simulations, where the S-D distance is set to 140-380 meters. Key parameters and their settings of simulations are summarized in Table 1.

Table 1. Simulation parameters and settings

Fig. 6 presents D2D link throughput versus S-D distance d^S_D. The throughput of all algorithms decreases as the distance increases. This is because increased S-D distance leads to more hops hence a higher chance for more limited throughput. It is observed that the throughput reduction of some data points is relatively insignificant. These data points represent the cases where the last cluster is a small one, which has relatively less impact on the D2D throughput. Proposed SUAA algorithm outperforms two benchmarks because its relay selection is based on SINR which is directly related to the link throughput. The SAA achieves less throughput than SUAA because of the extra constraint imposed on the relays’ allowable transmit power by social relationship.

Fig. 6. Throughput of D2D link versus S-D distance

Fig. 7 shows that the energy efficiency decreases as S-D distance increases. This is because a larger S-D distance decreases link throughput and increases total transmit power of D2D devices. At some data points, the reduction in energy efficiency is insignificant due to the same reason explained above. It is depicted that SUAA outperforms two benchmarks because the throughput of SUAA is larger while the total transmit powers of D2D devices of all three algorithms are not significantly different. Moreover, SAA considerably outperforms SUAA because the social relationship throttles relay’s transmit power leading to considerable reduction in total transmit power.

Fig. 7. Energy efficiency of D2D link versus S-D distance

D2D link throughput versus the number of IEs in a relay cluster is shown in Fig. 8. It is observed that as the number of IEs increases, the throughput of SUAA, MLS, and SAA increases, while that of HTPRS remains almost unchanged. The reason is that HTPRS algorithm selects relays in a more random fashion and cannot take advantage of having more candidate IEs.

Fig. 8. Throughput of D2D link versus number of IEs

Fig. 9 shows that the increased number of IEs does not change DEE of all algorithms considerably. This is because although the throughput of the first three algorithms increases with increased number of IEs, the total transmit power of the D2D devices also increases. HTPRS, unlike others, selects the relays more randomly, leading to unchanged throughput and transmit power of relays regardless of number of IEs.

Fig. 9. Energy efficiency of D2D link versus number of IEs

Fig. 10 studies the impact of protection area radii A_r on the D2D link throughput for SAA algorithm. It demonstrates that a lager A_r leads to increased throughput. This is because on one hand, a larger A_r will increase the distance between the relay and the BS, so the BS can tolerate the relay to transmit more power. On the other hand, the distance between the CU and the relay also increases, leading to reduced interference to the relay. Consequently, a higher SINR for the relay can be achieved hence a higher throughput of the D2D link.

Fig. 10. Throughput of D2D link for different protection area radii

In Fig. 11, it is shown that when A_r increases, the energy efficiency increases. This is because the throughput of the D2D link increases as A_r increases while the total transmit power is not affected, so the energy efficiency increases.

Fig. 11. Energy efficiency of D2D link for different protection area radii

To demonstrate the impact of social domain on the relay performances, a comparison of SAA and SUAA’s performances at different S-D distance d^S_D is summarized in Table 2. It can be seen that SAA and SUAA differ considerably in both throughput and energy efficiency. It therefore can conclude that the role of social domain information is significant enough not to be overlooked in the study of practical D2D communications.

Table 2. Performance comparison of SAA and SUAA

6. Conclusion

This paper proposed a novel relay selection algorithm for multi-hop full-duplex D2D communications underlaying cellular networks. The algorithm works in a reverse and semi-distributed manner to significantly reduce base station signalling overload. The social relationship between users is taken into account in the algorithm design, which is proved to be critical in practical systems. The proposed algorithm is thoroughly analyzed and compared against two benchmark algorithms. It is observed that the overall system throughput and power efficiency of proposed algorithm considerably outperform those of benchmarks.