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

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 tomitigate 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.


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][3][4]; however, additional manipulations, such as power control, distance limitation, and measures related to mode selection [2][3][4][5][6][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][6][7][8][9][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 1 +  times the chip rate in WCDMA system, where  is the roll-off factor of the root-raised cosine filter.This leaves the guard band (5 − 3.84(1 + )) 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.

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  = 1, 2, . . ., .A total of  − 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.
In what follows, we use DT  and DR  to denote the D2D transmitter and receiver, respectively, and the cellular user is denoted by CU  .The following three assumptions are underlying the system model.Assumption 1.The distance between DT  and DR  is assumed to be   , and the distances from BS to CU  and DT  are denoted by    and    , respectively.For any CU  , the probability density function (PDF) of its distance    from BS is where  is the cell radius.Moreover, resource sharing is region constrained such that if the DR  angle is  0 , the cellular user's angle   is uniformly distributed in [ 0 + /2,  0 + 3/2).And Ω denotes the set of CU  locations that meet the region constraint.Since   is much smaller than    , the distance from BS to DR  also approaches    .Assuming that the relative angle between DR  and CU  is , then the distance between CU  and DR  is given by Assumption 2. Let ℎ   and    denote the channel from CU  to DR  and DT  to DR  , respectively.Further, the channel from CU  to BS is denoted by ℎ   , and the channel from DT  to BS is given by    .If channel gain follows independent Rayleigh distribution, then, according to [13], |   | 2 and |ℎ   | 2 follow independent exponential distribution.In addition, the path loss factor  is set to be 4 [5].

Signal transmission link Interference
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    .In MODE2,    is chosen as the center of the guard band between two adjacent cellular channels; that is,    = (   +   +1 )/2.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 CU  and CU +1 .Denote the power of the interference coming from CU  as  I (which means integration over region I in Figure 3) and the power of the interference coming from CU +1 as  IV .Clearly, the cellular interference is  I +  IV .Define the interference fraction factor as ,  =  I /.

Proposition 4. If a guard band exists between two adjacent channels with center frequencies 𝑓 𝑐
and   +1 and the D2D user's center frequency    is equal to (   +  +1 )/2, the defined cellular interference fraction factor 0 <  < 0.5.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  =  I +  II +  III .Since  I =  −  II −  III and  I =  II ,  can be expressed as According to (3), it is obvious that 0 <  III / < 1.As a result, 0 <  < 0.5.
Equation (3) shows that  is affected by the ratio of the interference power in the guard band  III to the total power .For different CUs, the ratios are identical; that is, the interference fraction factor is also  for CU +1 .

Outage Probability Analysis in a Flat
where    () is additive white Gaussian noise with variance    .Assuming that   = |   | 2 and   = |   | 2 , in this paper, a widely used power control scheme for cellular user equipment (CU  ) 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 CU  .In addition, the cellular power   should satisfy its power constraint   ≤   max : The TSPC scheme is also applied to the D2D link.Two lemmas are utilized to derive the D2D outage probability.
Proof.The proof is presented in Appendix A.
Proof.The proof is presented in Appendix B.
The D2D conditional outage probability is given by ( 8), where  0 is the D2D SINR threshold and  , is the SINR for DR  , calculated by (9).  , () is the probability density function of  , .In (9),   is the power of the desired signal at receiver DR  , and    is the cellular interference: The difference between MODE1 and MODE2 lies in the cellular interference    , so we use a high SNR approximation; that is,    ≈ 0.

The Outage
where   =    −  /   −  .According to Lemma 5, the conditional outage probability of MODE1 can be written as  (1)   , ( The outage probability of MODE1 can be obtained by averaging over the positions of the cellular user CU  : Similarly, when averaging over the positions of CU  and CU +1 , the outage probability of MODE2 can be obtained: (15)

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   ISI 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  1 be the set of paths whose delays are less than one chip period   ; that is,  1 :  ∈ { , <   }; then, Intersymbol interference originates from multipath signals whose delays exceed one chip period.This set can be defined as  2 :  ∈ { , ≥   }: In MODE1, cellular interference    can be written as Substitute ( 18), ( 19), and (20) into (17); the SINR for MODE1 can be then expressed as  (1)  , = In MODE2, cellular interference    can be written as Substitute ( 18), (19), and ( 22) into (17); the SINR for MODE2 can be then expressed as 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.

Performance Comparison
This section presents a performance comparison between MODE1 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   is 260.42 ns (1/3.84 MHz).Assume the roll-off factor  to be 0.075.Since   = (1+)/  , 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 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 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,  > 1 means that the cellular capacity performance of MODE2 is better than that of MODE1.In other words, MODE2     (4, 5, and 6) are located in set  2 , 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, 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   ISI .The value of   ISI is determined by the D2D transmission power, and it changes with the D2D SNR, making the ISI interferences   ISI of the two modes identical.

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.

Figure 1 :
Figure 1: D2D links sharing uplink resources with cellular users.
-Fading Channel.Let    () represent the transmitted signal of CU  and    () denote the signal of DT  .In a flat-fading channel, the received D2D signal at DR  is

Figure 6 :
Figure 6: Cellular capacity improvement factor in a flat-fading channel.
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 MODE1 and MODE2, respectively.In MODE1, the D2D user's carrier frequency    is equal to its paired cellular user's center frequency    ; that is,    =    .As shown in Figure2,   , is the lower band bound and   , is the upper band bound of the DT  ;   , is the lower and 3.1.Scheme Description. , is the upper band bound of CU  .With   denoting the passband,   , =    −   /2,   , =    +   /2, and the same applies to   , and   , .Interference received by the D2D link  is caused by CU  , as seen in Figure 2. If the power of the cellular signal  is denoted by , then the cellular interference from CU  is .
where   , is the channel gain of the  th path from DT  to DR  and   , is the channel gain of the  th path from CU  to DR  .Here,

Table 2 :
Ped B channel parameters.The frequency-selective channel is modelled in accordance with the Ped B model defined by ITU.Table2presents 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  1 and can be processed by the RAKE receiver.As the other three paths