Performance of downlink schedulers with superposed or orthogonal transmissions

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1 Equation Chapter 1 Section 1 Thi full text paper a peer revieed at the direction of IEEE Communication Society ubject matter expert for publication in the IEEE ICC 1 proceeding Performance of donlink cheduler ith uperpoed or orthogonal tranmiion Adrian Agutin, Member IEEE, Joep Vidal, Member IEEE and Olga Muñoz Abtract Thi ork look into the extenion of the proportional fair ( cheduler to the multi-uer cae, here the ource i tranmitting everal meage under the uperpoition coding (SC trategy in a Gauian Broadcat channel. Jointly ith the eighted um-rate ( cheduling criterion, e derive guideline for -uer pairing, baed both on SNR and uer priority. We compare uperpoition coding acce ith frequency diviion multiple acce, hile time diviion i obtained naturally a a reult of the uer pairing. Reult elucidate that the -uer SC alay improve the ingle-uer in term of average throughput and delay reduction, and e compare it performance ith the -uer SC. Finally, the ho throughput gain imilar to the -uer SC for certain configuration of the cheduler. Index Term Scheduling, proportional fair, multiuer, broadcat channel I. INTRODCTION Wirele netork mut upport a large type of ervice, differing in throughput and delay contraint. Becaue of the carcity of the irele reource, it ue mut be efficiently managed. In [1] it a hon that the ytem throughput can be maximized by exploiting multi-uer diverity, i.e. electing the uer ith the bet channel condition. Hoever, uch greedy cheduler i unfair a ome uer may never be erved. The criterion of proportional fairne ( i introduced in [] in order to deal ith the tradeoff beteen the maximum ytem throughput and uer fairne. One example of ingleuer i the cheduler of the High Data Rate (HDR ytem [], here the uer ith the bet metric baed on channel tate and average erved throughput i elected. Enhancement of uch ytem for tatic propagation cenario can be found in [], here multiple antenna are employed to induce large and fat channel fluctuation in lo-fading cenario (opportunitic beamforming. Likeie, many other criteria for deigning the throughput and delay of a netork have been propoed, like max-min and the max um-rate, [], the eighted, [], or the eighted um-rate, [][]. The ingle-uer cheduler ha been extenively tudied in the literature, ee for intance [][1] here cloed-form expreion for the average throughput per uer are derived. Thi ork a upported in part by the European nion through project ROCKET ICT--1-1 and FEDER fund, and by the Spanih/Catalan Science and Technology Commiion through project: SGR-, TEC-1/TCM, and CONSOLIDER CSD-1 COMONSENS. A.Agutin, J.Vidal and O.Muñoz are ith the Dept. of Signal Theory and Communication. at PC, Barcelona, Spain. {adrian.agutin, joep.vidal, olga.munoz}@upc.edu. Although in [11] (chapter the benefit of the uperpoition coding for the multi-uer cae are pointed out, to the bet of our knoledge, the cheduler ha not been thoroughly tudied in that cae. Multi-uer cheduler baed on eighted um-rate ( and maximum um-rate (MSR criteria have been analyzed in multi-antenna configuration eizing the patial dimenion to erve more uer imultaneouly. Hoever, hen the MSR criterion i applied to the ingle antenna cae, the multi-uer cheduler doe not offer any gain over the time diviion multiple acce (TDMA [1], becaue the bet um-rate i obtained hen all reource are allocated to the uer ith the highet ignal-to-noie ratio (SNR. We look into multi-uer cheduler baed on the eighted um-rate ( and proportional fairne ( criteria for ingle-antenna cellular cenario in the donlink. The objective i to group to or three uer under unequal channel tate and prioritie by taking advantage of the large gain that uperpoition coding offer over the TDMA [11]. We alo compare it ith multiuer. The main contribution of thi paper are: - Analyi of multi-uer and cheduler under uperpoed tranmiion in the donlink. - Derivation of criteria for -uer pairing in both cae. II. SIGNAL MODEL AND SCHEDLERS The cenario conit of a bae tation (BS and N u mobile tation (MS, all equipped ith ingle antenna. The BS tranmit a pilot ignal hich i employed by every terminal to meaure the current SNR. Afterard, each receiver feed back that meaurement to the BS. The overhead rate introduced by thi feedback i not tackled in thi ork. The cheduling algorithm conider the channel tate of the MS to elect a ubet of them (denoted by to be erved imultaneouly. All the uer are aiting for receiving data (full data queue at BS. The three cheduler analyzed are: (or ingle-uer, and multi-uer. The cheduler elect jut one MS on each cheduling intant, maximizing the folloing metric: Q J k = krk (1 here k decribe the eight or priority for uer k and R k i the attained bitrate. The elected uer i denoted by the ubet of ize one Q. The achievable bitrate per uer i, Rk = log ( k ( here k tand for SNR at the receiver. The uer priority -1---/1/$. 1 IEEE

2 Thi full text paper a peer revieed at the direction of IEEE Communication Society ubject matter expert for publication in the IEEE ICC 1 proceeding introduced in (1 i inverely proportional to the average erved throughput, calculated a, 1 1 τ Ti n 1 + τri if i x i =, Ti n = ( T ( 1 ( 1 i τ Ti n otherie here T i n denote the average throughput at frame n, R i tand for the bitrate of the elected uer, x i equal to Q and τ i a tuning parameter that allo varying the performance of the cheduler, from greedy (τ cloe to to impoe trong uer fairne among MS (τ cloe to 1. The multi-uer cheduler elect K uer, denoted by the ubet, maximizing the average erved throughput, (, J = T j = Tj j= 1 j = 1 Thi criterion ha been applied in [1] for multicarrier ytem here i hon that can be tranformed into, log log ( τ R j J = log 1 + j j= 1 1 τ ( here j,τ are given in ( and R j i the bitrate of one elected uer, depending on the Gauian Broadcat channel (BC [1]. On the other hand, the eighted um-rate cheduler ( elect K uer, referenced by ubet, hich maximize, J jr j j= 1 = ( here R j denote the achievable rate of one of the elected uer. Thoe bitrate mut lie ithin the capacity region of the Gauian broadcat channel hen uperpoed tranmiion are enviioned [1] and the poer at the BS i ditributed among the meage to be tranmitted. The uer prioritie may be calculated according to (, albeit other criteria can be ued to derive them, like limiting the maximum delay or fitting ith the maximum tability region [1]. III. GIDELINES FOR -SER PAIRING Thi ection tudie the condition to be atified for to uer in order to be erved under the and criteria ( =, = and yet improve the um-rate attained under the cheduler. Becaue of the degradedne of our cenario, e aume there are a trong and a eak uer having SNR and ( ith uer prioritie,. A. (Q Thi cheduler elect the uer ith the bet metric (1, R if log ( log( JQ = ( R otherie here R, R are the bitrate, (, of the eak and trong uer. From (, the condition for electing only the eak one i, 1, ζ = = 1 ( Q here i the threhold for changing the uer election. B. Weighted um-rate ( The bitrate mut belong to the rate region of the BC [1], ( γ ( ( γ R log ( R log log here γ i the fraction of poer allocated to the ignal for the trong uer, hile the other uer i allocated 1-γ. Notice that the SNR, are meaured from the pilot ignal, but they do not correpond to the final SNR of the ignal to be decoded hoe SNR are 1 γ. It i knon that the maximization of J ith i obtained hen only the trong uer i elected. But, for < the poer allocation depend on the SNR configuration. The maximization of J ubject to ( i derived from, J J = =, < (1 γ γ γ γ γ and Thu the optimal poer allocation turn out to be, if > γ = 1 if ζ (11 if γ = if ζ < ζ ( 1 1 if > ζ here ζ, ζ are the threhold for cheduling only the eak or only the trong uer hen, if > ζ, 1 ( 1 1 = ζ = + (1 otherie Applying the optimal poer allocation, J reult in, R if ζ ( 1 + log + 1 J = (1 ( 1 + log if ζ < ζ R if > ζ The additive um-rate gain provided by the over the cheduler i therefore given by, log if ζ ζq < Δ = (1 log if ζq < ζ elehere here ubume the condition needed from erving the eak over the trong uer in the cheduler, (. Only in the firt interval of (1 provide a poitive um-rate gain. Therefore, the -uer pairing under hould atify, ζ < ζ (1 Q

3 Thi full text paper a peer revieed at the direction of IEEE Communication Society ubject matter expert for publication in the IEEE ICC 1 proceeding C. Multiuer Proportional Fairne ( Thi cheduler erve to uer imultaneouly, o that the achievable rate of the uer mut atify the capacity region of the BC. The poer at the BS i allocated among the tranmitted ignal a a reult of the maximization of J ubject to (. The fraction of poer devoted to the trong uer (γ atifie the equation, J τ τ = ( γ log γ 1 τ 1 τ 1 γ + (1 τ τ ( γ log ( γ = 1 τ 1 τ here, denote the SNR and, are the prioritie of the trong and eak uer, repectively. The condition to erve only the eak uer (γ= or the trong one (γ=1 become, ζ = =, ( 1 + τ 1 τ log ( 1 + (1 ζ ( 1 ( 1 ( ( 1 = + + τ τ log ( In term of um-rate gain over the cheduler, the gain are poitive hen the i electing both uer hile the elect jut the eak uer. The -uer pairing criterion for the become, ζ < ζq (1 Since ζ < ζ, the criterion offer more opportunitie to improve the cheduler than the. D. Weighted um-rate ( under With a light abue of the notation, e refer by - the cheduler that maximize ( erving the uer orthogonally in frequency. The bitrate of the uer are, R αlog ( γ α (1 R ( 1 log ( α 1 γ 1 α here α and γ tand for the fraction of bandidth and poer allocated to the trong uer, repectively. In thi cae the variable α and γ have to be optimized for maximizing the eighted um-rate, J α ( 1 α ( + =, γ = ( γ ( 1 α + α here J - conider the eighted um-rate of ( uing the bitrate defined in (1. By defining, α + ( 1 α + f α = (1 α ( 1 + α and conidering (, the optimal bandidth allocation become 1 ( ( + + log ( 1 * α + α + α = ( log f α + f α log = Since equation ( ha to be olved numerically, e define the folloing threhold to identifying hich uer i erved, ζ = γ =, α = ( ζ = γ = 1, α = 1 The um-rate gain provided by the - over the cheduler i given by, 1 α α f α log ( if ζ ζq Δ ( 1 α = α f α log ( if ζq ζ < here i defined in ( and function f in (1. um-rate τ=. elehere =., =.1 =1 db = + 1xlog(ζ (db ~ ζq τ=1 - - τ=. τ=1-1 ζ (linear ratio over Fig. 1. Sum-rate provided by the,, - and ith τ={., 1 - } a a function of the linear ratio ζ= /. er prioritie =., =.1, =1 db, = +1 log 1(ζ. In order to compare the performance of the different cheduler, Fig. 1 preent the um-rate attained by each one for a configuration here the uer-prioritie are fixed to =., =.1, the eak uer ha a SNR equal to =1 db and the SNR of the trong uer varie ith the parameter ζ a = +1 log 1 (ζ. We can oberve that the cheduler elect either the eak or the trong uer at. In the latter cae, the um-rate increae ith ζ becaue the SNR of the trong uer alo increae. For the - three different performance are oberved: only the eak uer (ζ, both, eak and trong (orthogonally, or jut the trong uer (ζ are erved. For the and the condition for erving jut the trong uer are not atified. The maximum gain ith repect to the cheduler i attained at ζ=, i.e. hile the cheduler elect the eak uer, the other cheduler are electing both uer. Finally, for the cheduler, e ketch the performance for to value of τ. When τ i cloe to zero the and get the ame performance, but for τ value cloe to one, there are ignificant difference in term of um-rate. Fig. 1 hoed that cheduler i uperior under ome circumtance. That eem to contradict the theory, hich tate that achievable rate region of TDMA ( i in general loer than (- and BC (,. Hoever, the um-rate provided by each cheduler depend on the uer priority,,. Fig. illutrate

4 Thi full text paper a peer revieed at the direction of IEEE Communication Society ubject matter expert for publication in the IEEE ICC 1 proceeding a configuration here the TDMA get the bet um-rate. Fig. aume the ame configuration a in Fig. 1 ith ζ=. bitrate trong uer =., =.1 =1 db = + 1xlog(ζ (db ζ= OP of TDMA OP of - OP: Operational point due to, OP of τ =. OP of TDMA 1 BC bitarate eak uer Fig.. Achievable rate region of TDMA (, (- and BC ( and. er prioritie =., =.1, =1 db, =. db (ζ=. IV. CELLLAR EVALATION The evaluation of the, and cheduler ha been done in a implified cenario here the MS are uniformly ditributed in a cell of radiu r= meter, being the BS at the cell centre. The pathlo exponent i. The noie poer, tranmitted poer and other contant have been configured o a to get SNR= db hen a MS i at the cell edge and db hen the uer i cloe to the BS. The channel coefficient are Rayleigh ditributed, contant over a frame and independent among uer. The imulation evaluate uer deployment, each one coniting of N u uer and imulated during frame. er feed back their current SNR to the BS. The elected uer maximize the different cheduling criteria, here their prioritie are given by (. Since e are dealing ith multiple uer under uperpoition coding trategy, the cheduler mut evaluate all the combination for the uer pairing. Thi tak i tractable for the -uer becaue there i a cloed-form expreion for the metric to be maximized, (1, albeit for more uer or the multi-uer cheduler the tak become cumberome. To thi end, and folloing imilar tep a in [], e conider a candidate lit Γ ith L uer ith the bet metric k R k, Γ= k 1, N R η, Γ = L ( { [ u] k k } here k and R k are the priority and the bitrate of the k-th uer auming that the BS allocate all the poer to that uer, (. The cheduler are compared in term of uer throughput, cell throughput and delay, defining delay a the average number of frame elaped beteen to conecutive election intant of the ame uer. A. Per-uer throughput and delay for -uer cheduler Thi ubection tudie the benefit in term of throughput and delay introduced by the -uer and cheduler in a cenario ith N u = MS. Fig. depict the 1%-outage throughput per uer a a function of τ for the, - uer and ith L={,}. Notice that in order to obtain that meaure e have conidered all uer preent in the cell. When τ goe to zero the 1%-outage throughput per uer tend to zero. Thi performance i caued by the election of the uer ith the bet channel condition. In uch a cae, the remaining uer are rarely erved, impoing a very lo throughput per uer. Accordingly, hen τ increae more uer are erved and the throughput improve. But at a certain point (τ= 1 - in Fig. the 1%-outage throughput per uer decreae a τ goe to 1. Thi i a conequence of erving the election of deprived uer in the cell due to their high uer priority, hich become more important than the current channel of the uer. The bet channel uer, hich could get larger bitrate, are le frequently elected. It i important to remark that the -uer cheduler ( and outperform the cheduler, except for the -uer ith τ>.1. In that latter cae, e have oberved (but not hoed here that the average number of erved uer decreae, explaining the peculiar behavior of -uer depicted Fig.. Finally, the performance of the -uer i almot independently of the value of Γ for L={,}. Prob (Throughput > y = % uer -uer L= -uer L= τ (parameter for calculating the average erved throughput Fig.. 1%-outage throughput per uer a a function of τ for the, -uer and ( ith L={,} cheduler. N u= MS. Average throughput per uer (bit//hz N u =.1 -uer. -uer L= -uer L= τ (parameter for calculating the average erved throughput Fig.. Average throughput per uer a a function of τ, for the, - uer and ( ith L={,} cheduler. N u= MS. The average throughput per uer i ketched in Fig. a a function of τ. The average throughput decreae monotonically a τ goe to 1 in all cae. Notice that for lo value of τ there i a ignificant difference beteen the average and the 1%-outage throughput (Fig.. That mean

5 Thi full text paper a peer revieed at the direction of IEEE Communication Society ubject matter expert for publication in the IEEE ICC 1 proceeding that uer throughput preent a dipere tatitic a a conequence of having a mall number of uer in good SNR condition. Likeie, the -uer cheduler alay improve the cheduler hile the -uer i clearly inferior to -uer for value of τ cloe to zero (greedy and cloe to one (round robin. The %-outage per-uer delay (in log cale i preented in Fig.. For lo value of τ, large delay are found becaue only a mall number of uer are erved. A τ increae the cheduler tend to get a contant delay of frame. The -uer reduce to one half the delay hile the cheduler achieve ome intermediate delay value. Prob ( log(delay > y = 1 % N u = Delay> frame Delay>1 frame -uer -uer L= -uer L= Delay Q ~ frame Delay ~ frame Delay ~ 1 frame τ (parameter for calculating the average erved throughput Fig.. %-outage delay (logarithm cale per uer a a function of τ for the, -uer and ( ith L={,} cheduler. N u= MS %-Cell throughput gain over the cheduler Proportional Fair ( criterion Zone 1 Zone Zone -uer N u = -uer N u = -uer L= N = u -uer L= N = u τ (parameter for calculating the average erved throughput Fig.. Percentage-ie cell throughput gain over the cheduler a a function of τ for the {,}-uer ith L= cheduler. N u={,} MS. B. Cell throughput ith -uer and -uer cheduler Here e invetigate cell throughput gain obtained by multiuer cheduler (-uer and -uer over the cheduler. The -uer cheduler deign the bit rate and poer allocation by maximizing ( taking into account the achievable rate region of the -uer BC [1]. A candidate lit of uer ith L= i aumed. Fig. preent the percentageie cell throughput gain for the cheduler ith N u ={,} hich can be divided in three zone. The -uer cheduler get the bet throughput in zone 1, hile -uer cheduler in zone (a gain around %. In zone, both cheduler attain a imilar performance. Although not hon, it ha been oberved than the delay for the -uer cheduler i 1/ the delay of the cheduler in zone and. V. CONCLSIONS Thi ork analyze multi-uer cheduler in the Gauian BC baed on uperpoition coding. The and cheduling criteria are compared ith the cheduler (ingle-uer in term of throughput and delay. er pairing criteria baed on SNR and uer priority are preented. Reult have hon that by erving multiple-uer under the criterion, the delay per uer i improved, but the throughput depend on the value of τ, hich tune the performance of the cheduler. In the etup decribed for greedy cheduler (τ cloe to it i preferable to chedule - uer, hile if fairer criterion i adopted (τ cloe to 1, -uer cheduling i better. The performance i in all cae improved ith repect to the cheduler. The cheduler i able to get a imilar performance than cheduler jut for certain intermediate value of τ. REFERENCES [1] R.Knopp, P.Humblet, Information capacity and poer control in ingle cell multiuer communication, in Proc. IEEE Intl. Conf. on Communication (ICC, 1. [] F.P.Kelly, A.K:Maulloo, D.K.H.Tan, Rate control in communication netork: hado price, proportional fairne and tability, Journal of the Operational Reearch Society, vol., April 1. [] A.Jalali, R.Padovani, R.Pankai, Data throughput of CDMA HDR a high efficiency-high data rate peronal communication irele ytem, in Proc. IEEE Vehicular Techn. Conf. (VTC Spring,. [] P.Vianath, D.N.C.Te, R.Laroia, Opportunitic beamforming uing dumb antenna, IEEE Tran. on Information Theory, vol., no., June. [] J.Mo, J.Walrand, Fair End-to-end indo-baed congetion control, IEEE/ACM Tran. Netorking, vol., no., Oct.. [] J.Liu, Y.T.Hou, Weighted Proportional Fairne Capacity of Gauian MIMO Broadcat channel, in Proc. IEEE Conf. on Computer Comm. (INFOCOM,. [] H.Vianathan, S.Venkatean, H.Huang, Donlink Capacity evaluation of cellular netork ith knon-interference cancellation, IEEE Journal on Selec. Area in Comm., vol.1, no., June. [] K.Jagannathan, S.Bort, P.Whiting, E.Modiano, Scheduling of Multiantenna Broadcat ytem ith heterogeneou uer, IEEE Journal on Selec. Area in Comm., vol., no., Sept.. [] J.G.Choi, S.Bahk, Cell-Throughput analyi of the proportional fair cheduler in the ingle-cell environment, IEEE Tran. on Vehicular Techn., vol., no., March. [1] E.Liu, K.K.Leung, Fair Reource allocation under Rayleigh and/or Rician fading environment, in Proc. IEEE Peronal Indoor Mobile Radio Communication (PIMRC, Sept.. [11] D.Te, P.Vianath, Fundamental of Wirele Communication, Cambridge niverity Pre,. [1] N.Jindal, A.Goldmith, Dirty-Paper coding veru TMDA for MIMO Broadcat Channel, IEEE Tran. on Information Theory, vol.1, no., May. [1] H.Kim, Y.Han, A Proportional Fair cheduling for multi-carrier tranmiion ytem, IEEE Comm. Letter, vol., no., March. [1] T.M.Cover, J.A.Thoma, Element of Information Theory, nd edition, Wiley, 11. [1] G.Song, Joint channel-aare and queue-aare data cheduling in multiple hared irele channel, Proc. of IEEE Wirele Conf. of Netorking and Comm. (WCNC, March.