1 Spectum Shaing between Public Safety and Commecial Uses in 4G-LTE Haya Shajaiah, Ahmed Abdel-Hadi and Chales Clancy Badley Depatment of Electical and Compute Engineeing Viginia Tech, Alington, VA, 22203, USA {hayajs, aabdelhadi, tcc}@vt.edu Abstact In this pape, we conside esouce allocation optimization poblem in fouth geneation long tem evolution 4G- LTE fo public safety and commecial uses unning elastic o inelastic taffic. Each mobile use can un delay-toleant o eal-time applications. In ou poposed model, each use equipment UE is assigned a utility function that epesents the application type unning on the UE. Ou objective is to allocate the esouces fom a single evolved node B enodeb to each use based on the use application that is epesented by the utility function assigned to that use. We conside two goups of uses, one epesents public safety uses with elastic o inelastic taffic and the othe epesents commecial uses with elastic o inelastic taffic. The public safety goup is given pioity ove the commecial goup and within each goup the inelastic taffic is pioitized ove the elastic taffic. Ou goal is to guaantee a minimum quality of sevice QoS that vaies based on the use type, the use application type and the application taget ate. A ate allocation algoithm is pesented to allocate the enodeb esouces optimally among public safety and commecial uses. Finally, the simulation esults ae pesented on the pefomance of the poposed ate allocation algoithm. Index Tems esouce Allocation, Application Taget ate, Elastic Taffic, Inelastic Taffic I. INTODUCTION The public safety wide aea wieless communication system is cuently sepaate fom the commecial cellula netwoks. Industies ae willing to suppot both communities by poviding a common technology. elease 12 of 3GPP LTE standads will enhance LTE to suppot public safety equiements. Advanced standads such as LTE povide multimedia capabilities and voice and messages sevices at multi-megabit pe second. The sevices that public safety netwoks povide such as communications fo police, fie and ambulance equie systems development to meet the communication needs of emegency sevices. A common technical standad fo commecial and public safety uses povides advantages fo both. The public safety systems maket is much smalle than the commecial cellula maket which makes it unable to attact the level of investment that goes in to commecial cellula netwoks and this makes a common technical standads fo both the best solution. The public safety community gains access to the technical advantages povided by the commecial cellula netwoks wheeas the commecial cellula community gains enhancement in thei systems and make it moe attactive to consumes. The USA has eseved spectum in the 700MHz band fo an LTE based public safety netwok. The cuent public safety standads suppot medium speed data which dives the need of new technology. In [1], the autho pesented a utility popotional fainess esouce allocation appoach, whee fainess is in utility pecentage, fo 4G-LTE that optimally allocate one enodeb esouces based on the optimization poblem that solves fo elastic and inelastic utility functions. The ate allocation algoithm in [1] gives pioity to eal-time applications ove delay-toleant applications and guaantees a minimum QoS when allocating esouces. In this pape, we focus on finding an optimal solution fo the esouce allocation poblem fo two goups of uses unning two types of applications pesented by logaithmic utility functions o sigmoidal-like utility functions. These utility functions ae concave and non-concave utility functions espectively. The optimization poblem allocates pat of the bandwidth fom one enodeb to each use subscibing fo a mobile sevice taking into consideation that each use is getting a minimum QoS. In addition, the public safety uses in emegency mode ae given pioity ove the commecial uses and within each goup the non concave functions that ae appoximated by sigmoidal-like functions and pesenting ealtime applications ae given pioity ove the concave functions appoximated by logaithmic functions and pesenting delay toleant applications. In ou system model, each public safety subscibe has an assigned application taget ate that vaies based on the application type and assigned to the public safety subscibe by the netwok. Ou esouce allocation algoithm fist allocates the application taget ate to each public safety UE when that UE is in emegency mode. It then allocates the emaining esouces among the commecial UEs subscibing fo esouces. A. elated Wok In [2], The authos intoduced bandwidth popotional fainess Fank Kelly algoithm. This algoithm is an iteative pocess fo detemining ate allocation as well as the pice the netwok should chage fo given sets of esouces. The iteative natue of the solution allows uses to bid fo esouces until the allocated ate matches the optimal ate based on bandwidth popotional fainess. In [3], the autho pesented a weighted aggegation of elastic and inelastic utility functions fo each UE. The utility functions ae then appoximated to the 978-1-4799-2358-8/14/$31.00 2014 IEEE 674
neaest concave utility function fom a set of functions using minimum mean squae eo. The esulting utility functions ae solved using a modified vesion of the distibuted ate allocation algoithm by Fank Kelly [2]. A ate allocation with caie aggegation is pesented in [4]. The authos used two stage modified Fank Kelly algoithm to allocate two caies esouces optimally among UEs with eal time applications o delay toleant applications. One of the caies is pimay caie and is used in the fist stage of the algoithm wheeas the othe is seconday caie and is used in the second stage. A pioity is given to the eal time applications pesented by a sigmoidal-like utility functions while allocating esouces in each stage. In [5], the authos pesented two stage esouce allocation algoithm to allocate optimal ates to uses unning multiple applications fom one enodeb. The poposed algoithm achieves the optimal ates without enodeb knowledge of the UEs utilities. In [6], a ound obin packet scheduling method is used to distibute the load acoss the netwok. This method is not fai fo esouce allocation as the netwok could be inefficient in bandwidth and thoughput. In [7] and [8], the authos used elastic and sigmoidal-like utility functions in a nonconvex optimization poblem to imize utility functions in wieless netwoks. Using -min achitectue, the authos in [9] poposed a utility popotional fai optimization appoach fo high SIN wieless netwoks. B. Ou Contibutions Ou contibutions in this pape ae summaized as: We pesent a esouce allocation optimization poblem to allocate the enodeb esouces optimally among public safety and commecial uses. The enodeb and the UE collaboate to allocate an optimal ate to each UE with pioity given to public safety uses. Within the same goup of uses, a pioity is given to eal time applications pesented by sigmoidal-like utility functions. We show that each of ou two cases esouce allocation A optimization poblems has a unique tactable global optimal solution. The emainde of this pape is oganized as follows. Section II pesents the poblem fomulation. In section III, we pesent the two cases esouce allocation optimization poblems. Section IV pesents ou distibuted caie aggegation ate allocation algoithm fo the utility popotional fainess optimization poblem. In section V, we discuss simulation setup and povide quantitative esults along with discussion. Section VI concludes the pape. II. POBLEM FOMULATION We conside single cell 4G-LTE mobile system with a single enodeb, N commecial UEs and M public safety UEs. The use i is allocated cetain bandwidth i based on the type of application the UE is unning. Each use is assigned a utility function U i i based on the application unning on the UE and whethe it is a commecial o public safety use. Ou goal is to detemine the optimal bandwidth that needs to be allocated to each use by the enodeb. The utility functions U i i ae assumed to be a stictly concave o a sigmoidal-like functions. The utility functions U i i have the following popeties: U i 0 = 0 and U i i is an inceasing function of i. U i i is twice continuously diffeentiable in i and bounded above. In ou model, we use the nomalized sigmoidal-like utility function pesented in [10], that is 1 U i i = c i 1 + e d aii bi i 1 whee c i = 1+ea i b i 1 and d e a i b i i = that satisfies U0 = 0 1+e a i b i and U = 1. The inflection point of the nomalized sigmoidal-like function is at i inf = b i. Additionally, we use the nomalized logaithmic utility function used in [9] to epesent a delay toleant application, this utility function can be expessed as U i i = log1 + k i i log1 + k i whee gives 100% utility pecentage fo any use and k i is the slope of the cuve of the logaithmic utility function that vaies fom use to use. So, it satisfies U0 = 0 and U = 1. The inflection point of nomalized logaithmic function is at i inf = 0 The basic fomulation of the esouce allocation poblem is given by the following optimization poblem: M N U i i,s U j j,c M N i,s + j,c, i,s t i,s, i = 1, 2,..., M j,c 0, j = 1, 2,..., N. whee is the imum achievable ate of the enodeb, = { 1,s,..., M,s, 1,c,..., N,c } whee i,s is the ate fo public safety use i, j,c is the ate fo commecial use j, i,s t is the application taget ate fo public safety use i which is the mnimum ate that the use wants to achieve, M and N ae the numbes of the public safety and commecial UEs, espectively. The esouce allocation objective function imizes the poduct of uses utilities system utility when allocating esouces to each use. Theefoe, it povides a popotional fainess among utilities. Public safety uses that ae unning eal-time applications ae given the pioity when allocating esouces by the enodeb. The next pioity is given to the elastic taffic unning by public safety uses. Once each public safety use satisfies its application taget ate the enodeb stats allocating esouces to commecial uses giving pioity to uses unning eal time applications. We assume that the public safety uses ae in an emegency mode, theefoe these uses ae given a highe pioity ove the commecial uses. The optimization poblem 3 has a unique tactable global optimal solution [1] that will be discussed in the next section. 2 3 2 675
We used utility popotional fainess model because nonzeo ate allocation is guaanteed to all uses. So it is impossible to set a uses allocation to zeo without setting the efficiency of the netwok to zeo. Because this esouce does not disenfanchise any given use, it will be consideed as an appopiate fainess model fo this poblem. III. ESOUCE ALLOCATION OPTIMIZATION POBLEM The esouce allocation fo public safety and commecial uses is divided into two cases. The fist case is when the imum available esouces fo the enodeb is less than the sum of the total application taget ates of the public safety UEs subscibing fo a sevice fom that enodeb and the second case is when is geate than that total. The two cases ae two diffeent optimization poblems that will be solved by ou poposed algoithm to obtain the optimal ate fo each UE. A. The Fist Case A Optimization Poblem when M t i,s As mentioned befoe the fist case optimization poblem is applied in the case of M t i,s. In this case the enodeb only allocates esouces to the public safety uses because they ae consideed moe impotant and the enodeb s available esouces doesn t exceed thei need. The commecial uses will not be given any of the enodeb esouces in this case. This optimization poblem can be witten as: M U i i,s M i,s, 0 i,s t i,s, i = 1, 2,..., M. whee U i is the public safety i th utility function and = { 1,s,..., M,s } and M is the numbe of public safety UEs in the coveage aea of the enodeb. The solution of the optimization poblem 4 is the optimal solution when M t i,s. This solution will guaantee the public safety uses pioity when allocating the enodeb esouces. The optimal ate fo each public safety UE is less than o equal to the application taget ate fo each public safety UE. The public safety uses unning eal time applications will be given pioity ove public safety uses with elastic taffic. The objective function in the optimization poblem 4 is M equivalent to log U i i,s. The optimization poblem 4 is a convex optimization poblem and thee exists a unique tactable global optimal solution as shown in Theoem III.1 [1]. This optimal solution gives each of the M uses an optimal ate opt i,s. B. The Second Case A Optimization Poblem when M t i,s < The second case optimization poblem is applied in the case of M t i,s <. The enodeb collaboate with the UEs to solve this optimization poblem. The enodeb allocates 4 esouces to both the public safety and commecial uses because its available esouces exceed the minimum need of the public safety UEs expessed by the application taget ates. As mentioned befoe, the enodeb gives pioity to the public safety uses and within the public safety goup the pioity is given to the UEs unning inelastic taffic. This optimization poblem can be witten as: M N U i i,s U j j,c M N i,s + j,c, i,s t i,s, i = 1, 2,..., M j,c 0, j = 1, 2,..., N. This optimization poblem is same as the one discussed in the poblem fomulation section II. Fist, the enodeb allocates the application taget ate to each public safety UE. It then stats allocating its emaining esouces both to the public safety and commecial UEs based on utility popotional fainess. The solution of the optimization poblem 5 is the global optimal solution that gives an optimal ate opt i,s public safety UE and an optimal ate opt i,c use UE. 5 to each to each commecial Poposition III.1. The optimization poblem 5 is a convex optimization poblem and thee exists a unique tactable global optimal solution. Poof. We intoduce a new paamete c i whee c i is the application taget ate fo the public safety UE wheeas it is 0 fo the commecial UE, the optimization poblem 5 can be ewitten as follows: M+N M+N U i i + c i i + c i, i 0, i = 1, 2,..., M + N. { t c i = i,s if public safety UE 0 if commecial UE whee is the imum achievable ate of the enodeb, = { 1,..., M, M+1,..., M+N } whee the fist M ates ae fo the M public safety uses and the last N ates ae fo the N commecial uses, U i i + c i is the UE utility function, this optimization poblem guaantees an optimal ate that is at least equal to the application taget ate fo the public safety UE. The objective function in the optimization poblem 6 can be witten as M+N log U i i + c i. The utility function U i i + c i fo the UE is stictly concave o sigmoidal-like function as mentioned in section II. As shown in Theoem III.1 [1], log U i i is a stictly concave function fo a stictly concave o sigmoidal-like utility function. It follows that the optimization poblem 6 that is equivalent to 5 is convex. Theefoe, thee exists a tactable global optimal solution fo the optimization poblem 5. 6 3 676
IV. ALGOITHM In ou poposed iteative algoithm, the enodeb and the UEs collaboate to allocate optimal ates fo the public safety and commecial uses subscibing fo a mobile sevice. Algoithm 1 and algoithm 2 ae the public safety UE and the commecial UE algoithms, espectively. Algoithm 3 is the enodeb algoithm. The algoithm stats when each UE tansmits an initial bid w i 1 to the enodeb. Additionally, each public safety UE tansmits its application taget ate to the enodeb. The enodeb checks whethe the M t i,s is less o geate than and send a flag with this infomation to each UE. In the case of M t i,s, the commecial UEs will not be allocated any of the esouces and will not be sending any futhe bids to the enodeb unless they eceive a flag fom the enodeb with M t i,s <. On the othe hand, each public safety UE checks whethe the diffeence between the cuent eceived bid and the pevious one is less than a theshold δ, if so it exits. Othewise, if the diffeence is geate than δ, enodeb calculates the shadow M pice pn = win. The estimated pn is then sent to the public safety UEs whee it is used to calculate the ate i,s n which is the solution of the optimization poblem i,s n = ag log U i i,s pn i,s. A new bid w i n i,s is calculated using i n whee w i n = pn i,s n. All public safety UEs send thei new bids w i n to the enodeb. The Algoithm is finalized by the enodeb. Each public safety UE then calculates its allocated ate opt i,s = win pn. In the case of M t i,s <, the enodeb sends a flag with this infomation to each UE. Each public safety and commecial UE checks whethe the diffeence between the cuent eceived bid and the pevious one is less than a theshold δ, if so it exits. Othewise, if the diffeence is geate than δ, M+N w enodeb calculates the shadow pice pn = in. The estimated pn is then sent to the public safety and commecial UEs whee it is used by the public safety UE to calculate the ate i,s n = i +i,s t which is the solution of the optimization poblem i,s n = ag log U i i + c i pn i + c i. i,s A new bid w i n is calculated by the public safety UE using i n whee w i n = pn i n + c i. All public safety UEs send thei new bids w i n to the enodeb. On the othe hand, the commecial UEs eceive pn and use it to calculate the ate i,c n which is the solution of the optimization poblem i,c n = ag log U i i,c pn i,c. A new i,c bid w i n is calculated by the commecial UE using i,c n whee w i n = pn i n. All public safety UEs send thei new bids w i n to the enodeb. The Algoithm is finalized by the enodeb. Each public safety UE then calculates its allocated ate opt i,s = win pn its allocated ate opt i,c = win pn. and each commecial UE calculates V. SIMULATION ESULTS We conside one enodeb with fou public safety UEs and anothe fou commecial UEs in its coveage aea. We use multiple sigmoidal-like and logaithmic utility functions in Algoithm 1 Public Safety UE Algoithm Send initial bid w i 1 to enodeb Send the application taget ate i,s t to enodeb loop t i,s fom enodeb do eceive shadow pice pn fom enodeb if STOP fom enodeb then Calculate allocated ate opt i,s = win pn Solve i,s n = ag i,s log U i i,s pn i,s Send new bid w i n = pn i,s n to enodeb t i,s < fom enodeb do eceive shadow pice pn fom enodeb if STOP fom enodeb then Calculate allocated ate opt i,s = win pn Solve i,s n = i + i,s t c i pn i + c i = ag log U i i + i Send new bid w i n = pn i n + c i to enodeb end loop Algoithm 2 Commecial UE Algoithm Send initial bid w i 1 to enodeb loop t i,s fom enodeb do Allocated ate opt i,c = 0 t i,s < fom enodeb do eceive shadow pice pn fom enodeb if STOP fom enodeb then Calculate allocated ate opt i,c = win pn Solve i,c n = ag i,c log U i i,c pn i,c Send new bid w i n = pn i,c n to enodeb end loop ou simulations and pesent two cases, one when the enodeb esouces is less than the total application taget ates of the public safety UEs and the othe when is geate than that total. We applied algoithm 1, 2 and 3 in C++ to the sigmoidallike and logaithmic utility functions. The simulation esults showed convegence to the optimal global point in both cases. We pesent the simulation esults fo eight utility functions that coespond to public safety and commecial UEs unning eal time application o delay toleant applications. We use two nomalized utility functions expessed in equation 1 with diffeent paametes a and b fo each utility function, a = 3, b = 20 fo the fist public safety use, a = 1, b = 30 fo the 4 677
Algoithm 3 enodeb Algoithm loop eceive bids w i n fom UEs {Let w i 0 = 0 i} eceive application taget ates fom public safety UES while M t i,s do Send flag M to all UEs t i,s if w i n w i n 1 < δ, i = {1,..., M} then STOP and allocate ates i.e opt i,s to public safety use i M win, i = {1,..., M} Calculate pn = Send new shadow pice pn to public safety UEs while M t i,s Send flag M < do t i,s < to all UEs if w i n w i n 1 < δ i then STOP and allocate ates i.e opt i,s o opt i,c M+N w Calculate pn = in Send new shadow pice pn to all UEs end loop to use i of them eaches its inflection point, which is equivalent to thei application taget ates, then uses with elastic taffic stat dividing the emaining esouces among them based on thei paametes while not exceeding thei application taget ates. In Figue 3, we show the shadow pice pn with the numbe of iteations whee the convegence behavio of the shadow pice with the numbe of iteations is shown. Fig. 1: The ates i n with the numbe of iteations n fo diffeent uses and = 70. second public safety use. We set the application taget ate i,s t fo these two uses to equal b that is 20 and 30 espectively. Anothe two nomalized utility functions ae used with the same a and b paametes to epesent two commecial uses unning eal time applications. Each sigmoidal-like function is an appoximation to a step function at ate b. We also use two logaithmic functions expessed in equation 2 with diffeent paametes k = 3 fo one public safety UE and k = 0.5 fo second public safety UE unning delay toleant application. We set the application taget ate i,s t fo each these two uses to equal 15. Anothe two logaithmic utility functions ae used with the same k paametes to epesent two commecial uses unning delay toleant applications. A. Convegence Dynamics fo = 70 whee M t i,s This epesents the fist case whee M t i,s. We set = 70 and δ = 10 2. As mentioned befoe, in this case the commecial UEs will not be allocated any of the enodeb esouces because does not exceed the public safety application taget ates which need to be satisfied befoe the enodeb stats allocating esouces to the commecial uses. In Figue 1, we show the simulation esults fo the ate of diffeent public safety uses and the numbe of iteations. The sigmoidal-like utility functions ae given pioity ove the logaithmic utility functions fo ate allocation. This explain the esults we got in Figue 1. In this case the final optimal ate does not exceed the use application taget ate. In Figue 2, we show the bids of the fou public safety uses with the numbe of iteations. As expected, use ates ae popotional to the use bids. The algoithm allows uses with eal-time applications to bid highe than the othe uses until each one Fig. 2: The bids convegence w i n with the numbe of iteations n fo diffeent uses and = 70. Fig. 3: The shadow pice convegence with the numbe of iteations n. B. Convegence Dynamics fo = 200 whee M t i,s < Figue 4 shows fou public safety nomalized sigmoidallike utility functions expessed in equation 1 coesponding to two public safety uses and anothe two commecial uses. We also show fou logaithmic functions expessed in equation 2, which epesent delay toleant applications fo two public safety uses and anothe two commecial uses. We set = 120 and δ = 10 2. This epesents the second case whee M t i,s <. In this case the public safety UES ae given pioity ove the commecial UEs. In Figue 5, we show the simulation esults fo the ate of diffeent public safety and commecial uses and the numbe of iteations., fist the algoithm allocates an equivalent amount of esouces to the application taget ate to each public safety use. It then stats allocating esouces to each commecial UE with 5 678
inelastic taffic until it eaches the inflection point of that use utility function. It then stats dividing the emaining esouces among all uses based on thei paametes. In Figue 6, we show the bids of the eight uses with the numbe of iteations. The algoithm allows public safety uses to bid highe than the othe uses until each one of them eaches its application taget ate. Commecial uses with inelastic taffic then stat bidding highe until they each each utility function eaches its inflection point. In Figue 7, we show the shadow pice pn with the numbe of iteations whee the convegence behavio of the shadow pice with the numbe of iteations is shown. Fig. 4: The uses utility functions U i i + c i. Fig. 7: The shadow pice convegence with the numbe of iteations n. utility functions based on the UE application type. One epesents eal time applications and the othe epesents delay toleant applications. We consideed two esouce allocation optimization poblems based on the amount of esouces available by the enodeb. One is when the enodeb esouces ae less than o equal to the total application taget ates of the public safety uses subscibing fo a sevice. The othe is when the enodeb esouces geate than that total. The solution to each optimization poblem is chaacteized by utility popotional fainess. We poposed an iteative decentalized algoithm fo the enodeb and both the public safety and commecial UEs. The algoithm povides a utility popotional fai esouce allocation which guaantees a minimum QoS based on the public safety UEs application taget ates, the goup that the UE belongs to and the enodeb available esouces. The public safety uses goup is given pioity ove the commecial uses goup and within each goup, uses unning eal time applications ae pioitized ove those unning delay toleant applications. We showed though simulations that ou algoithm conveges to the optimal ates. Fig. 5: The ates i n with the numbe of iteations n fo diffeent uses and = 200. Fig. 6: The bids convegence w i n with the numbe of iteations n fo diffeent uses and = 200. VI. SUMMAY AND CONCLUSIONS In this pape, we pesented a esouce allocation appoach to allocate a single enodeb esouces optimally among public safety and commecial uses in 4G-LTE. We consideed two EFEENCES [1] A. Abdel-Hadi and C. Clancy, A utility popotional fainess appoach fo esouce allocation in 4G-lte, Submitted to ICNC, 2013. [2] F. Kelly, A. Maulloo, and D. Tan, ate contol in communication netwoks: shadow pices, popotional fainess and stability, in Jounal of the Opeational eseach Society, vol. 49, 1998. [3]. L. Kule, esouce allocation fo smat phones in 4G lte advanced caie aggegation, Novembe 2012. [4] H. Shajaiah, A. Abdel-Hadi, and C. Clancy, Utility popotional fainess esouce allocation with caie aggegation in 4G-lte, Submitted to Milcom, 2013. [5] A. Abdel-Hadi, C. Clancy, and J. Mitola, A esouce allocation algoithm fo multi-application uses in 4G-lte, Submitted to CAB, 2013. [6] Y. Wang, K. Pedesen, P. Mogensen, and T. Soensen, esouce allocation consideations fo multi-caie lte-advanced systems opeating in backwad compatible mode, in Pesonal, Indoo and Mobile adio Communications, 2009 IEEE 20th Intenational Symposium on, pp. 370 374, 2009. [7] G. Tychogiogos, A. Gkelias, and K. Leung, A new distibuted optimization famewok fo hybid ad-hoc netwoks, in GLOBECOM Wokshops GC Wkshps, 2011 IEEE, pp. 293 297, 2011. [8] G. Tychogiogos, A. Gkelias, and K. Leung, Towads a fai nonconvex esouce allocation in wieless netwoks, in Pesonal Indoo and Mobile adio Communications PIMC, 2011 IEEE 22nd Intenational Symposium on, pp. 36 40, 2011. [9] G. Tychogiogos, A. Gkelias, and K. K. Leung, Utility-popotional fainess in wieless netwoks., in PIMC, pp. 839 844, IEEE, 2012. [10] J.-W. Lee,.. Mazumda, and N. B. Shoff, Downlink powe allocation fo multi-class wieless systems, IEEE/ACM Tans. Netw., vol. 13, pp. 854 867, Aug. 2005. 6 679