Limited Feedback Scheme for Device to Device Communications in 5G Cellular Networks with Reliability and Cellular Secrecy Outage Constraints

Transcription

1 Limited Feedback Scheme fo Device to Device Communications in 5G Cellula Netwoks with Reliability and Cellula Sececy Outage Constaints Faezeh Alavi, Nade Mokai, Mohammad R. Javan, and Kanapathippillai Cumanan axiv:78.798v [cs.it] 26 Aug 27 Abstact In this pape, we popose a device to device D2D communication scenaio undelaying a cellula netwok whee both D2D and cellula uses CUs ae discete powe-ate systems with limited feedback fom the eceives. It is assumed that thee exists an advesay which wants to eavesdop on the infomation tansmission fom the base station BS to CUs. Since D2D communication shaes the same spectum with cellula netwok, coss intefeence must be consideed. Howeve, when sececy capacity is consideed, the intefeence caused by D2D communication can help to impove the sececy communications by confusing the eavesdoppes. Since both systems shae the same spectum, coss intefeence must be consideed. We fomulate the poposed esouce allocation into an optimization poblem whose objective is to maximize the aveage tansmission ate of D2D pai in the pesence of the cellula communications unde aveage tansmission powe constaint. Fo the cellula netwok, we equie a minimum aveage achievable sececy ate in the absence of D2D communication as well as a maximum sececy outage pobability in the pesence of D2D communication which should be satisfied. Due to high complexity convex optimization methods, to solve the poposed optimization poblem, we apply Paticle Swam Optimization PSO which is an evolutionay appoach. Moeove, we model and study the eo in the feedback channel and the impefectness of channel distibution infomation CDI using paametic and nonpaametic methods. Finally, the impact of diffeent system paametes on the pefomance of the poposed scheme is investigated though simulations. The pefomance of the poposed scheme is evaluated using numeical esults fo diffeent scenaios. Index Tems Device to Device D2D communications, Limited Rate Feedback, Physical PHY laye secuity, Paticle swam optimization. I. INTRODUCTION A. Backgound and Motivation The gowth of the cellula netwoks and the numbe of uses as well as the emegence of the new multimedia based sevices esult in gowing demands fo high data ate and capacities which is beyond the capability of foth geneation 4G wieless netwoks. Recently, the fifth geneation 5G cellula netwok has tiggeed a geat attention to povide high data ate and low latency sevices in a powe and spectally efficient manne. Intoducing new applications like context-awae applications equies the diect communications of neighboing devices. In this context, device to device D2D communication has been consideed as a pomising technique fo 5G wieless netwoks [] [3]. D2D communication opeates as an undelay netwok to a cellula netwok [4] [6] and enables eusing the cellula esouces which inceases the spectal efficiency and the system capacity. In D2D communications, two neighboing devices use the cellula bandwidth to communicate diectly without the help of cellula base station BS. Although D2D communications can impove the spectal efficiency, it should povide access to licensed spectum with a contolled intefeence to avoid the uncetainties of the cellula netwok pefomance. Theefoe, intefeence management is a citical issue fo D2D undelaying cellula netwoks without consideing it, the effectiveness of D2D communication links will be deteioated. In this sense, seveal papes have poposed mechanisms fo intefeence mitigation and avoidance. To pefom intefeence management in D2D undelaying cellula netwok, one appoach is to conside coopeative communications. In this way, a D2D use equipped with multiple antennas acts as an in-band elay to a cellula link whee the multi-antenna elay is able to help decoding messages, cancelling intefeence, and poviding multiplexing gain in the netwok [7] [9]. In [], powe contol poblem fo the D2D uses is investigated in ode to optimize the enegy efficiency of the use equipments UEs as well as to ensue that the quality of sevice QoS of D2D devices and UEs does not fall below the acceptable taget. The poblem of intefeence management though multi ate powe contol fo D2D communications is studied in []. The tansmission powe levels of D2D uses ae optimized to maximize the cell thoughput while peseving the signal-to-intefeence-plusnoise atio SINR pefomance fo the cellula use. In [2], authos guaantee the eliability of D2D links and mitigate the intefeence fom the cellula link to the D2D eceives. A picing famewok has been suggested in [3] whee BS potects itself by utilizing game theoy appoach. To incease the secuity of wieless tansmission, physical laye secuity has been developed based on infomation theoetic concepts [4] [2]. Fom the physical laye point of view, the secuity is quantified by the sececy ate which is defined as the diffeence of achievable ate between the legitimate eceive and the ate ovehead by eavesdoppes [22]. In this sense, unlike the pevious wok on D2D undelaying cellula netwoks in which the focus is on the intefeence mitigation and avoidance, the intefeence woks well when sececy capacity of the cellula communication is taken into consideation [2]. In othe wods, it can be assumed that the D2D communication woks as a fiendly jamme and its intefeence is helpful fo the secue cellula netwok to impove sececy capacity. In pactice, since the eavesdoppe is a passive attacke, obtaining its channel state infomation CSI is impossible in many situations. In this case, the sececy outage pobability can be used as a secuity pefomance citeion. The pefomance of pevious woks is based on the fact that the pefect CSI of all links is available. Howeve, due to

2 2 the estimation eos and feedback delay, pefect CSI may not be available. In addition, the feedback channel has a limited capacity since tansmitting unlimited feedback infomation between tansmittes and eceives means passing a huge amount of bits fo signaling. To tackle this issue, the limited feedback channel model can be employed. In the limited feedback channel, the space of channel gains is divided into a finite numbe of egions, and instead of channel gain values, the index of the fading egion in which the actual channel gain lies is feedbacked [23] [25]. In [25], the authos study the effect of the feedback infomation on the pefomance of the D2D undelaying cellula netwoks and develop use selection stategies based on limited feedback. B. Contibutions and Oganization In this pape, we study D2D communications in the pesence of the cellula communications while thee exists a malicious use which wants to eavesdop the infomation tansmitted fom the BS to CU. We assume that the legitimate tansmittes do not have the pefect values of the channel powe gains and the knowledge about thei espective diect channel powe gains is obtained via thei dedicated limited ate feedback channel. In othe wods, we assume that the space of the channel gains is divided into a finite numbe of egions. Then given the actual value of the channel gains, the eceive detemines the index of the egion in which the channel gain lies and feedbacks the index of that egion to the coesponding eceive. Note that, the cellula system is supeio to D2D communication and D2D pai uses the spectum of cellula netwoks in an oppotunistic manne. The concuent tansmission of cellula netwok and D2D pai, if exists, degades the pefomance of both systems due to the coss intefeence between these two systems. Theefoe, in this pape, we conside the pefomance of the cellula system in both the pesence and the absence of D2D communication. ecisely, we equie that the aveage tansmission ate of cellula use in the absence of the D2D communication should be above a pedefined theshold while its pefomance in the pesence of the D2D communication, in tems of outage pobability, satisfies a pedefined theshold. Ou objective is to maximize the aveage achievable data ate of the D2D pai in the pesence of the cellula communication while individual constaints on the aveage tansmission powe of the cellula BS and the D2D pai should be satisfied. Due to non-convexity and nonlineaity of the poposed poblem, to find the optimal solution of the poblem, we use paticle swam optimization PSO method which is an evolutionay algoithm [26] [3]. In eality, the feedback channels can be affected by the noise which makes the tansmitte select an incoect code wod fom the designed code book. Theefoe, in this pape, we conside the effect of eo in the feedback channel on the pefomance of the poposed scheme by incopoating such eo into the poblem fomulation. We futhe study the effect of channel distibution infomation CDI impefectness. Paametic and nonpaametic methods ae investigated in estimating the CDI of the channels. The contibutions of this pape ae as follows: We develop a mathematical model fo the secue communication in D2D communication undelaying the cellula netwok in which the knowledge of tansmittes about the CSIs is obtained via a limited ate feedback channel. In ou model, we conside the coss intefeence between the cellula netwok and the D2D pai explicitly and fomulate the esouce allocation poblem as an optimization famewok. To solve this optimization poblem and obtain its solutions which ae the fading egions boundaies and tansmission powe levels, we use PSO algoithm which is an evolutionay algoithm. We futhe conside the effect of the noise in the feedback channel and incopoate it into ou optimization poblem. In this case, the eo in the feedback channel would lead the tansmittes to choose the incoect code-wods. We fomulate the coesponding optimization poblem and solve it using the PSO appoach. We also conside the effect of the CDI impefectness in ou poposed scheme. In this case, the CDI s paametes ae not pefectly known and paametic and non-paametic appoaches ae used to estimate the CDI paametes. Finally, the pefomance of the poposed scheme in diffeent scenaios is investigated via simulations. The pape is oganized as follows. System model is descibed in Section II. Limited ate feedback schemes ae poposed in Section III. The limited ate feedback esouce allocation poblem is fomulated and solved in Section IV. In Section V, pactical consideations, i.e., noisy feedback channel and CDI estimation eo, ae investigated. Simulation and numeical esults ae povided in Section VI and finally conclusions ae dawn in Section VII. II. SYSTEM MODEL We conside a D2D communication scenaio undelaying an existing cellula netwok. It is assumed the downlink tansmission in the cellula netwok whee the BS tansmits infomation to a cellula use while at the same time; the existing D2D pai pefoms its own tansmission on the same channel. Such a scenaio can be intepeted as thee ae many cellula uses in the netwok each of which is assigned to a channel ove which the BS sends infomation to them. Assuming this assignment is pefomed based on some netwok paametes and is fixed, two cellula uses exploit one of the available cellula channels to pefom thei infomation tansmission diectly. In this pape, we assume that this assignment is pedefined. In addition to cellula use and D2D pai, we assume that thee exists a malicious use which wants to eavesdop on the infomation tansmission of cellula netwok, i.e., fom the BS to the CU. Howeve, the malicious use does not eavesdop on the D2D pai. Such assumption can be justified when the malicious use is not awae of the existence of D2D pai as such shaing can be pefomed oppotunistically i.e., D2D pai may o may not exist at any time when the malicious use is not inteested in D2D pai infomation, o when the D2D pai applies uppe laye secuity measues, e.g., cyptogaphy. In such case, the malicious use teats the signals fom D2D pai as noise.

3 3 Fig.. A D2D communication undelaying an existing cellula netwok. Let h BC, h BD, h DD, h DC, h BE, and h DE denote, espectively, the noise nomalized channel powe gain of the channel fom BS to CU, fom BS to the eceive of D2D pai RD2D, fom the tansmitte of D2D pai TD2D to RD2D, fom TD2D to CU, fom BS to the eavesdoppe, and fom the TD2D to the eavesdoppe. We assume that all channels undego independent block fading with Rayleigh distibution meaning that the channel powe gains, i.e., h BC, h BD, h DD, h DC, h BE, and h DE, ae exponentially distibuted with the mean of h BC, h BD, h DD, h DC, h BE, and h DE, espectively. In this pape, we assume that the eavesdoppe has complete knowledge about the instantaneous channel powe gains and the CDI of the channels fom BS to CU and fom BS to itself. We futhe assume that the legitimate eceives, i.e., the cellula use and the RD2D, know the CDI of all channels and only the instantaneous channel powe gains of thei espective channels. We assume that, the legitimate tansmittes do not have pefect values of channel powe gains and the knowledge of legitimate tansmittes about thei espective diect channel powe gains is obtained via thei espective limited ate feedback channels. In this case, the space of h BC is divided into a finite numbe of M egions, i.e., [, h BC, [ h BC, h BC 2,, [ h BC, h BC M whee h BC M =. Similaly, fo D2D pai, the space of h DD is divided into a finite numbe of N egions, i.e., [, h DD, [ h DD, h DD 2,, [ h DD N, h DD N whee h DD N =. The eceive, i.e., CU, measues the channel powe gain h BC and feedbacks the index m if h BC lies in the egion [ h BC m, h BC m +. Similaly, RD2D measues the channel powe gain h DD and feedbacks the index n if h DD lies in the egion [ h DD n, h DD n+. In this pape, we assume that the feedback links ae confidential. This means that, the feedbacked index of the cellula netwok could not be ovehead by D2D pai and that of D2D pai could not be ovehead by the cellula netwok. In this case, the poweate tuples will depend only on the coesponding feedbacked index, i.e., we have p BC m, BC m,s BC m fo cellula communication which ae the tansmit powe, the tansmission ate and the sececy ate at which BS tansmits infomation to CU, espectively. Moeove, we conside p DD n, DD n fo D2D communications which ae the tansmit powe and the tansmission ate at which TD2D tansmits infomation to RD2D, espectively. In fact, the poposed schemes opeate in two phases. In the fist phase off-line phase, seveal paametes that ae late used fo esouce allocation ae computed. It is done befoe the communication established and based on the CDIs of the netwok s links the optimum bounday egions and code-books ae designed by the base station. At the end of this phase, all code-wods ae infomed to uses by BS. Howeve, the channel patitioning stuctue is kept at the CU. In the second phase on-line phase that is employed duing communication, the tansmittes use the paametes obtained in off-line phase. In fact, in the on-line phase, the CU and D2D eceive measue the elated CSIs and based on them find the elated channel patition and bounday egion. Then, they tansmit back the index to the base station and D2D tansmitte in ode to select the coesponding code-wod fom the obtained code-book. Note that the code-book, which contains a set of code-wods, is designed off-line and known by each node. The computational buden takes place duing the initialization off-line phase and equies a negligible buden duing the tansmission online phase and it is cetainly desiable fom an implementation pespective [3] [32]. In this pape, we conside that thee is a cental pocessing unit and some assignments ae pefomed in this step. Then, the netwok uses the infomation pepaed in the cental pocessing [33] [35]. Fo the esouce allocation, two appoaches could be adopted. One is to conside the poblem of paiing the D2D and cellula links as well as the designing limited feedback scheme jointly. In this way, the outcome of the esouce allocation poblem is which D2D link is paied with which cellula link as well as code-books powe allocation and bounday egions. Howeve, this appoach is much complex and would be computationally pohibitive. Anothe appoach which could lowe the complexity of the scheme is to conside the paiing poblem and limited ate feedback design sepaately. In this case, one fist solves the poblem of paiing D2D and cellula link. Then, given this paiing esult, the poblem of designing a limited ate feedback scheme could be fomulated and solved. In this pape, we assumed the second appoach and assumed that the D2D and cellula links ae paied and the paiing esult is available based on which we design the limited ate feedback scheme. The paiing pocess could be pefomed based on netwok paametes as well some degees of the equied QoS level. Fo example, one could fomulate a poblem in which the aim is to pai the D2D and cellula links based on the aveage channel gains instead of instantaneous o long tem channel consideations. Seveal authos have studied the poblem of paiing D2D links with CUs fo spectum shaing and focus on the selection of the D2D link and CUs as a pai fo bette pefomance [36] [38]. Howeve, in ou pape, we pesent the esouce allocation in D2D undelaying cellula netwok and focus on devising a limited ate feedback model as well as powe allocation poblem encompassing diffeent pefomance metics. In this way, fist, the D2D link and cellula communication link ae scheduled based on the mean of channel powe gain. In the next step, the esouce allocation can be obtained based on the poposed scheme in this pape. To obtain the best optimum solution, they should be solved at the same time; howeve, it causes a high computational complexity. To educe the complexity, they can be consideed sepaately at the cost of a slight pefomance loss. Howeve,

4 4 we can extend this appoach fo solving the poblem at the same time as futue woks. III. LIMITED RATE FEEDBACK SCHEMES A. Capacity of Links When the feedback links ae confidential, the feedbacked indices cannot be head by any paty othe than the eavesdoppe. In this case, we assume that, the cellula netwok quantizes the main channel powe gain, i.e., h BC, independent of the index feedbacked by the RD2D. Knowing that the index m is feedbacked by CU, fom the designed code bookc BC, BS chooses tansmit powe level p BC m to send its infomation. In othe wod, it chooses the tuple p BC m, BC m,s BCm whee BC m = log+ h BC mp BC m is the tansmission ate ove BS to CU. In this case, in the absence of D2D tansmission, the capacity of the link between BS and CU and its coesponding sececy capacity ae, espectively, given by C C m = log+h BC p BC m, C C S m = [ log+h BC p BC m log+h BE p BC m ] +, 2 while knowing indices n, the D2D pai chooses tansmit powe level p DD n to send its infomation. In othe wod, the D2D pai has chosen p DD n, DD n fo concuent tansmission with cellula netwok and the capacity of the link between BS and CU and its coesponding sececy capacity ae, espectively, given by Ĉ C m,n = log+ĥbc p BC m, 3 ĈS C m,n = [ log+ĥbc p BC m log+ĥbe p BC m ] +, 4 whee ĥbc h = BC +h DC p DD n and ĥbe h = BE +h DE p DD n ae the effective channel gains between BS and CU and between BS and eavesdoppe, espectively. Note that, the tansmission capacity in 3 and the sececy capacity in 4 can be achieved only if we have full knowledge of CSIs, i.e., the pefect values of ĥbc and ĥbe. On the othe hand, given that the index n is feedbacked by RD2D, fom the designed code book C DD, TD2D chooses the tuple p DD n, DD n whee DD n = log+ hdd np DD n. In this case, in the absence of cellula tansmission, the capacity of D2D link is given by C D n = log+h DD p DD n, 5 while given that BS has chosen the tuple p BC m, BC m,s BC m fo concuent tansmission with D2D pai, the capacity of the D2D link is given by Ĉ D m,n = log+ĥdd p DD n, 6 whee ĥdd = h DD +h BD p BC m is the effective channel gain between TD2D and RD2D. The pefect value ofĥdd is needed to achieve the tansmission capacity in 6. B. Outage Events In ou model, thee ae two types of outage, namely eliability outage which coesponds to the case whee the tansmission ate exceeds the channel capacity and sececy outage whose definition depends on the availability of CSI at the tansmitte. Moe pecisely, conside the case whee CU feedbacks the index m, i.e., BS chooses the tuple p BC m, BC m,s BC m. In the absence of D2D tansmission, eliability outage fo cellula communication occus if BC m > C C m whee C C m is given by. This event coesponds to the case whee h BC m > h BC which neve occus. In addition, the sececy outage occus if S BCm > CS Cm whee CC S m is given by 2. In this pape, howeve, we ae inteested in the outage event in the pesence of D2D pai communication. In this case, eliability outage fo cellula communication occus if BC m > ĈC m,n whee Ĉ C m,n is given by 3. This event coesponds to the case whee h BC m > ĥbc which is possible. Howeve, as we assume that only the knowledge of diect channels is available, the sececy outage does not coespond to the event S BCm > ĈS Cm,n whee ĈC S m,n is given by 4. Note that, given that the indices m and n ae feedbacked, the tansmission ate is fixed to BC m = log + h BC mp BC m. In this case, any sececy ate given by S BCm BC m e m is achievable whee e m is the maximum allowable equivocation ate of the eavesdoppe. Now, assume fo the feedbacked index m, the sececy ate is fixed to S BC m and hence we have e m = BC m S. BCm Theefoe, the sececy outage occus if the instantaneous capacity of the eavesdoppe exceeds the value of e m, i.e., we have ĈBE m,n = log + ĥbe p BC m > e m whee the dependence of the value of Ĉ BE m,n on the feedbacked index n is though h BE +h DE p DD n ĥ BE =. Theefoe, given that D2D pai chooses p DD n, DD n, the outage pobability fo cellula communication using tuple p BC m, BC m,s BC m is given by P outage = p BC m, BC m,s BCm,pDD n, DD n P success p BC m, BC m,s BCm,pDD n, DD n, 7 whee P success p BC m, BC m,s BCm,pDD n, DD n = BC m ĈC m,n,ĉbe m,n BC m S BC m, 8 and we assumed that h BC [ h BC m, h BC m+ and h DD [ h DD n, h DD n+. Using the above explanations and defining R BC m = [ h BC BC m, h m+ and RDD n = [ h DD DD n, h n+, the outage pobability fo cellula communication when it uses the tuple p BC m, BC m,s BC m is given by P outage p BC m, BC m, BC S m = N h DD R DD n P outage, p BC m, BC m,s BCm,pDD n, DD n n= 9 and the outage pobability of cellula link code book, i.e., C BC, is given by P outage = h BC R BC C BC m P outage m= p BC m, BC m,s BC m.

5 5 Details on obtaining the above pobabilities ae defeed to Appendix A. Similaly, fo the D2D pai, assume that the tansmitte chooses the pai p DD n, DD n. In the absence of cellula tansmission, eliability outage occus if DD n > C D n whee C D m is given by 5. This event coesponds to the case whee h DD n > h DD which neve occus. On the othe hand, in the pesence of cellula communication, eliability outage fo D2D communication occus if DD n > ĈD m,n whee ĈD m,n is given by 6. This event coesponds to the case whee h DD n > ĥdd which is possible. Note that, as we assumed the malicious use is not inteested in D2D communication, only eliable tansmission is consideed fo D2D pai and no sececy ate is defined. C. Tansmit Powes and Achievable Rates As we assumed, the tansmittes only know the egion numbe in which the channel powe gains of diect channels lay. This means that it is impossible to know the value of effective channel gains when a concuent tansmission is unning. Theefoe, fo cellula netwok the value of diect channel gain, i.e., h BC, and fo D2D pai, the value of h DD ae quantized. Given that h BC lies in the egion R BC m, BS chooses tuple p BC m, BC m,s BC m. Note that, egadless of the channel powe gains of othe links, i.e., h BD, h DD, h DC, h BE, and h DE, BS tansmits with powe level p BC m. Theefoe, in this case, the aveage tansmission powe of BS only depends on h BC and is given by P C = h BC R BC m p BC m, m= which is the same fo both cases whee D2D pai is not tansmitting o concuently tansmits infomation. Similaly, given that h DD lies in the egion R DD n, TD2D chooses the pai p DD n, DD n. As we assumed that the feedback link of cellula netwok is confidential, the tansmission powe of D2D pai, i.e.,p DD n, only depends onh DD. Theefoe, in this case, the aveage tansmission powe of D2D pai is given by N P D = h DD R DD n p DD n, 2 n= which does not depend on whethe BS is tansmitting concuently o not. In addition, fo cellula communication, the tansmission is assumed successful if no outage occus, i.e., we have both the eliable and secue communications. We define the aveage achievable sececy ate fo cellula communication as the adopted sececy ate, i.e., S BC m, times the pobability of success, i.e., no outage occus, summed ove all egions. When the D2D pai is absent, the aveage achievable sececy ate is given by R S C = h BC R BC m,bc S m CC S m S BC m, 3 m= whee CS C m is given by 2. Note that, it is not equied to include the tem BC m C C m in 3 because it is always satisfied. Please efe to Appendix B fo moe details on obtaining the pobability tems in 3. Since, we need only eliable tansmission fo D2D communication, the aveage achievable ate of D2D pai is defined as the adopted data ate. i.e., DD n, times the pobability of succeed, i.e., no outage occus, summed ove all egion. The aveage tansmission ate which is achievable by D2D pai in the pesence of cellula communication is given by R D = N m= n= h BC R BC m,hdd R DD n,dd n ĈD m,n DD n, 4 whee Ĉ D m,n is given by 6. Details on obtaining pobability tems in 4 can be found in Appendix C. IV. LIMITED RATE FEEDBACK RESOURCE ALLOCATION A. oblem Fomulation PROBLEM In this pape, we assume that D2D pai oppotunistically uses the cellula netwok esouces to maximize its aveage tansmission ate. Note that, geneally, D2D communication is undelay to cellula communication which means the late one is supeio and should be potected against the side effects of concuent tansmission of D2D pai. Thee ae seveal appoaches to achieve this. One appoach is to limit the amount of intefeence that D2D pai poduces on the cellula eceive. Such appoach can be seen exactly the same as the notion of intefeence tempeatue in cognitive adio netwoks [3]. Howeve, note that this appoach is effective when it is used in its instantaneous fom i.e., the exact amount of intefeence D2D pai poduces and not the aveaged one i.e., the aveage amount of intefeence D2D pai poduces. Howeve, since we only know the diect channel powe gains using limited ate feedback, applying instantaneous intefeence constaint is not possible. Anothe appoach is to maintain the aveage achievable ate of the cellula link above a pedefined theshold [], []. Moeove, the eliability of the cellula netwok is much of ou concen, paticulaly, in the case that the esouce is shaed with D2D links. To this end, outage based appoach is the next appoach in which the outage pobability fo cellula communication is kept below a pedefined theshold [], [2]. In this pape, we combine the last two appoaches. Moe pecisely, ou objective is to maximize the aveage achievable data ate fo D2D pai in the pesence of cellula communication, i.e., 4, while it is equied to maintain a minimum amount of the aveage achievable data ate of cellula link in the absence of D2D communication, i.e., 3, and the outage pobability fo cellula communication in the pesence of D2D communication, i.e.,, is kept below a pedefined theshold. In this way, we take into account the pefomance of cellula communication both in the absence and pesence of D2D communication. Indeed, by doing so, we equie that the aveage tansmission ate of cellula link in the absence of D2D pai to stay above a pedefined theshold while its pefomance in the pesence of D2D communication, which is given by the outage pobability, emains as satisfactoy as is equied. In addition, the aveage tansmit powe of the cellula link and D2D pai, which ae, espectively, given by and 2, should not exceed a pedefined value. Mathematically,

6 6 { defining A = h BC, h DD, p BC, p DD, BC S optimization poblem which is given by max A N m= n= s.t.: m= m= N n= m= }, we aim to solve the h BC R BC m,hdd R DD n, DD n ĈD m,n DD n, 5a h BC R BC m,bc S m CC S m h BC R BC m P outage S BC m R Cmin outage,max p BC m, BC m,s BC m PC BC S, 5b, 5c h BC R BC m p BC m P C,max, 5d h DD R DD n p DD n P D,max. 5e This optimization poblem is nonlinea and non-convex and it is had to solve it, hence, we utilize the PSO method which has been used to solve highly non-linea mixed intege optimization poblems in vaious eseach [27] [3]. Since PSO is a computational intelligence-based technique and has global seach ability, it can convege to the optimal solution and not lagely affected by the size and non-lineaity of the poblem [28]. B. Paticle Swam Optimization Method In this pape, to solve the optimization poblem, we apply elatively new technique, PSO algoithm which is a computational intelligence-based technique. PSO is based on a moment of the swam which seaches to find the best optimal solution by updating geneations [26], [3]. This method is not lagely affected by the size and nonlineaity of the poblem, and can convege to the optimal solution. In PSO algoithm, all paticles which ae the potential solutions, move towads its optimum value. Fo each iteation all the paticles in this swam ae updated by its position and velocity fo optimization ability and based on them the aim function fo the system is evaluated. PSO stats with the andom initialization of swam of paticles in the seach space. Then, by adjusting the path of each paticle to its own best location and the best paticle of the swam at each step, the global best solution is found. The path of each paticle in the seach space is adjusted by its velocity, accoding to moving expeience of that paticle and othe paticles in the seach space. In this pape, we { conside diffeent paticles } fo each vaiable, i.e, A = h BC, h DD, p BC, p DD, BC S, which denote a solution of the poblem. The PSO algoithm consists of A i as the vecto of i th paticle in d dimension, i.e, fo { h BC, p BC, BC S }, d is equal to M and fo { h DD, p DD }, d is equal to N [3]. The position and the velocity of the i th paticle in the d dimensional seach space can be shown as X i = [x i,,x i,2,...,x i,d ] T and V i = [v i,,v i,2,...,v i,d ] T, espectively. A best position of each paticle is denoted by pbest Pi = [p i,,p i,2,...,p i,d ] T, coesponding to the pesonal best objective value obtained at time t. The global best paticle, i.e., gbest p g, shows the best paticle at time t in the entie swam. The new velocity of each paticle can be obtained as follows [3]: v i,j t+ = wv i,j t+c p i,j x i,j t +c 2 2 p g x i,j t, j =,...,d, 6 whee c and c 2 ae constants called acceleation coefficients, w is the inetia facto, and 2 ae two independent andom numbes unifomly distibuted in [, ]. Thus, the position of each paticle is updated in each step as follows: x i,j t+ = x i,j t+v i,j t+. 7 The standad fom of PSO uses 6 to calculate the new velocity of each paticle based on its pevious velocity and the distance of its cuent position fom both its best position and global best position. To contol seach of paticles outside the seach space [Xi min,xi max ], we can limit the value of V i to the ange[vi min,vi max ] and accoding to 7, each paticle moves to a new position. The pocess is epeated until a stopping citeion is satisfied. This algoithm is summaized in Table.I [26]. A. CDI Estimation Eo V. PRACTICAL CONSIDERATION The most pactical assumption made in this pape is that the instantaneous channel powe gains of the eavesdoppe s links, i.e., h BE and h DE, ae not available which is mostly due to the fact that the eavesdoppe is passive and hence acquiing its channel powe gains ae not possible. Geneally, the CDI of a channel depends on the envionmental popety of the communication channel. If the popagation envionment is known, one can assume that the channel CDIs, including those of the eavesdoppe, ae available. The statistical popety of the signal popagation in the coveage aea of the netwok can be easily obtained as the legitimate uses ae pesent and can be involved in finding the equied statistical popeties. Since fo small geogaphical aeas, a unified distibution can be applied to all channels, we can have the CDIs of eavesdoppe s links at hand. Due to the availability of limited statistical data, the distibution function is had to dive and cannot be fit into the known ones, e.g., Rayleigh distibution. In such cases, schemes developed based on the availability of the pefect CDI may exhibit pefomance wose than that expected. Theefoe, the impefectness of CDIs should be taken into account. Geneally, such consideation can be pefomed by assuming that the tue distibution diffes fom the nominal distibution by the value known as Kullback Leible distance [39] and incopoate such inaccuacy into poblem fomulation [4] [42]. We investigate impefect CDI though two paametic and nonpaametic methods. This assumption is easonable when the size of the aea unde investigation is small which is the case fo nowadays cellula netwoks specially fo small cells.

7 7 TABLE I PSO SCHEME FOR OUR PROBLEM Initialization: Step MaxIt: Iteation numbe of PSO algoithm npop: Numbe of paticles of PSO algoithm { Fo each } vaiable of A = : h BC, h DD, p BC, p DD, BC S X i : Position of one paticle, i =,2,...,nPop V i : Velocity of one paticle, i =,2,..., npop Step 2 Evaluate 5a-5e as a cost fo all paticles, named cost i : Set pbest i = X i and pbest.cost i = cost i Set gbest and gbest.cost value equal to the value of the best initial paticle. Fo t =,2,...,MaxIt Fo i =,2,..., npop Use 6, 7 to update the velocity and position of paticles { fo all vaiables } of A = h BC, h DD, p BC, p DD, BC S Evaluate 5a-5e If cost i > pbest.cost i : pbest i = X i and pbest.cost i = cost i. If pbest.cost i > gbest.cost gbest = pbest i and gbest.cost = pbest.cost i. end end Paametic Method: In paametic methods, the effect of the impefect CDI is studied though the pefomance loss by simulations as in Section VI. This means that, we solve the optimization poblem 5a with the available channel CDIs and obtain the channel quantization and code books fo cellula link and D2D pai. Then, we evaluate the pefomance loss due to impefect CDI in tems of changes in the aveage achievable ates. In othe wods, we conside the impefect channel powe gain of each channel i which is exponentially distibuted with the mean of hi : h i = h i, 8 whee is pecent eo of impefect CDI. 2 Non-Paametic Method: Anothe way to estimate CDI is nonpaametic method which estimates the density based on the eceived samples fom the channel. In this pape, we adopt two nonpaametic methods: kenel density estimation KDE and obust KDE RKDE. 2.. Kenel Density Estimation KDE: One of the most well-known non-paametic density estimation methods is kenel density estimation [43]. When the samples, efeed to as the nominal data, ae noise fee, KDE can povide a good estimate of the density. A set of obsevations {x,...,x L } R j is used to estimate a andom vecto x with a density fx whee L is the numbe of obsevation vectos. Moeove, each x i = x i,...,x ij,i =,...,L is a sequence of j data in the vecto x i. The kenel density estimate of fx given by ˆf KDE x = L k δ x,x i, 9 L whee k δ x,x i is the kenel function which commonly is a Gaussian kenel: k δ x,x i = j exp x x i 2 2Πδ 2δ 2, 2 whee δ is the smoothing paamete and efeed to as the bandwidth. It is set to the median distance of a taining point x i to its neaest neighbo Robust Kenel Density Estimation: In pactice, the channel gain samples might include contaminated data, efeed to as outlie data, which makes it necessay to use obust density estimation methods such as obust KDE RKDE. In the pesence of the contaminated samples, RKDE can give obustness to contamination of the taining sequence and estimate the density. Contaminated data consists of ealizations fom both a nominal o clean distibution in addition to outlying o anomalous measuements. In an inceasing numbe of applications, data aises fom high dimensional o highthoughput systems whee the nominal distibution itself may be quite complex and not amenable to paametic modelling. The RKDE has the following fom: L ˆf RKDE x = ω i k δ x,x i, 2 i= i= whee k δ x,x i is a kenel function and ω i ae nonnegative weights that sum to one. The RKDE can be implemented based on the iteatively eweighed least squae IRWLS [44] algoithm in which the main goal is to find the optimal value of ω i. B. Noisy Feedback Channel So fa, we assumed that the feedback channels ae eo fee meaning that the eceived index is the same as the feedbacked one. Howeve, in eality, the feedback channel could be affected by the noise which makes tansmitte to select an incoect code wod fom the designed code book. Note that, designing limited ate feedback systems with incopoating feedback eo is complicated, especially fo ou scheme with two intefeing links. In this pape, to conside the feedback eo, we utilize the scheme which is commonly used in the liteatue [3], [45] [48]. We conside the memoyless feedback channel which chaacteized by index tansition pobabilities ρ C m,m m,m =,,M fo cellula link which is the pobability of eceiving indexmin BS given the indexm was sent by CU, and ρ C n,n n,n =,,N fo D2D pai which is the pobability of eceiving index n in TD2D given the index n was sent by RD2D. It is assumed b M = log 2 M bits feedback fo cellula link and b N = log 2 N bits feedback fo D2D pai. Let m m 2 m bm, m m 2 m b M, n n 2 n bm, and n n 2 n b M indicate the binay display of indices m, m, n, and n, espectively. We assume that the cellula and D2D pai s feedback channel can be consideed as, espectively, b M and b N independent use of binay symmetic channel BSC to sent each of the feedback bits pesented

8 8 in binay epesentations of cellula link and D2D pai s feedbacked indices. Let q C and q D epesent the coss ove pobabilities of the feedback channels of cellula link and D2D pai, espectively. The index tansition pobabilities of the feedback channels of cellula link and D2D pai can be obtained, espectively, by ρ C m,m = qc d m,m q C bm d m,m, 22 ρ D n,n = qd d n,n q D bn d m,m, 23 whee d m,m and d n,n denote the Hamming distances between, indices m and m and indices n and n, espectively [45] [47]. With the above definitions and assumptions, the aveage tansmission powes in and 2, aveage tansmission data ates in 3 and 4, and the outage pobabilities in 7, 8, 9, and should be manipulated to incopoate the effect of noisy feedback channel. Note that, choosing the tansmit powe level fom a code book only depends on the coesponding channel egion index which is feedbacked by the espective tansmitte. This mean that, in, we should only conside the noise effect of the feedback channel of cellula link, and in 2, we should only conside the noise effect of the feedback channel of D2D pai. Theefoe, the aveage tansmit powes of cellula link and D2D pai, when noisy channel feedback is assumed, ae given, espectively, by P C = m= m = N N P D = n= n = ρ C m,m h BC R BC m p BC m, 24 ρ D n,n h DD R DD n p DD n. 25 Fo the aveage tansmission data ate in 3, we assumed the D2D pai is absent, hence, it is not affected by the noise in feedback channel of D2D pai. Theefoe, the aveage tansmission data ate can be witten as R S C = m=m = h BC R BC m,m m, BC m C C m/m,c BE m e m S BC m, 26 whee e m = BC m S BCm and CBE m = log + h BE p BC m whee we note that actually, the value of C BE m does not depend on m. In 26, m m is the event that the feedbacked index m is eceived as m. Hee, we highlight that, in 26, C C m/m means that its value is given by with h BC R BC m and pbc m. Note that, hee, in contast to 3, we must include BC m C C m/m in 26 because eliability outage can occu when the feedback is noisy. Fom, we know that the event BC m C C m/m occus when m m. Theefoe, 26 can be ewitten as follows: R S C = m=m =m ρ C m,m h BC R BC m,ĉbe m e m S BC m. 27 The emaining steps ae simila to those in obtaining pobability tems in 3 in Appendix B, and hence omitted. Howeve, as we assumed in 4 that both the cellula link and D2D pai tansmit simultaneously, the coss effect of noisy feedback channel should be consideed. In othe wods, given that the tansmitted index m was eceived as m by BS and the tansmitted index n was eceived as n by tansmitte of D2D pai, the aveage data ate of D2D pai in the pesence of cellula communication with noisy feedback channels is given by R D = N N m=m =n=n = h BC R BC m,hdd R DD n, m,n m,n, DD n ĈD m,n/n DD n. 28 Note that, in 28, the value of ĈD m,n/n does not depend onm. In addition, the effect of noise in feedback channel of cellula link on the value of ĈD m,n/n appeas though the choice of tansmit powe level p BC m which affects the value of the effective channel gain ĥdd h = DD +h BD p BC m with h DD R DD n. Obtaining pobability tems in 28 is simila to obtaining pobability tems in 4 in Appendix C, and hence omitted. Like 28, fo the outage pobabilities in 7, 8, 9, and, we should conside the coss effect of noisy feedback channels. If we conside the noisy feedback channel effect in the outage pobability of cellula communication in the pesence of D2D pai, we obseve that given the feedback indices m and n wee eceived by the coesponding eceive as m and n, espectively, BS uses the code wod p BC m, BC m,s BCm while we have hbc R BC m and the tansmitte of D2D pai uses the code wod p DD n, DD n while we have h DD R DD n. In this case, the outage pobability is given by whee P outagem/m,n p BC m, BC m, BC S m,pdd n, DD n = P successm/m,n p BC m, BC m, BC S m,pdd n, DD n, 29 P successm/m,n = p BC m, BC m,s BCm,pDD n, DD n BC m ĈC m/m,n,ĉbe m,n BC m BC S m, whee ĈC m/m,n is given by 3 with ĥbc = 3 h BC +h DC p DD n and h BC R BC m, and ĈBE m,n = log +ĥbe p BC m with ĥ BE h = BE +h DE p DD n. To obtain 3 one can follow the simila steps as those fo 8 in Appendix A. Using the above explanations, the outage pobability fo cellula communication when it uses the tuple p BC m, BC m,s BC m and unde noisy feedback channel model, is given by N P outagem/m = N p BC m, BC m,s BCm n= n = ρ D n,n h DD R DD n P outagem/m,n p BC m, BC m,s BCm,pDD n, DD n, 3 and the outage pobability of cellula link code book, i.e., C BC, is given by

9 9.8 P outage C = BC m=m = ρ C m,m h BC R BC m P outage p BC m, BC m,s BCm. 32 To take the noisy feedback channel model into consideation, in the optimization poblem 5a, we must use 24, 25, 26, 28, and 32. VI. SIMULATION RESULTS In this section, numeical esults ae pesented to evaluate the pefomance of the poposed limited feedback scheme in a D2D communication though the simulations unde vaious system paametes. The channel gain is an exponential andom vaiable with the pobability density function PDF given by fh = σ exp h, 33 σ whee σ can be used to model the aveage channel gain as σ = s d d γ whee d is the distance between the tansmitte and the eceive,d is the efeence distance,γ is the amplitude path-loss exponent, and s chaacteizes the shadowing effect. The uses ae assumed to be unifomly distibuted in a cell of adius m. The small-scale channel fading is assumed to be Rayleigh distibuted. The path-loss exponent is equal to 4, and the shadowing effect follows a log-nomal distibution, i.e., log s N,8dB. System paametes ae equal to PD max = db, PC max = 5 db, Poutage max =., RC S min =. bps/hz, q C = q D =.25. We set the coefficients c = c 2 =.496 and w =.729 fo PSO algoithm and simulated fo iteations. A. Convegence Fig. 2 shows the convegence of the algoithm. Fo the limited feedback scheme, we conside, 2, and 3 bits to display the esults clealy. To demonstate the pefomance of the poposed system, the esults ae obtained fo non-noisy and noisy limited-feedback schemes fo both the pefect and impefect CDI. The PSO method, geneally, does not guaantee to achieve global optimum fo n-dimensional functions. It is difficult to pove and show mathematically that PSO can guaantee global optima in ou poblem. Howeve, we have used diffeent seaches to show the eliability of the PSO in Fig. 3. As it is shown, with diffeent andom initialization of swam of paticles in the diffeent pat of poblem space, all of the solutions convege to the same point. B. The Effect of the System Paametes In Fig. 4 and Fig. 5, the D2D aveage ate is plotted vesus the maximum tansmit powe of D2D use PD max and the diffeent numbe of BC and D2D feedback bits M,N. In Fig. 4, the D2D aveage ate is studied fo pefect CDI and paametic CDI estimation method as well as noisy feedback. Obviously with inceasing PD max, the aveage ate of D2D inceases due to inceasing the feasibility set of the esouce allocation poblem with the elaxation of constaint on the tansmit powe of D2D use. As we can see, some cuves ae flattened when the D2D powe constaint is inceased. This is because the cellula ate constaint becomes the dominant facto in the optimization poblem and D2D ate can not D2D Aveage Rate bps/hz Numbe of Iteations Pefect CDI, M=N Bit Pefect CDI, M=N 2 Bits Pefect CDI, M=N 3 Bits CDI Estimation with =.2, M=N Bit CDI Estimation with =.2, M=N 2 Bits CDI Estimation with =.2, M=N 3 Bits Noisy Feedback, M=N Bit Noisy Feedback, M=N 2 Bits Noisy Feedback, M=N 3 Bits Fig. 2. Achieved aveage ate of D2D vs. numbe of iteation fo PSO algoithm fo diffeent feedback bits as well as eo fee feedback, impefect CDI and noisy feedback. D2D Aveage Rate bps/hz Numbe of Iteations Fig. 3. Achieved aveage ate of D2D vs. numbe of iteation fo PSO algoithm fo diffeent andom initialization of paticles. System paametes: =.2 and M = N = 3 bits. D2D Aveage Rate bps/hz Pefect CDI, M=N Bit Pefect CDI, M=N 2 Bits Pefect CDI, M=N 3 Bits CDI Estimation with =.2, M=N Bit CDI Estimation with =.2, M=N 2 Bits CDI Estimation with =.2, M=N 3 Bits Noisy Feedback, M=N Bit Noisy Feedback, M=N 2 Bits Noisy Feedback, M=N 3 Bits Pd max db Fig. 4. Achieved aveage ate of D2D vs. P D,max, fo diffeent feedback bits as well as eo fee feedback, impefect CDI and noisy feedback. D2D Aveage Rate bps/hz Pefect CDI M=N Bit Pefect CDI M=N 2 Bits Pefect CDI M=N 3 Bits CDI Estimation with =., M=N Bit CDI Estimation with =., M=N 2 Bits CDI Estimation with =., M=N 3 Bits CDI Estimation with =.2, M=N Bit CDI Estimation with =.2, M=N 2 Bits CDI Estimation with =.2, M=N 3 Bits CDI Estimation with =.3, M=N Bit CDI Estimation with =.3, M=N 2 Bits CDI Estimation with =.3, M=N 3 Bits Pd max db Fig. 5. Achieved aveage ate of D2D vs. P D,max, fo paametic method and diffeent. incease with inceasing the tansmit powe. To study the effect of pecent eo of impefect CDI, in Fig. 5 the D2D

10 D2D Aveage Rate bps/hz Pefect CDI, M=N Bit Pefect CDI, M=N 2 Bits Pefect CDI, M=N 3 Bits CDI Estimation with =.2, M=N Bit CDI Estimation with =.2, M=N 2 Bits CDI Estimation with =.2, M=N 3 Bits Noisy Feedback, M=N Bit Noisy Feedback, M=N 2 Bits Noisy Feedback, M=N 3 Bits P outage max Fig. 6. Achieved aveage ate of D2D vs. P outage,max, fo diffeent feedback C bits as well as eo fee feedback, impefect CDI BC and noisy feedback. D2D Aveage Rate bps/hz C Rs min bps/hz Pefect CDI M=N, Bit Pefect CDI M=N, 2 Bits Pefect CDI M=N, 3 Bits CDI Estimation with =.2, M=N Bit CDI Estimation with =.2, M=N 2 Bits CDI Estimation with =.2, M=N 3 Bits Noisy Feedback, M=N Bit Noisy Feedback, M=N 2 Bits Noisy Feedback, M=N 3 Bits Fig. 7. Achieved aveage ate of D2D vs. minimum sececy ate of cellula netwok; R C min S, fo diffeent feedback bits as well as eo fee feedback, impefect CDI and noisy feedback. D2D Aveage Rate bps/hz q C, q D Noisy Feedback, M=N 3 Bits Noisy Feedback, M=N 2 Bits Noisy Feedback, M=N Bit Fig. 8. Achieved aveage ate of D2D vs. coss ove pobabilities of the feedback channels; q C,q D fo M = N = 2 bits. aveage ate is obtained fo diffeent eos. As it is shown, by inceasing the eo, the D2D achievable ate deceases. Fig.6 descibes the pefomance of D2D communication in tems of the maximum outage pobability fo cellula communication Poutage max and diffeent numbe of feedback bits. As the maximum outage pobability limit inceases, the D2D aveage ate inceases. Specifically, fo smalle Poutage, max the oveall D2D ate inceases faily apidly. Hence, if the cellula communication can withstand slight sececy outage pobability, simultaneous D2D communication can be a geat advantage. Simila to that of the pevious case, the cuves become flat since it is limited by D2D powe constaint. In Fig. 7, the effect of the minimum equied sececy ate of the cellula netwok RS C min on the D2D ate is illustated. Obviously, when the minimum sececy ate of the cellula netwok inceases, the opeation of D2D communication is limited. Theefoe, the D2D aveage ate is educed. In Fig. 8 the effect of q C and q D is studied. As it is shown, by gowing the eo pobability, i.e, the quality of the feedback link degades, we see the decline in the ate of D2D. As it is seen in all figues, the inceasing numbe of feedback bits esults in the impovement of the D2D pefomance, and the aveage ate inceases. Also, the esults demonstate that the pefomances of the limited-feedback scheme without noise have the bette pefomance in compaison with the noisy case. C. CDI Estimation Eo To check out the effect of CDI estimation on the pefomance of the system, is define as the pecent of the diffeence between the aveage ate of D2D obtained based on the pefect and estimated CDI. Fig. 9 demonstates as a function of the total numbe of uses fo diffeent numbes of the nominal data whee the numbe of outlie data is set to κ =. As the figue shows, fo small L both KDE and RKDE methods pefom vey poo. As L gows, the pefomance of both methods impoves, and fo L = 2, the aveage ate obtained based on RKDE is vey close to that of the pefect CDI case. In Fig., is plotted vesus the numbe of feedback bits fo the diffeent numbe of outlie data κ whee the numbe of nominal data is set to L = 2. As it is seen, the value of is close to zeo fo RKDE method with κ =. As κ gows, inceases implying the divegence fom the actual pdf. It is also obseved that the value of fo KDE is fa away fom zeo and the pefomance degades faste compaed to that of RKDE as κ gows. VII. CONCLUSIONS In this pape, we studied a limited-feedback adio esouce allocation poblem fo the D2D communication scenaio undelaying an existing cellula netwok with the objective of maximizing the D2D aveage ate subject to aveage uses tansmit powe limitations, the aveage sececy ate and outage pobability theshold fo the cellula netwok. Though the PSO algoithm, the appopiate code book fo the channel patitioning was designed. In addition, we solved the poblem when the feedback channel is noisy. To investigate the effect of the CDI impefectness on the pefomance, we applied both the paametic and non-paametic methods. Using simulations, we studied the impact of the system paametes, such as the maximum allowable tansmit powe of D2D use, the numbe of feedback bits, and the minimum sececy ate of cellula netwok, on the achievable ate of D2D. As it was shown, by moe feedback bits, bette D2D pefomance can be achieved. APPENDIX A FINDING OUTAGE PROBABILITY IN 7 To compute the outage pobability in 7, we should compute the success pobability in 8. Note that, we have h BC R BC m = [ h BC m, h BC m + ] and h DD R DD n = [ h DD n, h DD n+]. The success pobability can be witten as follows