REDUCING transmit power and bandwidth consumption. Joint User Association and Resource Allocation Optimization for Ultra Reliable Low Latency HetNets

Transcription

1 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP Jont User Assocaton and Resource Allocaton Optmzaton for Ultra Relable Low Latency HetNets Mohammad Yousefvand, Member, IEEE, Narayan B. Mandayam, Fellow, IEEE, arxv: v1 [cs.ni] 18 Sep 2018 Abstract Ensurng ultra-relable and low latency communcatons (URLLC) s necessary for enablng delay crtcal applcatons n 5G HetNets. We propose a jont user to BS assocaton and resource optmzaton method that s attractve for URLLC n HetNets wth Cellular Base Statons (CBSs) and Small Cell Base Statons (SBSs), whle also reducng energy and bandwdth consumpton. In our scheme, CBSs share portons of the avalable spectrum wth SBSs, and they n exchange, provde data servce to the users n ther coverage area. We frst show that the CBSs optmal resource allocaton (ORA) problem s NP-hard and computatonally ntractable for large number of users. Then, to reduce ts tme complexty, we propose a relaxed heurstc method (RHM) whch breaks down the orgnal ORA problem nto a heurstc user assocaton (HUA) algorthm and a convex resource allocaton (CRA) optmzaton problem. Smulaton results show that the proposed heurstc method decreases the tme complexty of fndng the optmal soluton for CBS s sgnfcantly, thereby beneftng URLLC. It also helps the CBSs to save energy by offloadng users to SBSs. In our smulatons, the spectrum access delay for cellular users s reduced by 93% and the energy consumpton s reduced by 33%, whle mantanng the full servce rate. Index Terms User assocaton, spectrum allocaton, power allocaton, cellular base statons, URLLC, HetNets. I. INTRODUCTION REDUCING transmt power and bandwdth consumpton of base statons are crucal to enhance the energy and spectral effcency of cellular networks, specally n hgh load stuatons where the user demands exceed avalable network resources [1]. In HetNets, t s well known that cellular base statons (CBSs) can save both spectrum and energy by offloadng users to overlad Small cell Base Statons (SBSs). To motvate SBSs to serve cellular users, the CBS grants some porton of ts lcensed spectrum to SBSs who serve the offloaded users, and the amount of granted bandwdth must be larger than that requred to serve the offloaded users. After offloadng, each CBS has to optmze ts bandwdth and power allocaton to those users who are retaned and need to be served drectly. Besdes reducng the overall transmt energy and bandwdth consumpton from the CBS pont of vew, specfcally for URLLC we need to reduce the spectrum access delay for the users to enable Ths work was supported n part by NSF under Grant No and Grant No. ACI M. Yousefvand s wth Wreless Informaton Network Laboratory (WIN- LAB, Rutgers Unversty, NJ E-mal: my342@wnlab.rutgers.edu. NB. Mandayam s wth Wreless Informaton Network Laboratory (WIN- LAB, Rutgers Unversty, NJ E-mal: narayan@wnlab.rutgers.edu. delay senstve applcatons. To do so, we need to fnd new resource allocaton mechansms for BSs that have a low tme complexty besdes beng energy and bandwdth effcent. In ths work we consder a HetNet model wth one CBS and multple SBSs, and show that the CBS s Optmal Resource Allocaton (ORA) problem, whch ncludes the jont user assocaton and bandwdth/power allocaton problems, s a non-convex NP-hard problem. It s actually a combnatoral problem whch s composed of three sub problems. The frst sub-problem s the users-to-bss assocaton problem whch assgns users to the CBS or SBSs and can be seen as a classfcaton problem. The second and thrd sub-problems are power and bandwdth allocaton problems, respectvely. Then, to make the orgnal ORA problem solvable n a reasonable tme for a HetNet wth a large number of users, we propose a new Relaxed Heurstc Method (RHM) whch ncludes a heurstc user assocaton algorthm, and a convex optmzaton problem for power/bandwdth allocaton. After solvng the user assocaton problem usng the proposed heurstc, and removng user assocaton optmzaton varables from the orgnal ORA problem, t reduces to a convex optmzaton problem that mnmzes the CBS s power consumpton, whle servng users wth the mnmum bandwdth possble. To further reduce the tme complexty of RHM and reduce the spectrum access delay, we use the Alternatng Drecton Method of Multplers (ADMM) to solve the resource allocaton optmzaton problem formulated n RHM. Smulaton results show that our proposed heurstc method can sgnfcantly reduce the tme complexty of fndng the optmal soluton for user assocaton and resource allocaton optmzaton problems n ORA. The rest of ths paper s organzed as follows. Secton II provdes the lterature revew, and secton III ntroduces the system and network model. The ORA problem s formulated n secton IV, and the heurstc method s descrbed n secton V. Smulaton results are presented n secton VI, and we conclude n secton VII. II. LITERATURE REVIEW In wreless HetNets, user assocaton, power allocaton and spectrum allocaton are tghtly coupled as has been shown n the vast amount of lterature [2] [12]. Most of these works are focusng on optmzng one of the BS resources whle dong the user assocaton. For example, n [2] a jont user assocaton and green energy allocaton scheme s proposed

2 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP for HetNets wth hybrd energy sources to mnmze the on-grd energy consumpton. A general framework for jont BS assocaton and power control for wreless HetNets s presented n [3], n whch a prce-based non-cooperatve game theory approach s taken to desgn a dynamc spectrum sharng algorthm for two-ter macro-femto networks. A dstrbuted backhaul-aware user assocaton and resource allocaton method s proposed n [4] for energy-constraned HetNets, where the authors used the Lagrange dual decomposton method to solve the user assocaton problem, and showed that for the optmal resource allocaton a BS ether assgns equal normalzed resources or provdes an equal long-term servce rate to ts served users. The authors n [5] nvestgated the optmal user assocaton and resource allocaton problem for a network scenaro wth one macro cell and several non-nterferng overlad pco cells, and proposed an algorthm for achevng a max-mn far throughput allocaton across all users. A self-organzng approach to jont user assocaton and resource blankng between network-ters n hghly dense HetNets s developed n [6] where resource blankng s used to partton tme slots nto two orthogonal groups and dedcate them to macrocells and small cells exclusvely usng a novel message-passng algorthm. In [7] a combnatoral optmzaton problem s formulated for jont optmzaton of user to base staton assocaton, and tme-frequency resource block and power allocaton. Then, the authors provded an approxmate soluton for t usng a polynomal complexty two phase approach based on semdefnte relaxaton wth randomzaton. In [8] the authors nvestgated the mpacts of mult-slope path loss models, where dfferent lnk dstances are characterzed by dfferent path loss exponents, and then proposed a framework for jont user assocaton, power and subcarrer allocaton on the downlnk of a HetNet. A novel framework for the jont optmzaton of user assocaton and nterference management n massve MIMO HetNets s presented n [9], n whch resource allocaton problem s cast as a network utlty maxmzaton (NUM) problem, and then a dual subgradent based algorthm s proposed whch converges toward the NUM soluton. In [10] a dstrbuted game model s presented for jont user assocaton and resource allocaton n HetNets. In [11] a Q-learnng based approach s proposed for adaptve resource optmzaton n mult-agent networks to satsfy users QoS demands and provde farness among them. In [12] the authors proposed a resource allocaton scheme for the HetNets wth one macro BS and several mmwave small cell BSs to maxmze the sum rate of the network whle ensurng the mnmum rate requrement for each user. However, most of these works propose combnatoral optmzaton problems wth NP-hard complextes whch cannot be solved n a reasonable tme for URLLC applcatons, as BSs acceptable delay for resource allocaton n 5G networks s bounded to a few mllseconds n 3gpp recommendatons. To address ths ssue, new resource allocaton technques [13] [17] n 5G networks ensure the feasblty of URLLC by jontly consderng the delay and relablty constrants whle optmzng the resource allocaton for BSs. For example, the authors n [13] proposed an optmal resource allocaton strategy for uplnk transmssons to maxmze the delay-senstve area spectral effcency as a performance metrc whle guaranteeng the QoS constrant on relablty. In [14] the authors proposed a method for maxmzng energy effcency for URLLC under strct QoS constrants on both end-to-end delay and overall packet loss. Sutton et al. [15] nvestgated the potentals of usng unlcensed spectrum for enablng ultra relable and low latency communcatons, and suggested some promsng use cases for that. J et al. [16] dscussed the physcal layer challenges and requrements for URLLC and presented several enablng technologes for such communcatons n 5G NR downlnk. Kasgar et al. [17] presented a network slcng based resource allocaton framework to provde relable and low latency communcatons to users wth such demands. Whle the works n [13] [17] dscuss URLLC, they do not consder the jont user-to-bs assocaton and resource optmzaton n ths context. In ths work, we frst prove that the jont user assocaton and resource allocaton optmzaton n HetNets s a NP-hard problem whch s ntractable for large number of users. Then, we decompose the orgnal optmzaton problem nto a low complexty heurstc algorthm for user assocaton and resource allocaton. To further mprove the tme complexty of our heurstc method so as to make t attractve for URLLC, we use the Alternatng Drecton Method of Multplers (ADMM) to solve the resource allocaton optmzaton problem defned n our heurstc method. A. Network Model III. SYSTEM MODEL We consder a HetNet model wth one cellular base staton at the center of the network who s responsble to ensure all cellular users wll receve ther requred data servce. We also have some overlad small cell base statons whch cover some of cellular users who located under ther coverage range. Fgure below show our network model, n whch CBS uses hgh power transmssons (denoted wth yellow lnks) to serve users who cannot be offloaded, whle SBSs use low power transmssons (denoted wth gray lnks) to serve cellular users under ther coverage. B. Aucton Model In our model, we assume at the begnnng of the offloadng procedure, each SBS k calculates ts bandwdth requrements to serve each covered cellular user, denoted asφ k, whch s a summaton of two terms:φ p k, whch s the requred bandwdth to serve cellular user, andφ s to serve ts own users. The k, second term s the amount of reward that SBSs ask n exchange for servng cellular users under ther coverage. So, the total amount of bandwdth asked by SBSs to serve any user s gven by Φ k, =Φ p k, +Φs k,. (1) Assumng the k-th SBS s transmt power-spectral densty s p s, and the channel fadng between the k-th SBS and the

3 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP Fg. 1. Network Model. -th cellular user s denoted by h s, the requred bandwdth by k, SBS k to serve cellular user,φ p can be derved by solvng k, the equaton r mn =Φ p k, log(1+(ps h s k, 2 )/N 0 ), (2) where, r mn s the mnmum data rate of cellular user that should be guaranteed by ts servng base staton. We also assume the overall cost of the cellular base staton s gven by C= µ c p p + c w w, (3) n whch,µ s the user assocaton varable where,µ = 0 f user s offloaded to SBSs, andµ = 1 f user s not offloaded; p s the transmsson power spectral densty of CBS whle servng cellular user ; w s the amount of bandwdth used by CBS to serve cellular user ; and U s the set of cellular users. IV. CBS OPTIMAL RESOURCE ALLOCATION (ORA) After defnng the cost functon of cellular base staton, we formulate and optmzaton problem to mnmze CBS s cost, whle guaranteeng the mnmum data rate for cellular users. The ORA problem formulaton s gven by: mn (µ,w,p ) (µ c p p + c w w ), (4) subject to : (µ w +β k, φ k, )=W, (5) w log(1+p h p 2 /N 0 ) µ r mn, U, (6) 0 p p max, U, (7) 0 w w max, U, (8) µ +β k, = 1 U. (9) The constrant n Eq. 26 ensures that the overall bandwdth used by cellular base staton to serve users locally or to offload them to SBSs wll not exceed the total avalable bandwdth, denoted as W. The constrant n Eq. 6 guarantees that the data rate offered to cellular users wll be hgher than the mnmum data rate requred by them. Note that n the rght hand sde of ths constrant r mn s multpled by the bnary user assocaton varable,µ, whch means that f user s not been offloaded (µ = 1), then cellular base staton has to guarantee r mn data rate, otherwse f user s offloaded (µ = 0), the rght hand sde becomes zero, meanng that cellular base staton does not requre to guarantee any data rate to ths user,.e. p = 0, w = 0. The constrants n Eq. 7 and Eq. 8 ensure that the allocated power and bandwdth to each user fall wthn the the feasblty regons for power and bandwdth varables, respectvely. And the last constrant n Eq. 27 ensures that each user can be served by ether cellular or a small cell base staton, and not both of them. Note thatβ k, s a bnary assocaton varable wthβ k, = 1 s user s offloaded to SBS k, andβ k, = 0, otherwse, where k s the ndex of the best servng SBS for each user A. Complexty and Scalablty ssues of ORA In the ntal ORA problem formulaton presented n prevous secton, snce t jontly optmzes all the user assocaton, power and bandwdth allocaton varables, t s a combnatoral problem wth hgh tme complexty [18]. In Theorem 1 we prove that the ORA problem s NP-hard. Hence, ts not scalable for large scale networks wth large number of users as t cannot be solved n polynomal tme; and also consderng the dynamcs of channel states n wreless networks whch are varyng by tme, we need to fnd a low complexty soluton to ORA problem to solve t wthn an acceptable tme. Theorem 1. The ORA problem s an NP-hard problem. Proof: We show that a smplfed verson of the ORA problem s reducble to the knapsack problem whch s a well known NP-hard problem [19]; hence, ORA s also NP-hard. For the datals of the proof, see Appendx A. To address the scalablty ssue of the ORA we can replace t wth a dstrbuted user assocaton and resource allocaton method and use the technques of game theory to solve t. For example, n [20] we modeled the user assocaton problem n HetNets n a form of a Stackelberg game between cellular and WF servce provders as the leaders, and users as the followers of the game, and we found the Nash equlbra solutons to that problem under dfferent condtons. The other soluton to the scalablty ssue of ORA, whch we propose n ths work s to change the ntal ORA formulaton by breakng t down nto two smaller sze problems wth low complextes. In ths work we replace the ntal ORA problem wth a heurstc user assocaton problem and a convex power/bandwdth allocaton problem. V. RELAXED HEURISTIC METHOD (RHM) As mentoned n prevous secton, we replace the NP-hard ORA problem wth a two phase low complexty soluton, n

4 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP whch we frst solve the user assocaton problem usng a heurstc user assocaton (HUA) algorthm, and then we optmze the CBS s power/bandwdth allocaton usng a Convex Resource Allocaton (CRA) algorthm. A. Heurstc User Assocaton (HUA) Snce the user assocaton varables n ORA optmzaton (µ, U) are bnary varable and optmzaton problems wth bnary optmzaton varables are often NP-hard, n ths secton we propose a heurstc low complexty soluton to user assocaton problem whch can be solved n polynomal tme. From the Shannon formula for the capacty of wreless lnks we have r = w log(1+ p h 2 /N 0 ). (10) If we rewrte ths formula n terms of transmt power we have p = N 0 (2 r /w 1)/ h 2, (11) and takng a dervatve of transmt power, p, wth respect to data rate, r, we have p r = N 02 r/w ln2 w h 2 > 0. (12) As we can see, p r, s always postve, meanng that CBS s requred transmsson power has a drect relaton wth the users offered data rate, and to mnmze power consumpton, base statons should mnmze ther offered data rate. So, t proves that the data rate constrants n ORA formulaton gven n Eq. 6 wll be always satsfed wth equalty,.e. to mnmze the power consumpton, the cellular base staton wll always offer the mnmum acceptable data rate to cellular users, r = r mn. Knowng that, we can replace the data rate varable r wth the mnmum data rate r mn. In ths case, the mnmum requred BW for cellular base staton to serve any cellular user, denoted as w mn can be derved by solvng r mn = w mn log(1+p max h p 2 /N 0 ), (13) where, p max s the maxmum power spectral densty of CBS, and h p s the channel gan between CBS and cellular user. After dervng the mnm bandwdth requred for servng all users, CBS consders w mn, and p max as a rough estmatons of the amount of bandwdth and power requred to serve each user, and uses ths parameters to estmate the cost of servng for each user. Then, CBS compares the cost of servng wth the cost of offloadng for each user to make a decson about servng t drectly or offloadng t to SBSs. Assumng c w as the unt cost of bandwdth and c p as the unt cost of power for cellular base staton, the servng cost of user can be estmated by c w w mn + c p p max. Also, the cost of offloadng for user s gven by c w φ k,, n whch k s the ndex of the best servng WF SP who asked for mnmum amount of bandwdth to serve user. After calculatng the cost of offloadng and the estmated cost of servng for each user, our heurstc algorthm wll solve user assocaton by smply comparng the offloadng and servng costs for each user. Algorthm 1 Heurstc User Assocaton (HUA) for users from 1.. N do k arg mn k φ k, fnd the best servng WF BS f ( c w φ k, (c w w mn + c p p max )) then Serve user locally:µ = 1, β k,= 0 else f ( c w φ k,< (c w w mn + c p p max )) then Offload user to WF BS k : µ = 0, β k, = 1 returnµ,β k, The proposed heurstc user assocaton algorthm s gven as follows: By runnng ths heurstc, cellular base staton determnes whch users should be offloaded and whch users should be served drectly, to mnmze ts cost. After runnng ths heurstc algorthm, the µ and β k, are known parameters to CBS and we do not need to defne them as varables n the optmzaton problem for resource allocaton. It smplfes the ntal ORA problem greatly by removng the bnary optmzaton varables from t and replacng them wth gven parameters. B. Convex Resource Allocaton (CRA) Knowng the values of user assocaton varables, we can smplfy the orgnal ORA problem by reformulatng t n a form of a convex optmzaton problem. To do that, we frst use the convex cost functon C=c T p p+γct ww, (14) to calculate the CBS s cost, whch s a lnear and convex functon n both p, and w varables. The frst term of ths cost functon denotes the CBS s power consumpton cost whch s the multplcaton of unt cost vector by the actual power allocaton vector of CBS, p. Also, the second term n Eq. 14 denotes the CBS s bandwdth cost regularzed by a regularzaton parameterγ, 0 < γ 1, whch models the trade-off between power and bandwdth costs. The vectors c p and c w are the unt cost vectors for power and bandwdth consumpton, respectvely. We rewrte the data rate constrant, gven n Eq. 6 of the orgnal ORA problem, n a form of a power allocaton constrant as p (e w µ r mn 1)N 0 / h p 2, U. (15) Snce all the parameters n the rght hand sde of Eq. 15 are gven parameters except the w, whch s the bandwdth allocaton varable, we use a change of varable σ = (e w µ r mn 1)N 0 / h p 2 (16) whereσ s just a functon of w, and f we know ts value, then w can be unquely derved from t. Now, we can rewrte the data rate constrant as a power allocaton constrant as p σ, U. Now that we replace all the constrants n ntal ORA problem wth lnear constrants, the Convex Resource Allocaton (CRA) problem can be formulated as:

5 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP mn w,p ct p p+γct ww, (17) subject to : µ T w W, (18) µ T σ p p max, U, (19) 0 w w max, U, (20) where, w s the bandwdth allocaton vector, p s the power allocaton vector, and σ s the vector of mnmum transmsson powers requred by CBS to serve each user. In the left hand sde vector of Eq. 19,µ σ s equal to 0 f user s offloaded, and s equal toσ, otherwse. Note that from Eq. 16, for every gven vector of w,σbecomes a known parameter; hence, ths CRA optmzaton problem turns nto a lnear problem (LP) n p. Smlarly, for every gven vector of p, the CRA problem wll become an LP n w. We can use ths fact to solve the CRA problem usng teratve numercal methods lke Alternatng Drecton Method of Multplers (ADMM). Defnng cost functons f(p)=c T p p, and f(w)=γct ww, the objectve of the CRA problem s to mnmze f(p)+ f(w)=c T p p+γc T ww as the objectve functon. The optmal soluton to such problem wll be (p,w )=n f{f(p)+ f(w) r mn = w log(1+(p h 2 )/N 0 )}. (21) To use ADMM to acheve ths soluton, we need to wrte the dual verson of the CRA problem. Snce we want to mnmze the dstance between offered data rate w log(1+ p h 2 /N 0 ) and the requred data rate r mn, n the Lagrangan functon, L p, we add a new varable y whch s equal to the dfference between the offered and the requred data rates, and s used to model the cost of devatng from target data rate. So, to use ADMM we use the Lagrangan functon below for each user and for each gven values of the varables p and w, whch are the amounts of power and bandwdth allocated to user L(p,w,y )= f(p )+ f(w )+y (r mn w log(1+ p h 2 /N 0 ). (22) Hence, the Lagrangan functon consderng all the users wll be gven as L(p,w,y)= f(p)+ f(w)+y(r mn wlog(1+ p h 2 /N 0 ), (23) n whch, p and w are power and bandwdth allocaton vectors for all users n our network, and r mn s a vector wth the same dmensons whch ncludes the mnmum data rates for all users. We denote the values of power and bandwdth allocaton varables at each step k as p k and w k, respectvely. To mnmze the Lagrangan functon usng an teratve updates, we start from two ntal values for power and bandwdth varables. Then, at each step k we use the values of these parameters p k and w k to fnd the best value for the varable y to be used n the next step, y k+1, by mnmzng the lagrangan functon wth respect to y. Then, usng the value of w k,y k+1 we fnd the value of p k+1, and usng the values of p k+1,y k+1 n the Lagrangan functon we fnd the best value of w k+1. Ths update procedure s gven n: Fg. 2. Smulated Network Scenaro. y k+1 = Arg mn y L(p k,w k,y), p k+1 = Arg mn p L(p,w k,y k+1 ), w k+1 = Arg mn w L(p k+1,w,y k+1 ). (24) We contnue ths teratve updates untl the convergence, whch s defned as the state n whch the offered data rates are very close to the requred data rates, and p and w have ther lowest possble value. Note that snce we removed the bnary user assocaton varables, now the Lagrangan functon s contnuous and dfferentable wth respect to all the varables p, w, and y. And we can smply take a dervatve from the lagrangan functon n each teraton to fnd ts optmal value w.r.t any varable whle the other two varables are gven parameters. VI. SIMULATION RESULTS To evaluate the effcency of our proposed heurstc method, we consder a HetNet scenaro n whch there s one CBS located n the center of a cell wth the radus of 1000 ft, and there are 8 overlad SBSs wth shorter coverage ranges of 300 ft wthn that cell who can serve the cellular users under ther coverage. We also assume that there are 300 cellular users who are randomly dstrbuted wthn the cell. The smulated HetNet s shown n the Fg. 2. For our frst experment, we assume that the mnmum acceptable data rate for users, b mn, s equal to 128 kbps. We solved the jont user assocaton and resource allocaton problem for the CBS usng both ORA and RHM methods, by mplementng these methods n Matlab. For better comparson, and to show the effects of users offloadng on reducng the CBS s cost, we also mplemented the Drect Servng Method (DSM) n whch CBS serves all the cellular users drectly wthout offloadng any of them to SBSs. In DSM method CBS optmzes ts bandwdth and power allocatons to mnmze ts servng cost usng the cost functon defned n Eq. 14. We compare the performance parameters of these three methods n Table VI.

6 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP Algorthm DSM ORA RHM Runng Tme (sec) Avg Cost Per User Servng Rate 100% 100% 100% Total Ofloaded Users As we can see from ths table, n both ORA and RHM methods 226 users (.e % of the total 300 users) have been offloaded to the overlad SBSs. Offloadng of these users reduces the CBS s average energy and bandwdth cost per user from unt cost (UC) n DSM method to UC and UC n ORA and RHM methods, respectvely whch leads to the reducton of CBS s total energy and bandwdth cost by nearly 33% as compared to DSM. Also, as we can see n Table VI, although the offloadng rate and the average cost per user n both ORA and RHM methods are the same, but the RHM s runnng tme s a fracton of the runnng tme for ORA method. In fact, usng the proposed heurstc method, we can reduce the resource allocaton tme for the CBS from sec n ORA (whch s an NP-hard method) to only 3.68 sec n RHM, whch leads to the 93% reducton n spectrum access delay for cellular users. For our smulatons we used a laptop wth an Intel core GHz processor, and usng a faster processor can further reduce the spectrum access delay to a few mllseconds. Fg. 3 compares the CBS s energy and bandwdth consumpton cost for each user n the ORA, RHM and DSM methods. As shown n ths fgure, for those users who have been offloaded by CBS usng ORA method (whch have servce costs less than 80), the cost of servng s the same n both RHM and ORA methods whch means that the RHM heurstc user assocaton method has acheved the same results for user assocaton as n ORA method. The reason s that the dfference between the cost of servng and offloadng for users who have been offloaded by ORA method s bg enough that the heurstc user assocaton method can also dentfy that offloadng those users has lower cost than servng them drectly. Also, t s shown n ths fgure that both RHM and ORA methods can reduce the CBS s average cost for the offloaded users sgnfcantly as compared the DSM method. The reason s that SBSs have better channel condtons and usually requre less power and bandwdth to serve to serve cellular users under ther coverage as compared to the CBS. So, by takng advantage of offloadng users to SBSs, the CBS can reduce ts energy and bandwdth consumpton cost by 33% as shown n the Table VI. To see the effects of load on the servng rate of cellular users n each of the ORA, RHM and DSM methods, we change the number of users n our HetNet model from 300 users to 500 users, by ncreasng t by 20 users n each step. We defne the servce rate as the percentage of users who are gettng a data servce wth a rate hgher than ther mnmum acceptable rate. The Fg. 4 compares the servce rates of DSM, ORA, and RHM methods under dfferent load stuatons. As we can see, by ncreasng the load the CBS s unable to serve all the users n DSM method, and the servce rate goes below 50% f number of users exceeds 600, whle n both ORA and RHM methods by explotng the cooperaton between CBS Fg. 3. Comparng cost per user n DSM, ORA and RHM. Servng Rate Servng Rate ORA Servng Rate RHM Servng Rate DSM Load (Number of Users) Fg. 4. Comparng Servce Rates whle ncreasng the load. and WBSs, and offloadng users to less congested small cells, the full servce rate can be mantaned despte the load. Smlar results are observed when we ncrease the mnmum acceptable data rate for users, from 128 kbps to 512 kbps, to see ts effects on the CBS s servng rate. Agan, the servce rates n DSM wll dmnsh by ncreasng the mnmum acceptable rate for users, whle ORA and RHM methods can preserve the full servce rate. VII. CONCLUSION In ths paper, we consdered a HetNet model to optmze the user-to-bs assocaton and resource allocaton for cellular base statons whle reducng the spectrum access delay for cellular users whch s requred for enablng URLLC n 5G. We frst proposed an optmzaton method for jont user-to- BS assocaton and resource allocaton n HetNets. In order to reduce the hgh tme complexty of the optmzaton method whch makes t ntractable for large number of users, we proposed a low complexty heurstc method whch breaks down the ntal optmzaton problem nto a smple heurstc user assocaton algorthm and a convex resource allocaton optmzaton method. To further reduce the tme complexty of the proposed soluton, we proposed an ADMM-based teratve soluton to the convex resource allocaton problem. Smulaton results valdated the effcency of the relaxed heurstc method, and showed that t can reduce the CBSs energy and bandwdth consumpton by 33%, whle reducng the spectrum access delay for cellular users by 93% whch s attractve to URLLC. Whle n ths paper, we used a HetNet model wth only one CBS and multple SBSs, the proposed approach s also

7 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP applcable n HetNets wth more than one CBS. In such a scenaro, for each user, the CBS wth the strongest rado lnk (channel gan and/or RSSI) wll serve as the prmary CBS among all the canddate CBSs, and that CBS wll make a decson about servng each user drectly or offloadng t to overlad SBSs to save energy and bandwdth followng a smlar procedure as outlned n the paper. APPENDIX A PROOF OF THE THEOREM 1 Proof. We prove ths theorem by showng that a smplfed verson of the ORA problem s reducble to the knapsack problem whch s a well-known NP-hard problem [19]. As shown n Eq. 11, to serve any user assocated to the CBS,.e µ = 1, the CBS s transmt power s a functon of ts data rate and bandwdth. Assumng the amount of bandwdth allocated to user, w, s fxed, the dervatve of p wth respect to r s gven n Eq. 12 where as we can see p r > 0. It means that by fxng the amount of bandwdth allocated to each user, w, the CBS transmt power ncreases by ncreasng the offered data rate to that user. Hence, the CBS wll always serve the cellular users wth the mnmum data rate acceptable by them, r mn, to mnmze ts power consumpton. So, we can smply remove the data rate constrant n Eq. 6 from the ORA problem snce t wll always be satsfed wth equalty. For any user assocated wth CBS, the mnmum bandwdth requred by CBS to serve that user, w mn, can be derved from the Eq. 13 when CBS s transmttng wth ts maxmum power,.e., p = p max. So, by settng p = p max and w = w mn n the ORA problem, the constrants n Eq. 7 and Eq. 8 can be removed, and the smplfed ORA problem can be rewrtten as: mn µ (µ c p p max + c w w mn ), (25) subject to : (µ w mn +β k, φ k, )=W, (26) µ +β k, = 1 U. (27) Snce by offloadng each user to SBSs, CBS can save the amount of p max w mn n transmt power, CBS should maxmze the number of offloaded users usng ts avalable bandwdth, to mnmze ts cost. Now, f we defne W = W as the maxmum amount of extra bandwdth at w mn CBS that can be granted to SBSs as an ncentve to serve cellular users, and φ k, = max { φ k, w mn, 0 } as an amount of extra BW requred by best servng SBS to serve user, then the smplfed ORA problem can be formulated as: max β k, p max w mn (28) Subject to: (β k,) β k, φ k, W. (29) whereβ k, s a bnary assocaton varable wthβ k, = 1 s user s offloaded to SBS k, andβ k, = 0, otherwse, where k s the ndex of the best servng SBS for each user. The above problem s exactly equvalent to the zero-one knapsack problem whch s an NP-hard problem. Hence, ORA problem s also NP-hard. REFERENCES [1] A. Hajsam, T. X. Tran and D. Pompl, Elastc-Net: Boostng Energy Effcency and Resource Utlzaton n 5G C-RANs, IEEE Internatonal Conference on Moble Ad Hoc and Sensor Systems (MASS), Orlando, FL, pp , [2] D. Lu, Y. Chen, K. K. Cha, T. Zhang and K. Han, Jont user assocaton and green energy allocaton n HetNets wth hybrd energy sources, IEEE Wreless Communcatons and Networkng Conference (WCNC), New Orleans, LA, pp , [3] Ekram Hossan; Long Bao Le; Dust Nyato, Resource Allocaton n CDMA-Based Mult-ter HetNets, Rado Resource Management n Mult-Ter Cellular Wreless Networks, Wley Telecom, 2014, pp.352-, do: / ch8 [4] Q. Han, B. Yang, G. Mao, C. Chen, X. Wang and X. Guan, Backhaul- Aware User Assocaton and Resource Allocaton for Energy-Constraned HetNets, IEEE Transactons on Vehcular Technology, vol. 66, no. 1, pp , Jan [5] S. Borst, S. Hanly and P. Whtng, Optmal resource allocaton n HetNets, IEEE Internatonal Conference on Communcatons (ICC), Budapest, pp , [6] S. H. Lee and I. Sohn, Message-Passng Strategy for Jont User Assocaton and Resource Blankng n HetNets, IEEE Transactons on Wreless Communcatons, vol. 17, no. 2, pp , Feb [7] H. U. Sokun, R. H. Gohary and H. Yankomeroglu, A Novel Approach for QoS-Aware Jont User Assocaton, Resource Block and Dscrete Power Allocaton n HetNets, IEEE Transactons on Wreless Communcatons, vol. 16, no. 11, pp , Nov [8] H. Munr, S. A. Hassan, H. Pervaz, Q. N and L. Musavan, Resource Optmzaton n Mult-Ter HetNets Explotng Mult-Slope Path Loss Model, IEEE Access, vol. 5, pp , [9] Q. Ye, O. Y. Bursaloglu, H. C. Papadopoulos, C. Caramans and J. G. Andrews, User Assocaton and Interference Management n Massve MIMO HetNets, IEEE Transactons on Communcatons, vol. 64, no. 5, pp , May [10] T. Z. Oo, N. H. Tran, T. LeAnh, S. M. A. Kazm, T. M. Ho and C. S. 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8 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING LATEX CLASS FILES, VOL., NO., SEP Mohammad Yousefvand s a phd canddate n Electrcal Engneerng n ECE department of Rutgers Unversty, New Brunswck, NJ, US. He s currently wth the Wreless Informaton Network Laboratory (WINLAB) at Rutgers Unversty where he works on several NSF funded projects n dfferent areas of wreless communcatons and networkng. He s the recpent of Gary Thomas doctoral fellowshp (annually 54, 000) from New Jersey Insttute of Technology for academc years, and professonal development fund from Rutgers Unversty for academc years. Hs research nterests nclude nterference mtgaton and resource allocaton n wreless heterogeneous networks, cogntve rado, prospect theory, game theory, and performance evaluaton. Narayan B. Mandayam (S89 M94 SM99 F09) receved the B.Tech (Hons.) degree n 1989 from the Indan Insttute of Technology, Kharagpur, and the M.S. and Ph.D. degrees n 1991 and 1994 from Rce Unversty, all n electrcal engneerng. Snce 1994 he has been at Rutgers Unversty where he s currently a Dstngushed Professor and Char of the Electrcal and Computer Engneerng department. He also serves as Assocate Drector at WINLAB. He was a vstng faculty fellow n the Department of Electrcal Engneerng, Prnceton Unversty, n 2002 and a vstng faculty at the Indan Insttute of Scence, Bangalore, Inda n Usng constructs from game theory, communcatons and networkng, hs work has focused on system modelng, nformaton processng and resource management for enablng cogntve wreless technologes to support varous applcatons. He has been workng recently on the use of prospect theory n understandng the psychophyscs of prcng for wreless data networks as well as the smart grd. Hs recent nterests also nclude prvacy n IoT, reslent smart ctes as well as modelng and analyss of trustworthy knowledge creaton on the nternet. Dr. Mandayam s a co-recpent of the 2015 IEEE Communcatons Socety Advances n Communcatons Award for hs semnal work on power control and prcng, the 2014 IEEE Donald G. Fnk Award for hs IEEE Proceedngs paper ttled âăijfronters of Wreless and Moble CommuncatonsâĂİ and the 2009 Fred W. Ellersck Prze from the IEEE Communcatons Socety for hs work on dynamc spectrum access models and spectrum polcy. He s also a recpent of the Peter D. Cherasa Faculty Scholar Award from Rutgers Unversty (2010), the Natonal Scence Foundaton CAREER Award (1998) and the Insttute Slver Medal from the Indan Insttute of Technology (1989). He s a coauthor of the books: Prncples of Cogntve Rado (Cambrdge Unversty Press, 2012) and Wreless Networks: Multuser Detecton n Cross-Layer Desgn (Sprnger, 2004). He has served as an Edtor for the journals IEEE Communcaton Letters and IEEE Transactons on Wreless Communcatons. He has also served as a guest edtor of the IEEE JSAC Specal Issues on Adaptve, Spectrum Agle and Cogntve Rado Networks (2007) and Game Theory n Communcaton Systems (2008). He s a Fellow and Dstngushed Lecturer of the IEEE.