# Guard Band-Based Resource Sharing for Device-to-Device Communications Underlying Cellular Network

Authors: Yue Li; Xuejun Sha; Liang Ye; Xiaojie Fang
Journal: Mathematical Problems in Engineering
 (2016)

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## 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.


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## Body

## 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 is1+μ times the chip rate in WCDMA system, where μ is the roll-off factor of the root-raised cosine filter. This leaves the guard band (5-3.84(1+μ)) 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, whereN active cellular users occupy N orthogonal channels in a cell, and there are no spare resources. Figure 1 depicts one BS (Base Station) and N orthogonal cellular users, with each user occupying a frequency band indexed by i=1,2,…,N. A total of N-1 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.Figure 1
D2D links sharing uplink resources with cellular users.In what follows, we useDTi and DRi to denote the D2D transmitter and receiver, respectively, and the cellular user is denoted by CUi. The following three assumptions are underlying the system model.Assumption 1.
The distance betweenDTi and DRi is assumed to be ρi, and the distances from BS to CUi and DTi are denoted by ric and rid, respectively. For any CUi, the probability density function (PDF) of its distance ric from BS is f(ric)=2ric/R2,ric∈(0,R] [5], where R is the cell radius. Moreover, resource sharing is region constrained such that if the DRi angle is θ0, the cellular user’s angle θi is uniformly distributed in [θ0+π/2,θ0+3π/2). And Ω denotes the set of CUi locations that meet the region constraint. Since ρi is much smaller than rid, the distance from BS to DRi also approaches rid. Assuming that the relative angle between DRi and CUi is θ, then the distance between CUi and DRi is given by (1)Li=ric2+rid2-2ricridcos⁡θ.Assumption 2.
Lethid and gid denote the channel from CUi to DRi and DTi to DRi, respectively. Further, the channel from CUi to BS is denoted by hic, and the channel from DTi to BS is given by gic. If channel gain follows independent Rayleigh distribution, then, according to [13], |gid|2 and |hid|2 follow independent exponential distribution. In addition, the path loss factor α 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 useri is denoted as fic and that of the D2D user i as fid.


## 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 asMODE1 and MODE2, respectively.InMODE1, the D2D user’s carrier frequency fid is equal to its paired cellular user’s center frequency fic; that is, fid=fic. As shown in Figure 2, BL,id is the lower band bound and BH,id is the upper band bound of the DTi; BL,ic is the lower and BH,ic is the upper band bound of CUi. With Bp denoting the passband, BL,id=fid-Bp/2, BH,id=fid+Bp/2, and the same applies to BL,ic and BH,ic. Interference received by the D2D link i is caused by CUi, as seen in Figure 2. If the power of the cellular signal i is denoted by P, then the cellular interference from CUi is P.Figure 2
Conventional resource sharing strategyMODE1.InMODE2, fid is chosen as the center of the guard band between two adjacent cellular channels; that is, fid=(fic+fi+1c)/2. As Figure 3 shows, when the D2D receiver obtains the desired signal with a band-pass filter with passband [BL,id,BH,id], it also picks up cellular interference from CUi and CUi+1. Denote the power of the interference coming from CUi as PI (which means integration over region I in Figure 3) and the power of the interference coming from CUi+1 as PIV. Clearly, the cellular interference is PI+PIV. Define the interference fraction factor as ε, ε=PI/P.Figure 3
Proposed resource sharing strategyMODE2.Proposition 4.
If a guard band exists between two adjacent channels with center frequenciesfic and fi+1c and the D2D user’s center frequency fid is equal to (fic+fi+1c)/2, the defined cellular interference fraction factor 0<ε<0.5.Proof.
For convenience, we calculate the parameterε in the baseband, as shown in Figure 4. P(f) is the power spectrum, Bp is the filter passband, and Bg is the guard band. Denote (2)PI=∫Bg/2Bp/2PfdfPII=∫-Bp/2-Bg/2PfdfPIII=∫-Bg/2Bg/2Pfdf.Let P=PI+PII+PIII. Since PI=P-PII-PIII and PI=PII, ε can be expressed as (3)ε=PIP=12P-PIIIP=121-PIIIP.
According to (3), it is obvious that 0<PIII/P<1. As a result, 0<ε<0.5.
Equation (3) shows that ε is affected by the ratio of the interference power in the guard band PIII to the total power P. For different CUs, the ratios are identical; that is, the interference fraction factor is also ε for CUi+1.Figure 4
Calculation ofε.


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

Letxjc(t) represent the transmitted signal of CUj and xid(t) denote the signal of DTi. In a flat-fading channel, the received D2D signal at DRi is (4)yidt=gidxidt+∑jhjdxjct+nidt,where nid(t) is additive white Gaussian noise with variance σid. Assuming that pj=Exjc2 and qi=Exid2, in this paper, a widely used power control scheme for cellular user equipment (CUj) 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 ξ, as shown in (5), where σjc is the variance of the zero-mean Gaussian noise for CUj. In addition, the cellular power pj should satisfy its power constraint pj≤Pcmax: (5)ξ=pjrjc-ασjc.The TSPC scheme is also applied to the D2D link. Two lemmas are utilized to derive the D2D outage probability.Lemma 5.
Letgid2 and hid2 follow independent exponential distribution with unit mean, x=gid2, and y=ahid2, (a>0). Then, the cumulative distribution function (CDF) of z=x/y is (6)FZz=1-11+az.Proof.
The proof is presented in AppendixA.Lemma 6.
Letgid2, hid2, and hi+1d2 follow independent exponential distribution with unit mean, and x=gid2 and y=ahid2+bhi+1d2, (a>0,b>0). Then, the CDF of z=x/y is (7)FZz=1-11+az1+bz.Proof.
The proof is presented in AppendixB.The D2D conditional outage probability is given by (8), where γ0 is the D2D SINR threshold and γi,d is the SINR for DRi, calculated by (9). fγi,d(γ) is the probability density function of γi,d. In (9), Ps is the power of the desired signal at receiver DRi, and Iic is the cellular interference: (8)Fγi,dγ0=Pγi,d<γ0=∫0γ0fγi,dγdγ(9)γi,d=Psσid+Iic.The difference betweenMODE1 and MODE2 lies in the cellular interference Iic, so we use a high SNR approximation; that is, σid≈0.


#### 3.2.1. The Outage Probability ofMODE1

InMODE1, Ps=gid2ρi-αqi and Iic=hid2Li-αpi; then, (10)γi,d1=gid2ρi-αqihid2Li-αpi=gid2p-ihid2,where p-i=piLi-α/qiρi-α. According to Lemma 5, the conditional outage probability of MODE1 can be written as (11)Fγi,d1γ0∣ric,θi=1-11+γ0p-i.The outage probability ofMODE1 can be obtained by averaging over the positions of the cellular user CUi: (12)Pout1=∫ΩFγi,d1γ0∣ric,θifricrfθiθdrdθ.


#### 3.2.2. The Outage Probability ofMODE2

InMODE2, Iic=ε∑j=i,i+1hjd2Lj-αpj; then, the SINR can be expressed as (13)γi,d2=gid2ρi-αqiε∑j=i,i+1hjd2Lj-αpj=gid2εp-ihid2+εp-i+1hi+1d2,where p-i=piLi-α/qiρi-α and p-i+1=pi+1Li+1-α/qiρi-α. The conditional outage probability of MODE2 can be evaluated with Lemma 6, which is shown by (14)Fγi,d2γ0∣ric,ri+1c,θi,θi+1=1-11+γ0εp-i1+γ0εp-i+1.Similarly, when averaging over the positions ofCUi and CUi+1, the outage probability of MODE2 can be obtained: (15)Pout2=∫Ω∫ΩFγi,d2γ0∣ric,ri+1c,θi,θi+1fric,ri+1cr1,r2fθi,θi+1θ1,θ2dr1dr2dθ1dθ2.


### 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(16)yidt=∑l=0L-1δi,ldxidt-τi,l+∑j∑l=0L-1λj,ldxjct-τj,l+nidt,where δi,ld is the channel gain of the lth path from DTi to DRi and λj,ld is the channel gain of the lth path from CUj to DRi. Here, δi,ld=gi,ldmi,ld and λj,ld=hj,ldmj,ld, where gi,ld and hj,ld represent Rayleigh fading and mi,ld,mj,ld 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 (17)γi,d=Psσid+Iic+IISId,where IISId 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 Ps to be written as (18). Let L1 be the set of paths whose delays are less than one chip period Tc; that is, L1:l∈τi,l<Tc; then, (18)Ps=∑l∈L1δi,ld2ρi-αqi.Intersymbol interference originates from multipath signals whose delays exceed one chip period. This set can be defined asL2:l∈τi,l≥Tc: (19)IISId=∑l∈L2δi,ld2ρi-αqi.In MODE1, cellular interference Iic can be written as (20)Iic=∑l=0L-1λi,ld2Li-αpi.Substitute (18), (19), and (20) into (17); the SINR for MODE1 can be then expressed as (21)γi,d1=∑l∈L1δi,ld2ρi-αqiσid+∑l=0L-1λi,ld2Li-αpi+∑l∈L2δi,ld2ρi-αqi.InMODE2, cellular interference Iic can be written as (22)Iic=ε∑l=0L-1λi,ld2Li-αpi+ε∑l=0L-1λi+1,ld2Li+1-αpi+1.Substitute (18), (19), and (22) into (17); the SINR for MODE2 can be then expressed as (23)γi,d2=∑l∈L1δi,ld2ρi-αqiσid+ε∑j=i,i+1∑l=0L-1λj,ld2Lj-αpj+∑l∈L2δi,ld2ρi-αqi.Substitute (21) and (23) into (8), respectively; then, the outage probabilities of MODE1 and MODE2 are obtained. In the following session, we will evaluate the system performance in the frequency-selective channel by simulation.


## 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 asMODE1 and MODE2, respectively.InMODE1, the D2D user’s carrier frequency fid is equal to its paired cellular user’s center frequency fic; that is, fid=fic. As shown in Figure 2, BL,id is the lower band bound and BH,id is the upper band bound of the DTi; BL,ic is the lower and BH,ic is the upper band bound of CUi. With Bp denoting the passband, BL,id=fid-Bp/2, BH,id=fid+Bp/2, and the same applies to BL,ic and BH,ic. Interference received by the D2D link i is caused by CUi, as seen in Figure 2. If the power of the cellular signal i is denoted by P, then the cellular interference from CUi is P.Figure 2
Conventional resource sharing strategyMODE1.InMODE2, fid is chosen as the center of the guard band between two adjacent cellular channels; that is, fid=(fic+fi+1c)/2. As Figure 3 shows, when the D2D receiver obtains the desired signal with a band-pass filter with passband [BL,id,BH,id], it also picks up cellular interference from CUi and CUi+1. Denote the power of the interference coming from CUi as PI (which means integration over region I in Figure 3) and the power of the interference coming from CUi+1 as PIV. Clearly, the cellular interference is PI+PIV. Define the interference fraction factor as ε, ε=PI/P.Figure 3
Proposed resource sharing strategyMODE2.Proposition 4.
If a guard band exists between two adjacent channels with center frequenciesfic and fi+1c and the D2D user’s center frequency fid is equal to (fic+fi+1c)/2, the defined cellular interference fraction factor 0<ε<0.5.Proof.
For convenience, we calculate the parameterε in the baseband, as shown in Figure 4. P(f) is the power spectrum, Bp is the filter passband, and Bg is the guard band. Denote (2)PI=∫Bg/2Bp/2PfdfPII=∫-Bp/2-Bg/2PfdfPIII=∫-Bg/2Bg/2Pfdf.Let P=PI+PII+PIII. Since PI=P-PII-PIII and PI=PII, ε can be expressed as (3)ε=PIP=12P-PIIIP=121-PIIIP.
According to (3), it is obvious that 0<PIII/P<1. As a result, 0<ε<0.5.
Equation (3) shows that ε is affected by the ratio of the interference power in the guard band PIII to the total power P. For different CUs, the ratios are identical; that is, the interference fraction factor is also ε for CUi+1.Figure 4
Calculation ofε.


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

Letxjc(t) represent the transmitted signal of CUj and xid(t) denote the signal of DTi. In a flat-fading channel, the received D2D signal at DRi is (4)yidt=gidxidt+∑jhjdxjct+nidt,where nid(t) is additive white Gaussian noise with variance σid. Assuming that pj=Exjc2 and qi=Exid2, in this paper, a widely used power control scheme for cellular user equipment (CUj) 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 ξ, as shown in (5), where σjc is the variance of the zero-mean Gaussian noise for CUj. In addition, the cellular power pj should satisfy its power constraint pj≤Pcmax: (5)ξ=pjrjc-ασjc.The TSPC scheme is also applied to the D2D link. Two lemmas are utilized to derive the D2D outage probability.Lemma 5.
Letgid2 and hid2 follow independent exponential distribution with unit mean, x=gid2, and y=ahid2, (a>0). Then, the cumulative distribution function (CDF) of z=x/y is (6)FZz=1-11+az.Proof.
The proof is presented in AppendixA.Lemma 6.
Letgid2, hid2, and hi+1d2 follow independent exponential distribution with unit mean, and x=gid2 and y=ahid2+bhi+1d2, (a>0,b>0). Then, the CDF of z=x/y is (7)FZz=1-11+az1+bz.Proof.
The proof is presented in AppendixB.The D2D conditional outage probability is given by (8), where γ0 is the D2D SINR threshold and γi,d is the SINR for DRi, calculated by (9). fγi,d(γ) is the probability density function of γi,d. In (9), Ps is the power of the desired signal at receiver DRi, and Iic is the cellular interference: (8)Fγi,dγ0=Pγi,d<γ0=∫0γ0fγi,dγdγ(9)γi,d=Psσid+Iic.The difference betweenMODE1 and MODE2 lies in the cellular interference Iic, so we use a high SNR approximation; that is, σid≈0.


### 3.2.1. The Outage Probability ofMODE1

InMODE1, Ps=gid2ρi-αqi and Iic=hid2Li-αpi; then, (10)γi,d1=gid2ρi-αqihid2Li-αpi=gid2p-ihid2,where p-i=piLi-α/qiρi-α. According to Lemma 5, the conditional outage probability of MODE1 can be written as (11)Fγi,d1γ0∣ric,θi=1-11+γ0p-i.The outage probability ofMODE1 can be obtained by averaging over the positions of the cellular user CUi: (12)Pout1=∫ΩFγi,d1γ0∣ric,θifricrfθiθdrdθ.


### 3.2.2. The Outage Probability ofMODE2

InMODE2, Iic=ε∑j=i,i+1hjd2Lj-αpj; then, the SINR can be expressed as (13)γi,d2=gid2ρi-αqiε∑j=i,i+1hjd2Lj-αpj=gid2εp-ihid2+εp-i+1hi+1d2,where p-i=piLi-α/qiρi-α and p-i+1=pi+1Li+1-α/qiρi-α. The conditional outage probability of MODE2 can be evaluated with Lemma 6, which is shown by (14)Fγi,d2γ0∣ric,ri+1c,θi,θi+1=1-11+γ0εp-i1+γ0εp-i+1.Similarly, when averaging over the positions ofCUi and CUi+1, the outage probability of MODE2 can be obtained: (15)Pout2=∫Ω∫ΩFγi,d2γ0∣ric,ri+1c,θi,θi+1fric,ri+1cr1,r2fθi,θi+1θ1,θ2dr1dr2dθ1dθ2.


## 3.2.1. The Outage Probability ofMODE1

InMODE1, Ps=gid2ρi-αqi and Iic=hid2Li-αpi; then, (10)γi,d1=gid2ρi-αqihid2Li-αpi=gid2p-ihid2,where p-i=piLi-α/qiρi-α. According to Lemma 5, the conditional outage probability of MODE1 can be written as (11)Fγi,d1γ0∣ric,θi=1-11+γ0p-i.The outage probability ofMODE1 can be obtained by averaging over the positions of the cellular user CUi: (12)Pout1=∫ΩFγi,d1γ0∣ric,θifricrfθiθdrdθ.


## 3.2.2. The Outage Probability ofMODE2

InMODE2, Iic=ε∑j=i,i+1hjd2Lj-αpj; then, the SINR can be expressed as (13)γi,d2=gid2ρi-αqiε∑j=i,i+1hjd2Lj-αpj=gid2εp-ihid2+εp-i+1hi+1d2,where p-i=piLi-α/qiρi-α and p-i+1=pi+1Li+1-α/qiρi-α. The conditional outage probability of MODE2 can be evaluated with Lemma 6, which is shown by (14)Fγi,d2γ0∣ric,ri+1c,θi,θi+1=1-11+γ0εp-i1+γ0εp-i+1.Similarly, when averaging over the positions ofCUi and CUi+1, the outage probability of MODE2 can be obtained: (15)Pout2=∫Ω∫ΩFγi,d2γ0∣ric,ri+1c,θi,θi+1fric,ri+1cr1,r2fθi,θi+1θ1,θ2dr1dr2dθ1dθ2.


## 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(16)yidt=∑l=0L-1δi,ldxidt-τi,l+∑j∑l=0L-1λj,ldxjct-τj,l+nidt,where δi,ld is the channel gain of the lth path from DTi to DRi and λj,ld is the channel gain of the lth path from CUj to DRi. Here, δi,ld=gi,ldmi,ld and λj,ld=hj,ldmj,ld, where gi,ld and hj,ld represent Rayleigh fading and mi,ld,mj,ld 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 (17)γi,d=Psσid+Iic+IISId,where IISId 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 Ps to be written as (18). Let L1 be the set of paths whose delays are less than one chip period Tc; that is, L1:l∈τi,l<Tc; then, (18)Ps=∑l∈L1δi,ld2ρi-αqi.Intersymbol interference originates from multipath signals whose delays exceed one chip period. This set can be defined asL2:l∈τi,l≥Tc: (19)IISId=∑l∈L2δi,ld2ρi-αqi.In MODE1, cellular interference Iic can be written as (20)Iic=∑l=0L-1λi,ld2Li-αpi.Substitute (18), (19), and (20) into (17); the SINR for MODE1 can be then expressed as (21)γi,d1=∑l∈L1δi,ld2ρi-αqiσid+∑l=0L-1λi,ld2Li-αpi+∑l∈L2δi,ld2ρi-αqi.InMODE2, cellular interference Iic can be written as (22)Iic=ε∑l=0L-1λi,ld2Li-αpi+ε∑l=0L-1λi+1,ld2Li+1-αpi+1.Substitute (18), (19), and (22) into (17); the SINR for MODE2 can be then expressed as (23)γi,d2=∑l∈L1δi,ld2ρi-αqiσid+ε∑j=i,i+1∑l=0L-1λj,ld2Lj-αpj+∑l∈L2δi,ld2ρi-αqi.Substitute (21) and (23) into (8), respectively; then, the outage probabilities of MODE1 and MODE2 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 betweenMODE1 and MODE2. 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 Tc is 260.42 ns (1/3.84 MHz). Assume the roll-off factor μ to be 0.075. Since Bp=(1+μ)/Tc, the signal bandwidth Bp is 4.12 MHz, making the guard band (Bg) 0.88 MHz. Equation (3) allows us to obtain the interference fraction factor ε, which is 0.3847.Table 1
Simulation parameters.
Parameters Values Cell radiusR 500 m Maximum cellular powerPcmax 20 dBm Distance between D2D TX and RXρi ~⁢U [50 m, 100 m] Distance between D2D TX and BSrid ~⁢U [250 m, 500 m] Channel spacing 5 MHz Pulse shaping filter RRC Gaussian noise powersσid and σic - 100 dBm D2D SINR thresholdγ0 0 dB


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

Figure5 shows the outage probability performance of D2D communication, indicating how the outage probability changes when the target cellular SNR ξ is set to 10 dB and 20 dB, respectively. It can be seen that MODE2 provides better outage probability performance than MODE1. At the same outage probability level, MODE2 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 5
D2D outage probability in a flat-fading channel.Figure6 gives the cellular network’s capacity improvement factor with the target cellular SNR ξ set to 5 dB, 10 dB, and 20 dB, respectively. Calculated with (26), the capacity improvement factor η is averaged over a range of channel states and cellular user positions. In Figure 6, η>1 means that the cellular capacity performance of MODE2 is better than that of MODE1. In other words, MODE2 provides better D2D outage probability performance while guaranteeing the cellular capacity: (24)Ri,c1=log⁡1+hic2ric-αpiσic+gic2rid-αqi(25)Ri,c2=log⁡1+hic2ric-αpiσic+ε∑j=i,i-1gjc2rjd-αqj(26)η=Ri,c2Ri,c1.Figure 6
Cellular capacity improvement factor in a flat-fading channel.


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

The frequency-selective channel is modelled in accordance with the Ped B model defined by ITU. Table2 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.Table 2
Ped B channel parameters.
Path number Relative delay Average power 1 0 ns 0 dB 2 100 ns - 3.6 dB 3 200 ns - 7.2 dB 4 300 ns - 10.8 dB 5 500 ns - 18.0 dB 6 700 ns - 25.2 dBSince WCDMA has a chip period of 260.42 ns, the first three paths (1, 2, and 3) are located in setL1 and can be processed by the RAKE receiver. As the other three paths (4, 5, and 6) are located in set L2, they are considered as ISI interference.Figure7 shows the outage probability performance in a frequency-selective channel with the target cellular SNR ξ set to 10 and 20 dB, respectively. At low and moderate SNRs, MODE2 achieves better outage probability performance than MODE1, 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 IISId. The value of IISId is determined by the D2D transmission power, and it changes with the D2D SNR, making the ISI interferences IISId of the two modes identical.Figure 7
D2D outage probability in a frequency-selective channel.


## 4.1. Performance in a Flat-Fading Channel

Figure5 shows the outage probability performance of D2D communication, indicating how the outage probability changes when the target cellular SNR ξ is set to 10 dB and 20 dB, respectively. It can be seen that MODE2 provides better outage probability performance than MODE1. At the same outage probability level, MODE2 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 5
D2D outage probability in a flat-fading channel.Figure6 gives the cellular network’s capacity improvement factor with the target cellular SNR ξ set to 5 dB, 10 dB, and 20 dB, respectively. Calculated with (26), the capacity improvement factor η is averaged over a range of channel states and cellular user positions. In Figure 6, η>1 means that the cellular capacity performance of MODE2 is better than that of MODE1. In other words, MODE2 provides better D2D outage probability performance while guaranteeing the cellular capacity: (24)Ri,c1=log⁡1+hic2ric-αpiσic+gic2rid-αqi(25)Ri,c2=log⁡1+hic2ric-αpiσic+ε∑j=i,i-1gjc2rjd-αqj(26)η=Ri,c2Ri,c1.Figure 6
Cellular capacity improvement factor in a flat-fading channel.


## 4.2. Performance in a Frequency-Selective Channel

The frequency-selective channel is modelled in accordance with the Ped B model defined by ITU. Table2 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.Table 2
Ped B channel parameters.
Path number Relative delay Average power 1 0 ns 0 dB 2 100 ns - 3.6 dB 3 200 ns - 7.2 dB 4 300 ns - 10.8 dB 5 500 ns - 18.0 dB 6 700 ns - 25.2 dBSince WCDMA has a chip period of 260.42 ns, the first three paths (1, 2, and 3) are located in setL1 and can be processed by the RAKE receiver. As the other three paths (4, 5, and 6) are located in set L2, they are considered as ISI interference.Figure7 shows the outage probability performance in a frequency-selective channel with the target cellular SNR ξ set to 10 and 20 dB, respectively. At low and moderate SNRs, MODE2 achieves better outage probability performance than MODE1, 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 IISId. The value of IISId is determined by the D2D transmission power, and it changes with the D2D SNR, making the ISI interferences IISId of the two modes identical.Figure 7
D2D outage probability in a frequency-selective channel.


## 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.



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*Source: 9547560-2016-07-28.xml*