#### Abstract

The performance of device-to-device (D2D) communication in a cellular network depends on the resource sharing between D2D links and cellular users. Existing researches on resource sharing mainly focus on power control between the D2D users and cellular users that operate in the same frequency band. However, the D2D outage probability performance is hampered by the cellular interference to D2D links. Therefore, the D2D users may not achieve satisfactory SINR performance when D2D users and cellular users are geographically located in a small area; as a result, the outage probability performance would be significantly degraded. In this paper, we provide a novel resource sharing strategy to mitigate the interference from cellular users to D2D receivers by utilizing the low energy characteristics of signals in the guard band and analyze the D2D outage probability performance mathematically. Both the mathematical analysis and numerical results show that the proposed resource sharing strategy provides 1.2 dB SNR gain in D2D outage probability performance while guaranteeing the cellular throughputs.

#### 1. Introduction

Device-to-device communication underlying the cellular network is a promising technology in future wireless networks to improve the resource utilization efficiency and extend coverage areas [1]. However, D2D communication in the cellular spectrum poses a host of challenges to the network. For example, new resource allocation schemes must be designed to mitigate or avoid interference between cellular and D2D links.

Resource allocation methods for D2D users can be categorized into two schemes: the orthogonal resource sharing and the nonorthogonal resource sharing. The former assigns dedicated resources to D2D users, and the latter requires them to share resources with cellular users. The nonorthogonal resource sharing scheme achieves better resource utilization efficiency [2–4]; however, additional manipulations, such as power control, distance limitation, and measures related to mode selection [2–7], are needed to suppress the interference between cellular users and D2D users.

In [2], a resource sharing algorithm is proposed to find the optimal transmission power for D2D communication without degrading the QoS of cellular users. Tang et al. present a series of distributed power control methods to avoid interference and to enhance radio resource utilization in cellular and D2D hybrid networks [3]. Further, Yu et al. employed different resource sharing modes to analyze optimal resource allocation and power control between cellular and D2D connections that share the same resources [4]. In [5–10], the authors considered the similar problems and presented a number of distance-dependent algorithms based on power optimization, uplink reuse allocation, and power management. However, all these solutions hinge on the condition that each D2D link and its paired cellular user operate in the same frequency band, which raises the issue that the D2D receiver may pick up total interference from its paired cellular user. Therefore, the D2D users may not achieve satisfactory SINR (Signal to Interference and Noise Ratio) performance when D2D users and cellular users are geographically located in a small area; as a result, the outage probability performance would be significantly degraded.

In communication systems, to reduce the impact of adjacent channel interference, nearly 10 percent of the system bandwidth at the edge of the allocated bandwidth is reserved as the guard band. For example, 3GPP TS 25.101 regulates that the adjacent carrier spacing is 5 MHz, but the actual occupied bandwidth is times the chip rate in WCDMA system, where is the roll-off factor of the root-raised cosine filter. This leaves the guard band MHz. In LTE, when the allocated bandwidth is 20 MHz, its actual occupied bandwidth is 18 MHz, leaving the guard band 2 MHz. Based on the guard band, Chen et al. proposed a novel scheme of utilizing the guard band in LTE uplink, which tried to optimize the overall spectrum efficiency of the two systems adjacently deployed on frequency [11].

In contrast to existing works, this paper considers the low energy characteristics of WCDMA signals in the guard band and presents a novel resource sharing strategy to mitigate cellular user-induced interference at the D2D receiver. In addition, the D2D outage probability performances are discussed mathematically in both flat-fading and frequency-selective channels. Numerical results show that the proposed resource sharing strategy outperforms the conventional strategy.

#### 2. System Model

In cellular networks, uplink resource sharing is a common technique, since uplink resources tend to be underutilized in frequency division duplexing (FDD) based cellular networks [12], especially in multimedia services. As a result, uplink resource sharing has been the subject of a number of D2D system designs.

This paper will explore resource sharing problems in one cell, leaving intercell interference out of discussion. Consider a scenario involving a fully loaded cellular network, where active cellular users occupy orthogonal channels in a cell, and there are no spare resources. Figure 1 depicts one BS (Base Station) and orthogonal cellular users, with each user occupying a frequency band indexed by . A total of D2D pairs exist in this network. The goal of our proposed scheme is to decrease the D2D users’ average outage probability with the proposed scheme.

In what follows, we use and to denote the D2D transmitter and receiver, respectively, and the cellular user is denoted by . The following three assumptions are underlying the system model.

*Assumption 1. *The distance between and is assumed to be , and the distances from BS to and are denoted by and , respectively. For any , the probability density function (PDF) of its distance from BS is [5], where is the cell radius. Moreover, resource sharing is region constrained such that if the angle is , the cellular user’s angle is uniformly distributed in . And denotes the set of locations that meet the region constraint. Since is much smaller than , the distance from BS to also approaches . Assuming that the relative angle between and is , then the distance between and is given by

*Assumption 2. *Let and denote the channel from to and to , respectively. Further, the channel from to BS is denoted by , and the channel from to BS is given by . If channel gain follows independent Rayleigh distribution, then, according to [13], and follow independent exponential distribution. In addition, the path loss factor is set to be 4 [5].

*Assumption 3. *The system has a guard band between two adjacent channels to suppress interferences between them. The carrier frequency of the cellular user is denoted as and that of the D2D user as .

#### 3. Guard Band-Based Resource Sharing

##### 3.1. Scheme Description

In this part, we will first present the conventional resource sharing technique and then propose a new one to improve the reliability of D2D communications. For convenience, the two strategies are denoted as and , respectively.

In , the D2D user’s carrier frequency is equal to its paired cellular user’s center frequency ; that is, . As shown in Figure 2, is the lower band bound and is the upper band bound of the ; is the lower and is the upper band bound of . With denoting the passband, , , and the same applies to and . Interference received by the D2D link is caused by , as seen in Figure 2. If the power of the cellular signal is denoted by , then the cellular interference from is .

In , is chosen as the center of the guard band between two adjacent cellular channels; that is, . As Figure 3 shows, when the D2D receiver obtains the desired signal with a band-pass filter with passband , it also picks up cellular interference from and . Denote the power of the interference coming from as (which means integration over region I in Figure 3) and the power of the interference coming from as . Clearly, the cellular interference is . Define the interference fraction factor as , .

Proposition 4. *If a guard band exists between two adjacent channels with center frequencies and and the D2D user’s center frequency is equal to , the defined cellular interference fraction factor .*

*Proof. *For convenience, we calculate the parameter in the baseband, as shown in Figure 4. is the power spectrum, is the filter passband, and is the guard band. Denote Let . Since and , can be expressed as According to (3), it is obvious that . As a result, .

Equation (3) shows that is affected by the ratio of the interference power in the guard band to the total power . For different CUs, the ratios are identical; that is, the interference fraction factor is also for .

##### 3.2. Outage Probability Analysis in a Flat-Fading Channel

Let represent the transmitted signal of and denote the signal of . In a flat-fading channel, the received D2D signal at is where is additive white Gaussian noise with variance . Assuming that and , in this paper, a widely used power control scheme for cellular user equipment () is considered, known as the target SNR power control scheme (TSPC) [14]. In this scheme, the cellular user’s power is selected to reach a fixed SNR (Signal to Noise Ratio) target , as shown in (5), where is the variance of the zero-mean Gaussian noise for . In addition, the cellular power should satisfy its power constraint :

The TSPC scheme is also applied to the D2D link. Two lemmas are utilized to derive the D2D outage probability.

Lemma 5. *Let and follow independent exponential distribution with unit mean, , and , . Then, the cumulative distribution function (CDF) of is *

*Proof. *The proof is presented in Appendix A.

Lemma 6. *Let , , and follow independent exponential distribution with unit mean, and and , . Then, the CDF of is *

*Proof. *The proof is presented in Appendix B.

The D2D conditional outage probability is given by (8), where is the D2D SINR threshold and is the SINR for , calculated by (9). is the probability density function of . In (9), is the power of the desired signal at receiver , and is the cellular interference:

The difference between and lies in the cellular interference , so we use a high SNR approximation; that is, .

###### 3.2.1. The Outage Probability of

In , and ; then, where . According to Lemma 5, the conditional outage probability of can be written as

The outage probability of can be obtained by averaging over the positions of the cellular user :

###### 3.2.2. The Outage Probability of

In , ; then, the SINR can be expressed as where and . The conditional outage probability of can be evaluated with Lemma 6, which is shown by

Similarly, when averaging over the positions of and , the outage probability of can be obtained:

##### 3.3. Outage Probability Analysis in a Frequency-Selective Channel

When the system’s communication bandwidth is much larger than the coherence bandwidth, the channel has a frequency-selective characteristic. In this case, the channel is modelled as a multipath fading channel, and the received signal is given by where is the channel gain of the path from to and is the channel gain of the path from to . Here, and , where and represent Rayleigh fading and represent multipath fading for each path. In contrast to a flat-fading channel, intersymbol interference (ISI) is easily introduced in the multipath environment. Its SINR is extended to where is the intersymbol interference. With a RAKE receiver, multipath components whose delays are less than one chip period can be used to increase the signal energy, thus allowing to be written as (18). Let be the set of paths whose delays are less than one chip period ; that is, ; then,

Intersymbol interference originates from multipath signals whose delays exceed one chip period. This set can be defined as : In , cellular interference can be written as

Substitute (18), (19), and (20) into (17); the SINR for can be then expressed as

In , cellular interference can be written as

Substitute (18), (19), and (22) into (17); the SINR for can be then expressed as

Substitute (21) and (23) into (8), respectively; then, the outage probabilities of and are obtained. In the following session, we will evaluate the system performance in the frequency-selective channel by simulation.

#### 4. Performance Comparison

This section presents a performance comparison between and . Table 1 gives the simulation parameters. In a WCDMA system, the channel spacing is 5 MHz, and the transmission pulse shaping filter is a root-raised cosine (RRC) function. The chip duration is 260.42 ns (1/3.84 MHz). Assume the roll-off factor to be 0.075. Since , the signal bandwidth is 4.12 MHz, making the guard band () 0.88 MHz. Equation (3) allows us to obtain the interference fraction factor , which is 0.3847.

##### 4.1. Performance in a Flat-Fading Channel

Figure 5 shows the outage probability performance of D2D communication, indicating how the outage probability changes when the target cellular SNR is set to 10 dB and 20 dB, respectively. It can be seen that provides better outage probability performance than . At the same outage probability level, provides an SNR gain of 1.2 dB, which accords with the theoretical analysis, verifying that our derivation for outage probability in a flat-fading channel is correct.

Figure 6 gives the cellular network’s capacity improvement factor with the target cellular SNR set to 5 dB, 10 dB, and 20 dB, respectively. Calculated with (26), the capacity improvement factor is averaged over a range of channel states and cellular user positions. In Figure 6, means that the cellular capacity performance of is better than that of . In other words, provides better D2D outage probability performance while guaranteeing the cellular capacity:

##### 4.2. Performance in a Frequency-Selective Channel

The frequency-selective channel is modelled in accordance with the Ped B model defined by ITU. Table 2 presents the channel parameters of this outdoor to indoor pedestrian model. Relative delay refers to a time difference relative to the first path, whereas average power refers to power fading relative to the first path.

Since WCDMA has a chip period of 260.42 ns, the first three paths (1, 2, and 3) are located in set and can be processed by the RAKE receiver. As the other three paths (4, 5, and 6) are located in set , they are considered as ISI interference.

Figure 7 shows the outage probability performance in a frequency-selective channel with the target cellular SNR set to 10 and 20 dB, respectively. At low and moderate SNRs, achieves better outage probability performance than , with an SNR gain of about 1.2 dB. However, at high SNRs, the outage probabilities of the two modes become equivalent, because, in a high SNR region, the outage probability is mainly affected by . The value of is determined by the D2D transmission power, and it changes with the D2D SNR, making the ISI interferences of the two modes identical.

#### 5. Conclusion

This paper investigated resource sharing strategies for D2D communications in a cellular network. In contrast to previous research, we aimed at mitigating cellular interference on the basis of the low energy characteristics of signals in the guard band and proposed a novel resource sharing strategy. Mathematical analysis and simulation results show that, in a flat-fading channel, the proposed strategy could improve the outage probability performance. And in a frequency-selective channel, the advantage of the proposed method was obvious in low and moderate SNR regions.

#### Appendix

#### A. Proof of Lemma 5

Let and follow independent exponential distribution with unit mean, , and . The PDF of and are expressed as and , respectively. According to [15] (6–43), the PDF of is Substituting and into (A.1), Using integration by parts, the PDF in (A.2) can be evaluated as The CDF of variable can be expressed as Thus, the desired result (6) is obtained.

#### B. Proof of Lemma 6

Let , , and follow independent exponential distribution with unit mean, and and . The PDF of is expressed as . Let and . According to [15] (6–41), the PDF of is Since the cellular position is randomly generated, it is more common that , so we consider the first case. According to (A.1), Applying integration by part to the first and second term of (B.2), respectively, we obtain The CDF of variable can be expressed as By substituting and with and , respectively, the desired result (7) is obtained.

#### Competing Interests

The authors declare that they have no competing interests.

#### Acknowledgments

This work was supported by the 973 Program under Grant no. 2013CB329003 and the National Science and Technology Major Project under Grant no. 2012ZX03003011-004.