# Channel Access and Power Control for Mobile Crowdsourcing in Device-to-Device Underlaid Cellular Networks

Authors: Yue Ma; Li Zhou; Zhenghua Gu; Yang Song; Bin Wang
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

With the access of a myriad of smart handheld devices in cellular networks, mobile crowdsourcing becomes increasingly popular, which can leverage omnipresent mobile devices to promote the complicated crowdsourcing tasks. Device-to-device (D2D) communication is highly desired in mobile crowdsourcing when cellular communications are costly. The D2D cellular network is more preferable for mobile crowdsourcing than conventional cellular network. Therefore, this paper addresses the channel access and power control problem in the D2D underlaid cellular networks. We propose a novel semidistributed network-assisted power and a channel access control scheme for D2D user equipment (DUE) pieces. It can control the interference from DUE pieces to the cellular user accurately and has low information feedback overhead. For the proposed scheme, the stochastic geometry tool is employed and analytic expressions are derived for the coverage probabilities of both the cellular link and D2D links. We analyze the impact of key system parameters on the proposed scheme. The Pareto optimal access threshold maximizing the total area spectral efficiency is obtained. Unlike the existing works, the performances of the cellular link and D2D links are both considered. Simulation results show that the proposed method can improve the total area spectral efficiency significantly compared to existing schemes.


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## Body

## 1. Introduction

With the development of intelligent handheld devices, mobile crowdsourcing is emerging as an efficient strategy to improve the user experiences of applications in wireless networks [1]. With the help of ubiquitous mobile users who can share the information between each other, the large-scale crowdsourcing tasks can be facilitated [2]. The D2D communications can realize the high-speed data transmission among mobile users with lower power and shorter delay, which largely eases collaborations among participants [3–6]. Therefore, the D2D cellular network is more preferable for mobile crowdsourcing than conventional cellular network [2].Despite making full use of radio resources, the underlaid scenario leads to the coexistence of cellular and D2D communications in the same frequency band, which brings cross-tier and cotier interferences. Therefore, interference management becomes essential in the underlaid scenario. Transmit power control and channel allocation are widely used to mitigate interference in wireless networks. Different from ad hoc networks and traditional D2D technologies (e.g., WiFi direct), the base station (BS) can assist the DUE pieces in controlling transmit power and allocate the subchannels in the underlaid D2D cellular networks [7]. Compared to DUE pieces, the BS has a more powerful signal processing ability and more easily obtains useful information for resource allocation. Generally, the resource management methods in D2D underlaid cellular networks can be classified into two main categories: the network-controlled device-assisted method and the network-assisted device-decided method [8–14]. In the network-controlled device-assisted method, each DUE needs to report its own information (e.g., channel state information, CSI) to the BS, and then the BS allocates the radio resource to each DUE [8–10]. In [8], a joint power control and mode selection strategy was proposed to improve the overall system performance. To protect existing cellular links, the authors in [9] proposed a dynamic power control method to limit the D2D transmission power. In [10], the centralized algorithm was used to control the power of both the cellular user equipment (CUE) and DUE pieces. Note that the network-controlled device-assisted method requires global information at the BS. However, when the density of DUE pieces is high, the overhead to transmit global information to the BS will reduce the system efficiency significantly and it may be unacceptable for real-time processing.For the network-assisted device-decided method, each DUE selects suitable channels and decides the transmission power according to a minimum transmit power criterion and the power control instruction from the BS [11]. In this scheme, the BS does not need to know global information about each DUE and the overhead can be reduced significantly. In [11], the authors proposed a network-assisted device-decided scheme to jointly select the channels and adjust the transmission power for DUE pieces. However, the number of active DUE pieces on one certain channel is not limited, which may lead to severe interference among the DUE pieces. In [10], based on the statistical features of CSI, distributed on-off power control algorithm was proposed and the fixed threshold was applied to control the number of active DUE pieces. The fixed threshold in [10] is the same for all DUE pieces. In [12], to minimize the D2D transmit power, a statistical features-based power control with opportunistic access control was proposed. Unlike [10], each DUE has its own optimal access threshold in [12].However, most existing channel access schemes only consider the performance of DUE pieces, while the performance of the cellular user is ignored [10–12]. Moreover, although the works in [10, 12] control the power of DUE pieces according to a minimum transmit power criterion, the interference from DUE pieces to the cellular user is not controlled accurately. In this paper, we focus on the power and channel access control problem in a network-assisted device-decided scheme. The main contributions of this paper are as follows:(1)
A novel network-assisted power and channel access control scheme is presented. The proposed scheme can control the interference from DUE pieces to the cellular user accurately. Moreover, the proposed scheme is semidistributed, which can guarantee the performances of both the cellular link and D2D links without high information feedback overhead.(2)
For the proposed method, we apply the stochastic geometry tool and derive analytic expressions including the coverage probabilities of both the cellular link and D2D links.(3)
The Pareto optimal access threshold maximizing the total area spectral efficiency is obtained. Different from the existing works, the performances of the cellular link and D2D links are both considered in obtaining the optimal access threshold.In the D2D cellular network, both the cellular users and D2D users may participate in the crowdsourcing tasks. The proposed scheme considers the performances of both the cellular link and D2D links, which can allow cellular users and D2D users to better carry out crowdsourcing tasks. On the other hand, large-scale crowdsourcing tasks need the participation of ubiquitous mobile users, which is based on the network with high performance. The proposed scheme can improve the system efficiency significantly without high information feedback overhead, which is preferable for large-scale crowdsourcing tasks.


## 2. System Model

The architecture of a D2D underlaid network is considered, as shown in Figure1. In this model, we denote the circular disk C with radius R as the coverage region of a base station (BS) centered at the origin. There are one BS (i.e., k0) and Ndtol D2D pairs. We assume that the cell has one cellular user equipment (CUE) piece on one subchannel. Denote the CUE as s0. Each D2D pair comprises one transmit DUE (TU) piece and one DUE reception (RU) piece. Denote TU and RU pieces as (ut1,ut2,…,utNdtol) and (ur1,ur2,…,urNdtol). The DUE pieces can share the uplink subchannel of the CUE s0. All nodes are equipped with one antenna. The CUE is uniformly located in the region C. The locations of the TU pieces follow the independent homogeneous Poisson point processes (PPPs) ΦDU with density λDU. The intended RU pieces are uniformly and independently located within the distance Rd of their associated TU pieces. Under the given assumptions, ENdtol=λDUπR2. The CUE operates at a fixed transmission power, defined as Ps0.Figure 1
Illustration of a D2D underlaid cellular network.


## 3. Network-Assisted Channel Access and Power Control for DUE Pieces

### 3.1. Semidistributed Channel Access

In this subsection, we present a semidistributed channel access method, which is an effective interference mitigation method that requires assisted information from the BS. In Figure2, the subchannel represents a particular time slot. For example, at slot 1, the active TU1, TU2, TU3, and TU4 use the same frequency band. As in [10–12], the link-gain is applied as the access metric. We use a nonnegative threshold to limit the number of DUE pieces on the subchannel and reduce the interference to cellular users. Moreover, each D2D pair has its own threshold, which is calculated by itself based on the statistical parameters from the BS. The access threshold is calculated in TU. The RU can obtain the link-gain by channel estimation and feed back it to the TU. Gun,i denotes the threshold for the D2D pair un (i.e., utn,urn) on the subchannel i. Then, in order to avoid the overheads for reporting global information to the BS, each D2D pair decides whether to access the current subchannel solely based on its own link-gain and the threshold independently. Specifically, when the link-gain of the D2D pair un on subchannel i is larger than Gun,i, the D2D pair un is active on the subchannel i; otherwise, the D2D pair un is idle on the subchannel i.Figure 2
The illustration of D2D user’s channel access.The transmit probability of the D2D pairun in the subchannel i is given by (1)PSun,i=Phutn,urn,i2dutn,urn-α>Gun,i=exp⁡-Gun,idutn,urnα,where hutn,urn,i and dutn,urn represent the small-scale fast fading and distance from TU utn to RU urn on subchannel i, respectively. α is the path-loss exponent. The Rayleigh distribution is assumed (i.e., hutn,urn,i~CN(0,1)). The proposed algorithm is semidistributed as each D2D pair decides whether to access the subchannel by its own channel gain hutn,urn,i2 and network-assisted threshold Gun,i. Note that the threshold Gun,i not only has an influence on the performance of cellular users, but also determines the performance of the D2D links. On the one hand, larger Gun,i reduce both the interference from DUE pieces to cellular users and the inter-D2D interference. On the other hand, larger Gun,i leads to smaller number of active DUE pieces. Therefore, in order to balance these two competing factors, Gun,i is optimized in Section 5.


### 3.2. Semidistributed Power Control

Based on the channel access method in Section3.1, the semidistributed power control strategy is presented as shown in Figure 3.Figure 3
Network-assisted, device-decided channel access and power control scheme.The core idea of the proposed power control strategy mainly includes the following.Step 1.
The BS broadcasts the statistical parameters for each D2D pair to calculate the thresholdGun,i.Step 2.
Each D2D pair decides whether to access the current subchannel by its own channel gainhutn,urn,i2 and threshold Gun,i and then transmits the result to the BS.Step 3.
The BS calculates the allowable power for each TU according to both the CUE performance requirement and the number of active D2D pairs on the current subchannel and then transmits the allowable power to each TU.Step 4.
According to the assistant power instruction broadcasted from the BS and the maximum transmission power for the TU, each TU autonomously adjusts the transmit power independently.Steps1 and 2 refer to Section 3.1. In the following, without loss of generality, we take the subchannel i as an example and the index of subchannel i will be ignored. For example, hutn,urn,i will be replaced by hutn,urn. The detailed processes of Steps 3 and 4 will be presented. The conclusions can be easily extended to other subchannels.In order to ensure the link reliability of the CUE, the proposed power control aims at adjusting the transmission power of TU pieces. Denote the targetIk0 as the allowable interference power from TU pieces to the CUE on the subchannel i. According to Steps 1 and 2 of the proposed power control algorithm, the BS can count the number of active TU pieces that prefer the subchannel i to perform the D2D communications. Hence, the allowable transmission power unit for TU utn is given by (2)PLutn=Ik0Ndhutn,k02dutn,k0-α,where Nd is the number of active D2D pairs on the subchannel i, and ENd=λDUPSunπR2. PSutn is the access probability for D2D links on the subchannel i. hutn,k0 and dutn,k0 represent the small-scale fast fading and distance from TU utn to BS k0 on ith subchannel, respectively. The Rayleigh distribution is assumed (i.e., hutn,k0~CN(0,1)). From (2), it can be observed that less interference link-gain leads to larger allowable transmission power unit, which means that the TU far from the BS is more likely to transmit with larger power.Thus, the transmission power of TUutn can be expressed as(3)Putn=min⁡PLutn,Putn,max,where Putn,max is the maximum transmission power for TU utn on ith subchannel. Moreover, we can get(4)Putn=PLutn,withPb,utnPutn,max,with1-Pb,utn,where Pb,utn denotes the probability given by(5)Pb,utn=PPutn,max>PLutn=Phutn,k02dutn,k0-α>Ik0NdPutn,max=exp⁡-dutn,k0-αIk0NdPutn,max.Note that the proposed power control is semidistributed as each TU decides the transmission power according to the allowable transmission power unit broadcasted by the BS and its own maximum power.


## 3.1. Semidistributed Channel Access

In this subsection, we present a semidistributed channel access method, which is an effective interference mitigation method that requires assisted information from the BS. In Figure2, the subchannel represents a particular time slot. For example, at slot 1, the active TU1, TU2, TU3, and TU4 use the same frequency band. As in [10–12], the link-gain is applied as the access metric. We use a nonnegative threshold to limit the number of DUE pieces on the subchannel and reduce the interference to cellular users. Moreover, each D2D pair has its own threshold, which is calculated by itself based on the statistical parameters from the BS. The access threshold is calculated in TU. The RU can obtain the link-gain by channel estimation and feed back it to the TU. Gun,i denotes the threshold for the D2D pair un (i.e., utn,urn) on the subchannel i. Then, in order to avoid the overheads for reporting global information to the BS, each D2D pair decides whether to access the current subchannel solely based on its own link-gain and the threshold independently. Specifically, when the link-gain of the D2D pair un on subchannel i is larger than Gun,i, the D2D pair un is active on the subchannel i; otherwise, the D2D pair un is idle on the subchannel i.Figure 2
The illustration of D2D user’s channel access.The transmit probability of the D2D pairun in the subchannel i is given by (1)PSun,i=Phutn,urn,i2dutn,urn-α>Gun,i=exp⁡-Gun,idutn,urnα,where hutn,urn,i and dutn,urn represent the small-scale fast fading and distance from TU utn to RU urn on subchannel i, respectively. α is the path-loss exponent. The Rayleigh distribution is assumed (i.e., hutn,urn,i~CN(0,1)). The proposed algorithm is semidistributed as each D2D pair decides whether to access the subchannel by its own channel gain hutn,urn,i2 and network-assisted threshold Gun,i. Note that the threshold Gun,i not only has an influence on the performance of cellular users, but also determines the performance of the D2D links. On the one hand, larger Gun,i reduce both the interference from DUE pieces to cellular users and the inter-D2D interference. On the other hand, larger Gun,i leads to smaller number of active DUE pieces. Therefore, in order to balance these two competing factors, Gun,i is optimized in Section 5.


## 3.2. Semidistributed Power Control

Based on the channel access method in Section3.1, the semidistributed power control strategy is presented as shown in Figure 3.Figure 3
Network-assisted, device-decided channel access and power control scheme.The core idea of the proposed power control strategy mainly includes the following.Step 1.
The BS broadcasts the statistical parameters for each D2D pair to calculate the thresholdGun,i.Step 2.
Each D2D pair decides whether to access the current subchannel by its own channel gainhutn,urn,i2 and threshold Gun,i and then transmits the result to the BS.Step 3.
The BS calculates the allowable power for each TU according to both the CUE performance requirement and the number of active D2D pairs on the current subchannel and then transmits the allowable power to each TU.Step 4.
According to the assistant power instruction broadcasted from the BS and the maximum transmission power for the TU, each TU autonomously adjusts the transmit power independently.Steps1 and 2 refer to Section 3.1. In the following, without loss of generality, we take the subchannel i as an example and the index of subchannel i will be ignored. For example, hutn,urn,i will be replaced by hutn,urn. The detailed processes of Steps 3 and 4 will be presented. The conclusions can be easily extended to other subchannels.In order to ensure the link reliability of the CUE, the proposed power control aims at adjusting the transmission power of TU pieces. Denote the targetIk0 as the allowable interference power from TU pieces to the CUE on the subchannel i. According to Steps 1 and 2 of the proposed power control algorithm, the BS can count the number of active TU pieces that prefer the subchannel i to perform the D2D communications. Hence, the allowable transmission power unit for TU utn is given by (2)PLutn=Ik0Ndhutn,k02dutn,k0-α,where Nd is the number of active D2D pairs on the subchannel i, and ENd=λDUPSunπR2. PSutn is the access probability for D2D links on the subchannel i. hutn,k0 and dutn,k0 represent the small-scale fast fading and distance from TU utn to BS k0 on ith subchannel, respectively. The Rayleigh distribution is assumed (i.e., hutn,k0~CN(0,1)). From (2), it can be observed that less interference link-gain leads to larger allowable transmission power unit, which means that the TU far from the BS is more likely to transmit with larger power.Thus, the transmission power of TUutn can be expressed as(3)Putn=min⁡PLutn,Putn,max,where Putn,max is the maximum transmission power for TU utn on ith subchannel. Moreover, we can get(4)Putn=PLutn,withPb,utnPutn,max,with1-Pb,utn,where Pb,utn denotes the probability given by(5)Pb,utn=PPutn,max>PLutn=Phutn,k02dutn,k0-α>Ik0NdPutn,max=exp⁡-dutn,k0-αIk0NdPutn,max.Note that the proposed power control is semidistributed as each TU decides the transmission power according to the allowable transmission power unit broadcasted by the BS and its own maximum power.


## 4. Performance Analysis

In this section, we analyze the proposed scheme in terms of the coverage probability. The performances of the cellular link and D2D links are both analyzed.


### 4.1. The Cellular Coverage Probability

The uplink SINR from CUE to the BS onith subchannel can be expressed as [11](6)γ~s0,k0=Ps0hs0,k02ds0,k0-αIk0+σk02,where Ps0 denotes the transmission power of CUE on ith subchannel. hs0,k0 and ds0,k0 represent the small-scale fast fading and distance from CUE s0 to BS k0 on ith subchannel, respectively. hs0,k0~CN(0,1). Ik0=∑utn∈ΦDUPutnhutn,k02dutn,k0-α represents the total uplink interference from TU pieces to CUE s0 in the BS k0 on the ith subchannel. σk02 is the power of the additive Gaussian white noise at k0.Lemma 1.
The coverage probability of the cellular link can be expressed as(7)Pccη=Eds0,k0exp⁡-A1X1-A2X12/α,where A1=σk02η, A2=(πλDUPSutnη2/α/sin⁡c(2/α))E[Putn2/α],  X1=Ps0-1ds0,k0α, and η represents the minimum SINR value for reliable uplink connection.Proof.
The coverage probability of the cellular link can be expressed as [10, 12](8)Pccη=Pγ~s0,k0≥η=PPs0hs0,k02ds0,k0-αIk0+σk02≥η=Phs0,k02≥ηPs0-1ds0,k0αIk0+σk02=aEexp⁡-ηPs0-1ds0,k0αIk0+σk02=Ee-ηPs0-1ds0,k0ασk02e-ηPs0-1ds0,k0α∑utn∈ΦDUPutnhutn,k02dutn,k0-α,where in the equality a we use the fact that hs0,k02~exp⁡(1) [10]. Denote X1=Ps0-1ds0,k0α. Conditioning on ds0,k0α, we can obtain(9)Pγ~s0,k0≥ηds0,k0α=e-ηPs0-1ds0,k0ασk02e-ηPs0-1ds0,k0α∑utn∈ΦDUPutnhutn,k02dutn,k0-α.
The Laplace transform is applied as follows [15]:(10)LΦDs=e-s∑utn∈ΦDUPutnhutn,k02dutn,k0-α=e-πλDUPSutn/sinc2/αEPutn2/αs2/α.
Deconditioning with respect tods0,k0α, we combine (9) and (10), and then (7) can be obtained.
According to (7), we can observe that the D2D-related parameter EPutn2/α affects the cellular link coverage probability. In the following, by giving the expression of EPutn2/α, we will present how the proposed power control method affects the performance of the cellular link.
Denotez=hutn,k02dutn,k0-α; then EPutn2/α can be expressed as(11)EPutn2/α=∫0+∞min⁡PLutn2/α,Putn,max2/αfzdz=∫0+∞min⁡Ik0Ndz2/α,Putn,max2/αfzdz.
Conditioning on the distancedutn,k0 and Ik0, E[Putn2/α] is given by(12)EPutn2/αdutn,k0=∫0+∞min⁡Ik0Nddutn,k0-αx2/α,Putn,max2/αexp⁡-xdx=min⁡∫0+∞Ik0Nddutn,k0-αx2/αexp⁡-xdx,∫0+∞Putn,max2/αexp⁡-xdx=min⁡∫0+∞Ik0Nddutn,k0-αx2/αexp⁡-xdx,Putn,max2/α=min⁡Ik0Nddutn,k0-α2/αΓ-2+αα,Putn,max2/α,where Γx denotes the gamma function. Then, deconditioning with respect to dutn,k0, we can obtain(13)EPutn2/α=min⁡EIk0Nddutn,k0-α2/αΓ-2+αα,Putn,max2/α=min⁡EIk0Nd2/αΓ-2+ααdutn,k02,Putn,max2/α=min⁡Ik0Nd2/αΓ-2+ααEdutn,k02,Putn,max2/α=amin⁡Ik0Nd2/αΓ-2+ααR2,Putn,max2/α,where Edutn,k02=R2 given in [13]. From (13), we can see that the proposed network-assisted power control method can control the interferences from TU pieces to the CUE accurately by adjusting the parameter Ik0. The coverage probability of the cellular link decreases with Ik0. Larger Ik0 leads to more serious interference.
Generally, we setIk0 to keep the uplink SINR of the CUE to be above the target η. In D2D underlaid cellular networks, the communication link is usually more severely affected by the interference compared with the noise. Hence, we ignore the effect of noise by setting σk02=0 to facilitate the theoretical analysis. In the interference limited regime (σk02=0), we have(14)Ik0=Ps0hs0,k02ds0,k0-αη.
Then, plugging (14) into (13) and deconditioning with respect to hs0,k02, it can be obtained that(15)EPutn2/α=min⁡EIk0Nd2/αΓ-2+ααR2,Putn,max2/α=min⁡EPs0hs0,k02ds0,k0-αηNd2/αΓ-2+ααR2,Putn,max2/α=amin⁡Ps0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2,Putn,max2/α,where the equality (a) follows from hs0,k02~exp(1).


### 4.2. The Performance of D2D Links

The SINR at RUurn on ith subchannel can be expressed as [11](16)γ~utn,urn=Putnhutn,urn2dutn,urn-αID,urn+Ps0hs0,urn2ds0,urn-α+σurn2,where Putn denotes the transmission power of TU utn. hutn,urnand dutn,urn represent the small-scale fast fading and distance between TU utn and its corresponding RU urn, respectively. hutn,urn~CN(0,1). ID,urn=∑uti∈ΦDU\utnPutihuti,urn2dutn,urn-α is the total interference from other D2D pairs to RU urn. Ps0hs0,urn2ds0,urn-α is the interference from the CUE s0 to RU urn. σurn2 is the power of the additive Gaussian white noise at urn.Lemma 2.
Conditioning on the distancedutn,utn, the coverage probability of RU urn in the interference limited regime (σurn2=0) is given by(17)Pdcβdutn,urn≈EPutnexp⁡-B1Putn-2/α11+B2Putn-2/α,where B1 = πλDUPSunβ2/α/sinc2/αE[Putn2/α]dutn,urn2, B2=(βPs0)2/α((45π)2dutn,urn2/(128R)2), and β represents the minimum SINR value for reliable D2D connection.Proof.
The coverage probability of RUurn can be expressed as [10, 12](18)Pdcβdutn,urn=Pγ~ut1,ut1≥βdutn,urn=PPutnhutn,urn2dutn,urn-αID,urn+Ps0hs0,urn2ds0,urn-α≥β=Phut1,ut12≥Putn-1dutn,urnαβID,urn+Ps0hs0,urn2ds0,urn-α=Ee-Putn-1dutn,urnαβID,urn+Ps0hs0,urn2ds0,urn-α.
We use Slivnyak’s theorem [16] as follows: (19)LΦDU\utns=Ee-s∑uti∈ΦDU\utnPutihuti,urn2dutn,urn-α=LΦDUs=e-πλDU/sinc2/αEPutn2/αs2/α.
Conditioned onPutn, (18) can be written as(20)Pdcβdutn,urn=e-πλDUβ2/α/sinc2/αEPutn2/αdutn,urn2Putn-2/αEe-Putn-1dutn,urnαβPs0hs0,urn2ds0,urn-α,where Ee-Putn-1dutn,urnαβPs0hs0,urn2ds0,urn-α=Eds0,urn1/(1+βPs0Putn-1dutn,urnαds0,urn-α).
Furthermore, we use the approximationEds0,urn1/(1+k/ds0,urnα)≃1/(1+k2/α/Eds0,urn2) in [10] and Eds0,urn=128R/45π in [13]. Equation (20) can be expressed as in (17).
In (17), we can see that the coverage probability of the D2D link is determined by two factors: (a) the total interference power created by other active D2D links (i.e., B1Putn-2/α) and (b) the approximated effect of the uplink interference from the CUE (i.e., 1/1+B2Putn-2/α).
Unlike intuition, it is interesting to find that the coverage probability of the D2D link does not necessarily increase with the parameterIk0 for any given dutn,urn, dutn,k0, and hutn,k02. (21)Pdcβdutn,urn,dutn,k0,hutn,k0≈exp⁡-πλDUPSunβ2/αsin⁡c2/αEPutn2/αPutn2/αdutn,urn211+βPs0/Putn2/α45π2dutn,urn2/128R2.
According to (3), (13), and (21), there are four cases as follows:(1)
(Ik0/Nd)2/αΓ((-2+α)/α)R2≤Putn,max2/α and Putn,max2/α≤(Ik0/Nd)2/αhutn,k0-22/αdutn,k02, Pdc(β) decrease with Ik0.(2)
(Ik0/Nd)2/αΓ((-2+α)/α)R2≤Putn,max2/α and (Ik0/Nd)2/αhutn,k0-22/αdutn,k02≤Putn,max2/α, Pdc(β) increase with Ik0.(3)
Putn,max2/α≤(Ik0/Nd)2/αΓ((-2+α)/α)R2 and Putn,max2/α≤(Ik0/Nd)2/αhutn,k0-22/αdutn,k02, Pdc(β) do not change with Ik0.(4)
Putn,max2/α≤(Ik0/Nd)2/αΓ((-2+α)/α)R2 and (Ik0/Nd)2/αhutn,k0-22/αdutn,k02≤Putn,max2/α, Pdc(β) increase with Ik0.
For case(1), the channel gain from TU utn to BS k0 is small; TU utn can transmit with the maximum transmission power Putn,max. However, for other TU pieces, the transmission powers are limited by Ik0. When Ik0 increases, the transmission power of TU utn does not change and the average transmission power of other TU pieces (i.e., E[Putn2/α]) increases, which reduces the coverage probability of the D2D link utn,urn.


## 4.1. The Cellular Coverage Probability

The uplink SINR from CUE to the BS onith subchannel can be expressed as [11](6)γ~s0,k0=Ps0hs0,k02ds0,k0-αIk0+σk02,where Ps0 denotes the transmission power of CUE on ith subchannel. hs0,k0 and ds0,k0 represent the small-scale fast fading and distance from CUE s0 to BS k0 on ith subchannel, respectively. hs0,k0~CN(0,1). Ik0=∑utn∈ΦDUPutnhutn,k02dutn,k0-α represents the total uplink interference from TU pieces to CUE s0 in the BS k0 on the ith subchannel. σk02 is the power of the additive Gaussian white noise at k0.Lemma 1.
The coverage probability of the cellular link can be expressed as(7)Pccη=Eds0,k0exp⁡-A1X1-A2X12/α,where A1=σk02η, A2=(πλDUPSutnη2/α/sin⁡c(2/α))E[Putn2/α],  X1=Ps0-1ds0,k0α, and η represents the minimum SINR value for reliable uplink connection.Proof.
The coverage probability of the cellular link can be expressed as [10, 12](8)Pccη=Pγ~s0,k0≥η=PPs0hs0,k02ds0,k0-αIk0+σk02≥η=Phs0,k02≥ηPs0-1ds0,k0αIk0+σk02=aEexp⁡-ηPs0-1ds0,k0αIk0+σk02=Ee-ηPs0-1ds0,k0ασk02e-ηPs0-1ds0,k0α∑utn∈ΦDUPutnhutn,k02dutn,k0-α,where in the equality a we use the fact that hs0,k02~exp⁡(1) [10]. Denote X1=Ps0-1ds0,k0α. Conditioning on ds0,k0α, we can obtain(9)Pγ~s0,k0≥ηds0,k0α=e-ηPs0-1ds0,k0ασk02e-ηPs0-1ds0,k0α∑utn∈ΦDUPutnhutn,k02dutn,k0-α.
The Laplace transform is applied as follows [15]:(10)LΦDs=e-s∑utn∈ΦDUPutnhutn,k02dutn,k0-α=e-πλDUPSutn/sinc2/αEPutn2/αs2/α.
Deconditioning with respect tods0,k0α, we combine (9) and (10), and then (7) can be obtained.
According to (7), we can observe that the D2D-related parameter EPutn2/α affects the cellular link coverage probability. In the following, by giving the expression of EPutn2/α, we will present how the proposed power control method affects the performance of the cellular link.
Denotez=hutn,k02dutn,k0-α; then EPutn2/α can be expressed as(11)EPutn2/α=∫0+∞min⁡PLutn2/α,Putn,max2/αfzdz=∫0+∞min⁡Ik0Ndz2/α,Putn,max2/αfzdz.
Conditioning on the distancedutn,k0 and Ik0, E[Putn2/α] is given by(12)EPutn2/αdutn,k0=∫0+∞min⁡Ik0Nddutn,k0-αx2/α,Putn,max2/αexp⁡-xdx=min⁡∫0+∞Ik0Nddutn,k0-αx2/αexp⁡-xdx,∫0+∞Putn,max2/αexp⁡-xdx=min⁡∫0+∞Ik0Nddutn,k0-αx2/αexp⁡-xdx,Putn,max2/α=min⁡Ik0Nddutn,k0-α2/αΓ-2+αα,Putn,max2/α,where Γx denotes the gamma function. Then, deconditioning with respect to dutn,k0, we can obtain(13)EPutn2/α=min⁡EIk0Nddutn,k0-α2/αΓ-2+αα,Putn,max2/α=min⁡EIk0Nd2/αΓ-2+ααdutn,k02,Putn,max2/α=min⁡Ik0Nd2/αΓ-2+ααEdutn,k02,Putn,max2/α=amin⁡Ik0Nd2/αΓ-2+ααR2,Putn,max2/α,where Edutn,k02=R2 given in [13]. From (13), we can see that the proposed network-assisted power control method can control the interferences from TU pieces to the CUE accurately by adjusting the parameter Ik0. The coverage probability of the cellular link decreases with Ik0. Larger Ik0 leads to more serious interference.
Generally, we setIk0 to keep the uplink SINR of the CUE to be above the target η. In D2D underlaid cellular networks, the communication link is usually more severely affected by the interference compared with the noise. Hence, we ignore the effect of noise by setting σk02=0 to facilitate the theoretical analysis. In the interference limited regime (σk02=0), we have(14)Ik0=Ps0hs0,k02ds0,k0-αη.
Then, plugging (14) into (13) and deconditioning with respect to hs0,k02, it can be obtained that(15)EPutn2/α=min⁡EIk0Nd2/αΓ-2+ααR2,Putn,max2/α=min⁡EPs0hs0,k02ds0,k0-αηNd2/αΓ-2+ααR2,Putn,max2/α=amin⁡Ps0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2,Putn,max2/α,where the equality (a) follows from hs0,k02~exp(1).


## 4.2. The Performance of D2D Links

The SINR at RUurn on ith subchannel can be expressed as [11](16)γ~utn,urn=Putnhutn,urn2dutn,urn-αID,urn+Ps0hs0,urn2ds0,urn-α+σurn2,where Putn denotes the transmission power of TU utn. hutn,urnand dutn,urn represent the small-scale fast fading and distance between TU utn and its corresponding RU urn, respectively. hutn,urn~CN(0,1). ID,urn=∑uti∈ΦDU\utnPutihuti,urn2dutn,urn-α is the total interference from other D2D pairs to RU urn. Ps0hs0,urn2ds0,urn-α is the interference from the CUE s0 to RU urn. σurn2 is the power of the additive Gaussian white noise at urn.Lemma 2.
Conditioning on the distancedutn,utn, the coverage probability of RU urn in the interference limited regime (σurn2=0) is given by(17)Pdcβdutn,urn≈EPutnexp⁡-B1Putn-2/α11+B2Putn-2/α,where B1 = πλDUPSunβ2/α/sinc2/αE[Putn2/α]dutn,urn2, B2=(βPs0)2/α((45π)2dutn,urn2/(128R)2), and β represents the minimum SINR value for reliable D2D connection.Proof.
The coverage probability of RUurn can be expressed as [10, 12](18)Pdcβdutn,urn=Pγ~ut1,ut1≥βdutn,urn=PPutnhutn,urn2dutn,urn-αID,urn+Ps0hs0,urn2ds0,urn-α≥β=Phut1,ut12≥Putn-1dutn,urnαβID,urn+Ps0hs0,urn2ds0,urn-α=Ee-Putn-1dutn,urnαβID,urn+Ps0hs0,urn2ds0,urn-α.
We use Slivnyak’s theorem [16] as follows: (19)LΦDU\utns=Ee-s∑uti∈ΦDU\utnPutihuti,urn2dutn,urn-α=LΦDUs=e-πλDU/sinc2/αEPutn2/αs2/α.
Conditioned onPutn, (18) can be written as(20)Pdcβdutn,urn=e-πλDUβ2/α/sinc2/αEPutn2/αdutn,urn2Putn-2/αEe-Putn-1dutn,urnαβPs0hs0,urn2ds0,urn-α,where Ee-Putn-1dutn,urnαβPs0hs0,urn2ds0,urn-α=Eds0,urn1/(1+βPs0Putn-1dutn,urnαds0,urn-α).
Furthermore, we use the approximationEds0,urn1/(1+k/ds0,urnα)≃1/(1+k2/α/Eds0,urn2) in [10] and Eds0,urn=128R/45π in [13]. Equation (20) can be expressed as in (17).
In (17), we can see that the coverage probability of the D2D link is determined by two factors: (a) the total interference power created by other active D2D links (i.e., B1Putn-2/α) and (b) the approximated effect of the uplink interference from the CUE (i.e., 1/1+B2Putn-2/α).
Unlike intuition, it is interesting to find that the coverage probability of the D2D link does not necessarily increase with the parameterIk0 for any given dutn,urn, dutn,k0, and hutn,k02. (21)Pdcβdutn,urn,dutn,k0,hutn,k0≈exp⁡-πλDUPSunβ2/αsin⁡c2/αEPutn2/αPutn2/αdutn,urn211+βPs0/Putn2/α45π2dutn,urn2/128R2.
According to (3), (13), and (21), there are four cases as follows:(1)
(Ik0/Nd)2/αΓ((-2+α)/α)R2≤Putn,max2/α and Putn,max2/α≤(Ik0/Nd)2/αhutn,k0-22/αdutn,k02, Pdc(β) decrease with Ik0.(2)
(Ik0/Nd)2/αΓ((-2+α)/α)R2≤Putn,max2/α and (Ik0/Nd)2/αhutn,k0-22/αdutn,k02≤Putn,max2/α, Pdc(β) increase with Ik0.(3)
Putn,max2/α≤(Ik0/Nd)2/αΓ((-2+α)/α)R2 and Putn,max2/α≤(Ik0/Nd)2/αhutn,k0-22/αdutn,k02, Pdc(β) do not change with Ik0.(4)
Putn,max2/α≤(Ik0/Nd)2/αΓ((-2+α)/α)R2 and (Ik0/Nd)2/αhutn,k0-22/αdutn,k02≤Putn,max2/α, Pdc(β) increase with Ik0.
For case(1), the channel gain from TU utn to BS k0 is small; TU utn can transmit with the maximum transmission power Putn,max. However, for other TU pieces, the transmission powers are limited by Ik0. When Ik0 increases, the transmission power of TU utn does not change and the average transmission power of other TU pieces (i.e., E[Putn2/α]) increases, which reduces the coverage probability of the D2D link utn,urn.


## 5. Optimizing D2D On-Off Threshold

In this section, we assume that each TU has the same maximum transmission power (i.e.,Putn,max=Pu,max). In the following, we first introduce the area spectral efficiency of D2D links and the cellular link. Second, the upper bound of the area spectral efficiency of D2D links and the lower bound of the area spectral efficiency of the cellular link are obtained, respectively. Third, we optimize the D2D on-off threshold by maximizing the approximated total area spectral efficiency.Since the analysis performed for a typical link indicates the spatially averaged performance of the network by Slivnyak’s theorem [16, 17], for any given dutn,urn, dutn,k0, and hutn,k02, the area spectral efficiency of D2D communications is given as [12, 18](22)ΥDβ=λDUPSunlog2⁡1+βPγ~utn,urn≥β≈λDUPSunexp⁡-πλDUPSunβ2/αsin⁡c2/αEPutn2/αPutn2/αdutn,urn2log2⁡1+β1+βPs0/Putn2/α45π2dutn,urn2/128R2.The area spectral efficiency of the cellular link is as follows [10]:(23)ΥCη=log⁡21+ηPccηπR2.According to (22) and (23), the optimal access probability for D2D links can be obtained by solving the following optimization problem:(24)maxPSutn:ω1ΥCηmaxPSutn:ω2ΥDβs.t.0<PSutn<1,where ω1 and ω2 are the introduced scalar weights, which represent the priorities of CUE and DUE pieces, respectively. Note that Υtotal(η,β)=ω1ΥC(η)+ω2ΥD(β) can represent the total area spectral efficiency including both the cellular link and D2D links. Note that it is difficult to obtain the closed-form solution of the original optimization problem. Therefore, in order to facilitate the analysis and reduce the computational complexity, we introduce the upper bound of the area spectral efficiency of D2D links and the lower bound of the area spectral efficiency of the cellular link.Lemma 3.
The upper bound of the area spectral efficiency of D2D communications is obtained as(25)ΥDβ≤ΥupperDβwith (26)ΥupperDβ=λDUPSunD2exp⁡-D1,forPs0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2≥Pu,max2/αλDUPSunD2exp⁡-D1Ps0ds0,k0-α/Ndη2/αΓ-2+α/αΓ2+α/αR2Pu,max2/α,forPs0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2<Pu,max2/α,where D1=πλDUPSunβ2/α/sinc2/αdutn,urn2, D2=log2(1+β)/(1+(β(Ps0/Pu,max))2/α((45π)2dutn,urn2/(128R)2)).Proof.
See AppendixA.Conditioning on the distanceds0,k0, we also compute a lower bound of the coverage probability of the cellular link by setting E[Putn2/α]=Pu,max2/α in the interference limited regime (σk02=0), which can be expressed as(27)Pcc,lowη=exp⁡-πλDUPSutnη2/αsin⁡c2/αPu,max2/αPs02/αds0,k02.The lower bound of the area spectral efficiency of the cellular link is given by(28)ΥlowCη=log⁡21+ηPcc,lowηπR2.According to (25) and (28), original problem (24) can be approximated as follows:(29)maxPSutn:ω1ΥlowCηmaxPSutn:ω2ΥupperDβs.t.0<PSutn<1which is a multicriteria optimization problem. According to (25) and (28), ΥlowC(η) decreases with PSutn, while ΥupperD(β) is nonmonotonic with PSutn. Generally, it is difficult to maximize the two objectives simultaneously. In order to balance these two objectives, the weighted sum method in multicriteria optimization is used to obtain the Pareto optimal solution [19]. Then, the multicriteria optimization with high complexity can be converted into a simpler single objective optimization problem given by(30)maxPSutn:ω1ΥlowCη+ω2ΥupperDβs.t.0<PSutn<1.The solution of (30) is a Pareto optimal solution to the optimization problem of (29) [19].Theorem 4.
For the optimization problem(31)max:fx=ε1e-ax+ε2xe-bxs.t.0<x<1with ε1≥0, ε2≥0, a>0, and b>0, the optimal solution x∗ is obtained as(32)xopt=max⁡min⁡x^,1,0with (33)x^=1b+1qω-pqe-q/bb,where p=aε1/ε2, q=a-b, and ωx denotes the Lambert ω function defined as the inverse function of g(x)=xex.Proof.
See AppendixB.According to Theorem4, the optimal access threshold can be obtained as(34)PSutn∗=max⁡min⁡PS∧utn,1,0with (35)PS∧utn=1ρ2+1ϕ2ω-ϕ1ϕ2e-ϕ2/ρ2ρ2,where (36)ϕ1=ρ1ε1ε2,ϕ2=ρ1-ρ2,ε1=ω1log21+ηπR2,ρ1=πλDUη2/αsin⁡c2/αPu,maxPs02/αds0,k02,ε2=ω2λDUlog21+β1+βPs0/Pu,max2/α45π2dutn,urn2/128R2,ρ2=πλDUβ2/αsin⁡c2/αdutn,urn2,forPs0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2≥Pu,max2/απλDUβ2/αsin⁡c2/αPs0ds0,k0-α/Ndη2/αΓ-2+α/αΓ2+α/αR2Pu,max2/αdutn,urn2,forPs0ds0,k0-αNdη2/αΓ-2+ααΓ2+ααR2<Pu,max2/α.Then, the optimal access threshold is designed according to the optimal access probability. According to (1) and (34), the optimal access threshold for the D2D pair un is given as(37)Gmin,utn∗=-ln⁡PSutn∗dutn,urnα.One D2D pair decides whether to access the current subchannel based solely on the knowledge of its own communication distance, channel gain, and the optimal access threshold. In order to calculate the access threshold, each TU needs some system parameters (e.g.,λDU, Ps0, and ds0,k0). Compared with DUE pieces, the BS is more convenient for obtaining these parameters and broadcasting them to each TU. Then, each D2D pair can calculate its own optimal access threshold according to (34) and (37) based on the system parameters and dutn,urn independently. dutn,urn can be easily known by the associated TU utn. Since (34) and (37) have the closed-forms, the computational burden is quite low for each TU.Note that the parameterρ2 in (35) has two possible expressions due to the relationship between Pu,max2/α and (Ps0ds0,k0-α/Ndη)2/αΓ((-2+α)/α)Γ((2+α)/α)R2. However, the number of active TU pieces (i.e., Nd) cannot be known before all the D2D pairs decide whether to access the current subchannel. In this paper, we average over the past subchannels as in Algorithm 1 and apply N^d,i as the estimation of Nd,i that is used to calculate ρ2 in (35).Algorithm 1:Estimating the number of active TUs for optimal access threshold.
(
1
) Initial set: N^d,1=Ndtol
(
2
) For i=2:M
(
3
)  N^d,i=N^d,1+⋯+N^d,i-1/i-1 is used to calculate the optimal access as in Eq. (25) and Eq. (34).
(
4
)  Count the real number of active Nd,i on ith sub-channel.
(
5
)  N^d,i=Nd,i
(
6
) endThoughN^d,i is not the real number of active TU pieces on the subchannel i, the optimal access threshold based on N^d,i can achieve a good performance, which will be verified by the extensive simulations in the following. This is because N^d,i represents the statistical average of Nd,i and N^d,i is close to Nd,i with high D2D link density λDU.


## 6. Simulation Results

To evaluate the proposed scheme, we carry out extensive simulations by the Matlab tool and discuss the results in this section. The path-loss exponentα=4. We assume the average radius of a cell is 500 m; that is, R=500m. The BS is located at the center and the CUE is uniformly located in the cell of radius R. The transmit power of CUE Ps0=100mW. Given the D2D communication range Rd=50m, each intended RU is uniformly and independently located within Rd of its associated TU in the isotropic direction. The maximum transmit power of TU pieces Putn,max=Pu,max=0.1mW. The scalar weight factor for the DUE is ω2=1. The performance of the proposed method is compared with three other strategies:(1)
NADD: network-assisted, device-decided scheme [11](2)
SFPC: statistical features-based power control scheme [12](3)
NPC: all D2D pairs access the current subchannel. There is no power control and all TU pieces transmit with maximum transmit powerPu,max(4)
Proposed: the proposed method.In Figure4, the area spectral efficiency performances versus target SIR threshold according to different power control methods are shown. We can see that the proposed method improves the area spectral efficiency compared to other algorithms, especially in the high target SIR regime. This implies that the proposed method is efficient at mitigating both intra-D2D and cross-tier interference when D2D links communicate with a high data rate. Moreover, it is interesting to see that the NADD method is even worse than NPC in terms of the area spectral efficiency. This is because though the NADD method guarantees the performance of the CUE, the NADD method leads to a sharp performance fall for D2D links, which results in the area spectral efficiency decrease in the end.Figure 4
The area spectral efficiencyΥtotal(β) versus target SIR threshold according to different strategies with η=β, λDU=3×10-5, and ω1=10.Figure5 shows the coverage probabilities of CUEs and DUE pieces versus target SIR threshold according to different power control methods. In Figure 5, it can be observed that the proposed method achieves the best performance for both the CUE and DUE pieces in terms of the coverage probability in the high target SIR regime. Although the proposed method does not have the highest coverage probabilities for the CUE and DUE pieces in the low target SIR regime (e.g., the target SIR = −4 dB), it can achieve the best area spectral efficiency as shown in Figure 4. This is because there are more active DUE pieces for the proposed scheme as shown in Figure 6.Figure 5
Coverage probability performance of both the CUE and the DUE according to different strategies withη=β, λDU=3×10-5, and ω1=10.Figure 6
The active D2D link density versus target SIR threshold according to different strategies withη=β, λDU=3×10-5, and ω1=10.In Figure6, the active D2D link density versus target SIR threshold is shown. We can observe that the active D2D link densities of the proposed method and the SFPC decrease with the target SIR threshold, and the active D2D link densities of the NADD and NPC do not change with the target SIR threshold. On the one hand, compared with the NADD and NPC, the proposed method and the SFPC can limit the active D2D link density to guarantee the area spectral efficiency performance. On the other hand, though the active D2D link density of the proposed method is lower than the other methods in the high target SIR regime, the proposed method can achieve the best area spectral efficiency performance. This is because the proposed method can achieve the best performance for both the CUE and DUE pieces in terms of the coverage probability in the high target SIR regime.Figure7 plots the area spectral efficiency versus D2D link density λDU. The proposed method can improve the area spectral efficiency significantly compared to other schemes. With the increase of λDU, for NADD and NPC, the area spectral efficiency decreases. This is because the number of active DUE pieces increases with λDU and the intra-D2D and cross-tier interferences become more serious. For the proposed scheme, the area spectral efficiency does not decrease with λDU according to the optimal threshold that balances the performances of the CUE and DUE pieces.Figure 7
The area spectral efficiencyΥtotal(β) versus D2D link density λDU according to different strategies with η=β=6dB and ω1=10.In Figures8 and 9, the numbers in the x-axis represent different schemes as follows: (1) the proposed method; (2) NADD; (3) NPC; (4) SFPC. Figures 8 and 9 show ω1ΥC(β) and ω2ΥD(β) according to ω1=5 and ω1=15, respectively. Comparing Figure 8 with Figure 9, we can see that the percentage of ω1ΥC(β) for the proposed scheme increases with ω1. This is because the priority of the CUE increases with ω1 and the larger percentage of ω1ΥC(β) leads to a larger total area spectral efficiency. While the percentage of ω1ΥC(β) for the other schemes also increases, the improved range of the proposed scheme is the largest, leading to greatest performance improvement. Moreover, the performance of NADD (case (2)) is worse than NPC (case (3)) for ω1=5, while it is opposite for ω1=15. This is because NADD can guarantee the performance of the CUE. When the priority of the CUE increases with ω1, the performance of NADD becomes better than NPC in terms of total area spectral efficiency.Figure 8
The figure showsω1ΥC(β) and ω2ΥD(β) with ω1=5, η=β=6dB, and λDU=3×10-5, respectively.Figure 9
The figure showsω1ΥC(β) and ω2ΥD(β) with ω1=15, η=β=6dB, and λDU=3×10-5, respectively.


## 7. Conclusions

The D2D cellular network is an efficient way to carry out mobile crowdsourcing. For D2D underlaid cellular networks, the channel access and power control issue is investigated. In order to limit the cross-tier and intratier interferences, we propose a novel semidistributed network-assisted power and channel access control scheme for DUE pieces. In the proposed semidistributed scheme, with the help of assistant information from the BS, each D2D pair decides whether to access the subchannel and adjusts the transmit power independently. The BS plays a role in offering assistant information, which can maximize the total area spectral efficiency on the condition of guaranteeing the performance of the cellular link. Moreover, assistant information from the BS is statistical, and the optimal access threshold has the closed-form expression. The proposed scheme has the low computational burden and low overhead to broadcast assistant information, which is quite suitable to the practical systems.



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*Source: 7192840-2018-01-04.xml*