Delay Constrained Multiuser Scheduling Schemes Based on Upper-Layer Performance

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1 Delay Constraned Multuser Schedulng Schemes Based on Upper-Layer Performance Hongyuan Zhang Dept. Electrcal and Computer Engneerng North Carolna Unversty Ralegh, NC USA Huayu Da Dept. Electrcal and Computer Engneerng North Carolna Unversty Ralegh, NC USA Abstract Dfferent from conventonal multuser schedulng schemes targetng on optmzng the physcal layer performance crtera such as Shannon capacty and error probablty, n ths paper we propose a famly of new schedulng methods that take the packet throughput n upper-layer protocols nto consderatons. Ths new performance metrc appears to be an elegant combnaton of spectral effcency and channel relablty, whch are two usually compettve performance ndcators for practcal transmtters and recevers. Our results show that regardng the packet throughput, the proposed schedulers may result n great performance advantage over conventonal schemes, especally at low to ntermedate SNR. Furthermore, the amount of system delay for each user s nvestgated together wth packet throughput for schedulng algorthm desgns. A novel scheduler, consderng both system performance and user delays, s then proposed, and the correspondng delaythroughput tradeoff curve s drawn, whch actually provdes a useful and flexble platform to evaluate any schedulng schemes, f both factors are under concern. Keywords-delay outage, packet throughput, schedulng, throughput-delay tradeoff I. INTRODUCTION It s well-known that outdoor and ndoor wreless channels are tme-varyng n a random manner because of multpath fadng. In a pont-to-pont scenaro, channel fadng s usually a negatve factor for the performance, mpactng both the data rate and relablty. However, when multple users are nvolved n wreless communcaton, a wsely desgned user scheduler may utlze the fluctuaton of the fadng channels across ndependent users, to explore the favorable peaks of ther channel condtons [1][2]. On the other hand, to enhance channel relablty or to ncrease data rate, multple antenna schemes (e.g. MIMO technques) are wdely studed n lterature, and have already made ther debut for commercal applcatons, e.g. n the emergng standards of the next generaton moble communcatons and wreless LAN/MAN. Multuser schedulng schemes explorng MIMO channels then attract research nterest recently, e.g. n [7][8][9][10][13]. MIMO systems can be exploted for ether spatal dversty (SD) or spatal multplexng (SM) gans [15], the latter of whch mproves the data rate dramatcally wthout ncreasng the requred bandwdth, and wll be our focus n ths paper. However, n hghly populated envronments where multuser MIMO s appled n conjuncton wth conventonal tme and frequency dvson mult-access protocols, due to the ncrease n the transmt sgnal energy and the number of spatal data streams, the nterference level may be ncreased for other users smultaneously served n the same frequency band and tme slot [17], whch not only advocates the need for sophstcated transmtter and recever desgn n multuser MIMO channels, but also requres a well-desgned hgher layer scheduler, such that a group of users wth relatvely less spatal correlatons may share the same frequency-tme grd. A large quantty of exstng studes on MIMO multuser dversty use the physcal (PHY) layer metrcs such as sum capacty, as the performance crtera, e.g. n [7][8]; whle some others pay more attenton to the jont effect of system performance and user delays, e.g. n [9][10][13]. Meanwhle, except frequency band, tme slot, and orthogonal sgnature codes, the spatal sgnatures n MIMO can also be utlzed to separate dfferent users (.e. SDMA), whch s broadly dscussed recently n the lterature ([16] and the references theren). Then the problem of how to choose a group of SDMA users bearng optmal jont performance n one frequency-tme slot, attracts much research nterest recently. It has already been shown that schedulng multple users at each tme nstance acheves some advantage over sngle user schedulers, regardng both sum capacty and delays [7][8][13]. However, any communcaton lnk works wth fnte modulaton alphabet, and the channel encodng s usually not capacty-achevng. Therefore error probablty s another mportant PHY layer performance ndcator when practcal transmtters and recevers are nvolved. Wth a fxed power constrant, data rate and error rate are typcally two performance metrcs competng wth each other. Furthermore, n packet-swtched communcaton networks, the maxmzaton of PHY layer data rate may not be the rght way to maxmze the effectve packet throughput n the systems contanng data-lnk and transport protocols, because when retransmsson protocols such as TCP are deployed, any erroneous packet wll result n retransmsson, reducng the effectve packet throughput seen by hgher layers. It s then worthwhle to jontly consder data rate and error probablty when desgnng multuser schedulng schemes. Ths work was supported n part by the Natonal Scence Foundaton under Grant CCF

2 In ths paper, by mplementng practcal MIMO transmtter and recever processng structures, we propose to utlze the packet throughput, whch appears to be a decent combnaton of the data rate and the packet error probablty, as the performance crteron for desgnng schedulng algorthms. The underlyng dea s that we utlze the PHY layer measurements to predct the hgherlayer throughput, by whch the schedulng s conducted. Analytcal and numercal results show that the proposed schedulng scheme sgnfcantly outperforms conventonal schemes n terms of the new performance metrc effectve packet throughput. Furthermore, when user delays are concerned, we propose a schedulng algorthm jontly consderng packet throughput and delay outage, wth an adjustable weghtng factor. A novel delay-throughput fgure s then drawn to ndcate the tradeoff between the two compettve factors. Numercal results show that a wsely desgned weghtng factor can result n much better performances than some exstng schedulers. Therefore the proposed tradeoff fgure may serve as a basc framework to evaluate dfferent multuser schedulers, as well as one scheduler wth dfferent PHY layer sgnalng schemes. Here we dfferentate the term throughput n ths paper, whch means packet throughput seen by the hgher layers, from that n [16] and references theren, referrng to sum capacty seen by PHY layer. The rest of the paper s organzed as follows, the system model s provded n Secton II; Secton III ntroduces the new schedulng method that maxmzes the packet throughput, whle Secton IV takes user delay nto consderatons; fnally Secton V gves some concluson remarks. II. SYSTEM MODEL In an nfrastructure wreless network, K moble users (MU) n the same frequency band are randomly located n the area served by a sngle data access pont (DAP). We are nterested n the downlnk communcatons, whch s expected to be the bottleneck of future hgh data rate communcaton networks. Each MU s equpped wth N R antennas, whle the DAP s equpped wth N T N R antennas. Therefore at a tme slot, n whch user k s beng scheduled, ts receved sgnal can be expressed as: yk = HT k ASx+ n, (1) where x s the N S 1 transmtted sgnal wth N S N T, and T AS s an NT NS spatal mapper (from data streams to antennas) representng antenna selecton [18], therefore t shall contan N S non-zero columns, each wth only one 1 element ndcatng the mappng of a data stream to a partcular antenna, as wll be dscussed n the next secton. For smplcty, Hk and n are modeled wth ndependent and dentcally dstrbuted (..d.) normalzed complex Gaussan entres,.e. here we assume frequency flat fadng and addtve whte Gaussan nose. Note that the extenson of our schedulng methods to frequency selectve channels s straghtforward. We assume that uncoded ndependent sgnals are transmtted wth equal rate and equal power across spatal data streams. Dfferent streams may contan sgnals for one user or multple users, accordng to the schedulng rules. Also, channels for dfferent users are ndependent wth each other. A scheduler located at the DAP decdes the user(s) scheduled n each tme slot, based on the nformaton fed back from the MU s n the servce area. III. PACKET THROUGHPUT MAXIMIZATION SCHEDULER As dscussed above, the schedulng rule that maxmzes the PHY layer nformaton rate may not be the rght way to optmze the effectve packet throughput seen at hgher layers, whch s ultmately what s seen by the applcaton. The basc reason s that, the transport protocols usually contan some retransmsson mechansms. Specfcally, an ntator runnng such a protocol shall wat for the acknowledgement (ACK) response of each transmtted data packet from the destnaton, and retransmsson wll occur f an error ndcator (nstead of ACK) s receved, or no response s receved after a tmeout wndow W, whch s set to be longer than the measured round-trp tme τ RTT [3]. Relevant protocols nclude Go-back-N ARQ [6] and TCP [5]. Therefore, gven the transmt power, choosng a hgher PHY layer data rate (thus bgger modulaton constellaton sze or lower channel codng effcency) typcally wll reduce the error performance, leadng to data packets more vulnerable to wreless channels under adverse condtons, a destructve factor for hgher layer throughput. As ndcated by [3][4], the throughput expresson for Go-back-N ARQ protocol s also a good approxmaton of that for TCP, whch can be explctly expressed as; 1 P pkt S.log 2. 1 Ppkt + W. Ppkt I = N M, (2) where NS s the number of data streams whose correspondng transmt antennas can be selected durng the schedulng process; M s the (equal) constellaton sze employed n each stream; W s the tmeout wndow sze, equal to one when select-repeat ARQ s used [6]; and P pkt s the packet error rate (PER) approxmately gven by L/ NS NS Ppkt = 1 (1 Pe _ n), (3) n= 1 where L s the number of symbols per data packet, and P e_ n s the symbol error rate (SER) for the nth data stream. Note that the maxmzaton of (2) requres both hgh spectral effcency NS.log 2 M and low packet error rate, therefore t appears to be a good combnaton of these two mportant PHY layer performance ndcators. From (2)(3) we see that by measurng some PHY layer ndcators and feedng them back, we are capable of predctng the hgher-layer packet throughput to facltate the scheduler desgns. Intutvely, at low to ntermedate SNR regme, snce packet retransmssons wll domnate the effectve

3 packet throughput, a hgh value of (2) may prefer a small N S, n another word more relablty n each stream; whle at hgh SNR, larger N S s more favorable for most of the tme, snce packets can usually be relably receved. Ths predcton wll be verfed by numercal result. Regardng the schedulng algorthm, we propose to select one or multple users at each tme slot to maxmze the packet throughput seen by the DAP on the downlnk, based on the appled PHY layer sgnalng scheme. In the frst scenaro where the DAP does not have channel state nformaton (CSI), zero-forcng (ZF) space equalzaton s mplemented at each of the moble recevers for nterstream nterference mtgatons. N S data streams are transmtted by the selected N S transmt antennas out of the N T canddates, so the zero-one antenna selecton spatal mapper T AS s correspondngly determned. Such antenna selecton s conducted at the MU (who has the knowledge of the correspondng full-sze channel H k ) and fed back to the DAP n sngle user schedulng schemes; and s jontly conducted at the DAP based on the performance ndcators fed back from MUs, f multple users can be selected smultaneously. Note that the value of NS s not fxed. In practce, t s reasonable for each recever to know not only the CSI by effectve channel estmatons, but also the post-processng sgnal-to-noseplus-nterference-rato (SINR). Therefore for any modulaton sze (and/or channel codng), the SER of each data stream can be estmated analytcally or through experments, e.g. by a pre-desgned look-up table (located ether at the MUs or at the DAP, as wll be dscussed n the followng). Such a look-up table should nclude at least a gross SER estmaton correspondng to dfferent SINR levels, whle the number of entres n the table can be reduced by quantzng the SINR levels wth larger ntervals. Gven these SER estmatons, from (2)(3), PER and packet throughput can be readly calculated. In the smulaton, we assume that there are K = 5 actve users, also NT = 4, NR = 2, L = 600, W = 6, and M = 4 (.e. QPSK). We compare the followng four schedulng rules. 1. One user Max Shannon Capacty: Each MU selects the antenna subset wth the cardnalty NS [1, 2] that maxmzes the Shannon capacty, and feedback the correspondng capacty value and antenna subset to the DAP, where one best user wth the largest capacty s selected n each tme slot, and the correspondng antenna subset s used for the transmsson. 2. One user Max Packet Throughput: The same as above, except usng packet throughput as the performance crteron, and applyng ZF recever at MUs. Also, the packet throughput s calculated at the recever by the lookup table, as descrbed above. 3. Multuser Max Packet Throughput wth N S = 2 : In each tme slot, for each possble antenna subset of sze N R = 2, the DAP selects one best user for each data stream, based on the post-processng SINR fed back from the MUs equpped wth ZF equalzers, as ntroduced n [8]. Then the DAP selects the subset correspondng to the largest packet throughput. The look-up table and throughput calculaton then need to be conducted at the DAP, and each MU s requred to calculate and feedback the SINR for each streams correspondng to dfferent transmt antenna subsets. Moreover, any scheduled user may only decode the data streams assgned to hm. 4. Multuser Max Packet Throughput wth 1 N S 2: the same as scheduler 3, except that N S can be any number no larger than N R = 2. Ths scheduler performs better than schedulers 1~3 (Fgure 1), at the expense of ncreased calculatons and feedback overhead for the MU s. In the second scenaro, we assume CSI s known at the transmtter, so that the jont transmsson-zero forcng (JT- ZF) pre-equalzer [11][12] can be employed at the DAP before transmsson, resultng n smplfed recever structure (matched-fler only). Therefore, we propose the followng schedulng rule: 5. JT-ZF wth User Selecton: N S can be ether 2 or 4, so 1 or 2 users are selected n each tme slot w.r.t. maxmum packet throughput, and both the nter-user nterference and nter-stream nterference can be pre-canceled by JT-ZF. All the calculatons are conducted at the DAP. Fgure 1. Performance Comparsons of Schedulers 1~5 Fgure 1 provdes the smulaton results, where we can see that the packet throughput based schedulers outperform the frst scheduler based on Shannon capacty. The optmal average packet throughput tends to select a mode wth N S = 1 at low to ntermedate SNR, so those packet throughput maxmzng schedulers conductng antenna selecton wth arbtrary N S (schedulers 2 and 4) greatly outperform the other schemes. At hgh SNR, all schedulers

4 for the frst scenaro (1 through 4) concde wth each other because the domnant factor becomes the spectral effcency nstead of relablty; whle the JT-ZF scheme assumes great advantage, because more than 2 streams are allowed. Ths observaton verfes our predctons as descrbed above. IV. PACKET THROUGHPUT BASED SCHEDULING WITH DELAY CONSTRAINTS The mplementaton of the throughput maxmzaton schedulers ntroduced above reles on the fact that many data servces are delay tolerant,.e. farness s not the key consderaton n such systems. On the other hand, some other servces may mpose lmts on the amount of packet delays, e.g. vdeo streams. Therefore, a tradeoff between the system throughput performance and user delays exsts n the scheduler desgns. Instead of the average delay, smlar as n [10] we use the delay outage probablty, whch defnes the probablty that the per-user nter packet delay exceeds a certan threshold: P = Pr( T Th), (4) out where T s the watng tme between the recepton of two consecutve packets for one user, whch s measured n number of tme slots, and Th s a pre-determned threshold. A large P out means poor farness among users. The throughput maxmzaton schedulers acheve hgh packet throughput wthout consderng user delays. On the other extreme, the smple round-robn (or frst-come-frst-serve) scheduler acheves zero delay outage when Th > K (snce n ths case T = K wth probablty one), at the expense of poor packet throughput. Some works n the lterature desgn schedulers by jontly consderng PHY layer capacty and delays, e.g. the antenna-asssted round-robn scheduler (AA-RRS) n [13], and the proportonally far (PF) scheduler n [14]. In our work, a novel schedulng rule s proposed by combnng packet throughput wth user delays. The followng jont performance metrc s to be maxmzed for selectng the best user(s): I T M = q (1 q) max I + max T, (5) u_ k k where represents the ndex for one selected user combnaton; I s the calculated packet throughput for ths user combnaton; T s a certan functon of the delays for the selected users; and T u_ k s the delay for user k, whch should be set to zero after each tme slot beng scheduled. The weghtng factor q s n the range from 0 to 1: q = 0 represents the round-robn scheduler, whle q = 1 corresponds to the schedulng scheme wthout delay constrant (Secton III). Suppose that we evaluate any schedulng scheme on both throughput and delay outage, then an I P tradeoff ~ out curve can be drawn (e.g. Fgure 2), wth respect to a fxed SNR (usually a ntermedate value). In such a fgure, by usng the scheduler (5) wth the same q, we can compare the throughput and delay outage propertes of dfferent PHY layer transmtters and/or recevers (correspondng to the ponts n dfferent curves), or dfferent schedulng settngs wth the same PHY layer sgnalng (ponts on one curve for dfferent q s n (5)). The jont performance for other schedulers (e.g. AA-RRS and PF) can also be evaluated n such a tradeoff fgure, wth the understandng that a better scheduler or PHY structure corresponds to a pont located more upper-left n the fgure, whch means lower delay outage wth hgher packet throughput. In the smulaton, we use the same parameter settngs as n Secton III, except that there are K = 20 actve users n the system. Followng the goals of packet throughput maxmzaton and delay mnmzaton, two schedulng schemes usng (5) wth dfferent PHY sgnalng structures are nvestgated: 1. One user: The same as scheduler 2 n Secton III, except usng M as the crteron. 2. JT-ZF Multuser: The same as scheme 5 n Secton III, except usng M as the crteron, wth T defned as T = max( Tu_ 1, Tu_ 2), f N S = 4 and users 1 and 2 (belongng to the th user combnaton) are scheduled smultaneously. For comparson purpose, we also evaluate PF and AA- RRS, replacng the channel capacty component n the orgnal schedulers by the packet throughput. Specfcally: 3. PF [14]: Wth ZF recever, each MU evaluates ts favorable transmt antenna subset wth NS 2, correspondng to the optmal packet throughput I and feeds them back to the DAP, where the user wth the largest relatve packet throughput s selected at each tme slot: I X = arg max, (6) [1, K] J where the runnng average throughput J for user s updated at each tme slot as: 1 I (1 ) J_ old + ; = X J = B B, (7) 1 (1 ) J_ old; X B where B represents the effectve memory of throughput average wndow, and a larger B wll result n longer delays. 4. AA-RRS [13]: ZF recever s mplemented, and N S s constraned to be N R = 2. To guarantee user farness, all

5 the K users are dvded nto K / N S groups, each of whch contans N S users. Dfferent groups are selected n a round-robn fashon. Durng the servce perod of one user group, N S users are mapped to N S data streams one by one to maxmze the packet throughput, so that certan amount of multuser dversty can be acheved. smlar reason, AA-RRS performs poorly, compared wth the other three schedulers. Fgure 2. The Delay-Throughput Tradeoff Curve, SNR=12dB. In Fgure 2, we choose the delay threshold to be 25 tme slots, whle 12dB transmt SNR s assumed. The fve ponts for schedulers 1 and 2, from lower-left to upperrght, represent q = 0, 0.25, 0.5, 0.75, 1 n (5), respectvely, whle the fve ponts of scheduler 3 n the same order correspond to B = 5, 10, 15, 20, 25 n (7) respectvely. From the fgure, we can see that for large values of q, the multuser scheduler 2 assumes better delay performance than the sngle user scheduler 1, whch concdes wth the conclusons n [8] for q = 1 cases. Although achevng a round-robn-lke delay property, the multuser dversty gan obtaned by AA-RRS s margnal n the consdered scenaro. Regardng the packet throughput, the multuser scheduler 2 performs much better than the sngle user scheduler 1, whle the proposed schedulers usng the metrc (5) perform better than PF. The proposed schedulers wth a q around 0.5, or PF usng a B around 10 appear to be promsng choces, snce the correspondng packet throughputs are not far from the ther optmal values, whle the delays are relatvely short. To fulfll dfferent QoS requrements, approprate parameters can be chosen based on ther locatons n the tradeoff fgure. It s also nterestng to nvestgate the packet throughputs when q = 0. Note that the multuser scheduler 2 performs worse than the sngle user scheduler 1 at ths pont, snce at an ntermedate SNR (c.f. Fgure 1 ) and when delay s an domnant factor n (5), the multuser scheduler does not assume any advantage over the sngle user scheduler, and N S = 1 may frequently be chosen by the scheduled user, whle scheduler 2 does not allow such a mode. For a Fgure 3. The Delay-Throughput Tradeoff Curve, SNR=13dB. From Fgure 1, we see that the throughput s very senstve to the SNR values n the ntermedate SNR regme. We therefore nvestgate the above schedulers by ncreasng the SNR by 1 db n Fgure 3, where we found that compared wth Fgure 2, the delay outage s sgnfcantly reduced, and the PF scheduler acheves almost the same packet throughput as that of scheduler 1, wth smaller delays. An ntutve explanaton s: from Fgure 1, we can see that the throughput s near saturaton at ths SNR value and bears lttle fluctuaton across dfferent users or user groups (because the SNR s hgh enough to transmt relable packets), so delay plays a more mportant role n both (5) and (6) for any q and B, respectvely. V. CONCLUSIONS In ths paper, conventonal schedulers that optmze PHY layer capacty are modfed by consderng the hgher layer packet throughput, whch appears to be a good combnaton of data rate and packet error probablty. When user delays are under consderatons together wth packet throughput, we propose a novel schedulng rule jontly consderng both factors, and a delay-throughput fgure can be drawn to comprehensvely evaluate dfferent schedulers. REFERENCES [1] R. Knopp, and P. A. Humblet, Informaton capacty and power control n sngle-cell multuser communcatons, Proc. IEEE Internatonal Conference on Communcatons 1995, ICC 95, vol. 1, pp , June [2] D. N. Tse, Optmal power allocaton over parallel Gaussan broadcast channels, Proc. IEEE Internatonal Symposum on Info. Theory 1997, ISIT 97, pp. 27, June [3] A. DeSmone, M. C. Chuah, and O.-C. Yue, Throughput performance of transport-layer protocals over wreless Lans, Proc. IEEE GLOBECOM 93, pp , Dec

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