APSIPA ASC 2011 X an Throughput Maxmzaton by Adaptve Threshold Adjustment for AMC Systems We-Shun Lao and Hsuan-Jung Su Graduate Insttute of Communcaton Engneerng Department of Electrcal Engneerng Natonal Tawan Unversty, Tape Emal: d95942014@ntu.edu.tw, hjsu@cc.ee.ntu.edu.tw Abstract The mechansms of adaptve modulaton and codng (AMC) and hybrd automatc repeat request (HARQ) are two mportant schemes n modern wreless communcaton systems. In practcal system desgn, the AMC mechansm s usually mplemented wth fxed swtchng thresholds for the modulaton and codng schemes (MCS), and suffers from performance degradaton. To mtgate ths problem, a novel algorthm s proposed n ths paper to maxmze the system throughput. The algorthm adaptvely adjusts the AMC threshold values accordng to the HARQ acknowledge (ACK) feedback nformaton n each transmsson round so that the AMC mechansm can select the best MCS wth nearly optmal thresholds. Smulatons are conducted to show that the system throughput s ndeed mproved by the proposed adaptve threshold adjustment algorthm. I. INTRODUCTION In the communcaton systems developed n recent years, the data applcatons are becomng more and more mportant than the tradtonal voce servce. Contrary to the voce servce that has both delay and qualty constrants, data applcatons are usually more tolerant of delay, thus allowng explotaton of the theoretcal tme-doman water-fllng beneft. The most common water-fllng approach s adaptve modulaton and codng (AMC) whch adjusts the transmsson power, modulaton and codng rate accordng to the nstantaneous channel condton to maxmze the average throughput [1]. Because of the popularty and mportance of wreless data servces, AMC has been a key technology, whch s adopted n modern wreless systems such as 3GPP Hgh Speed Downlnk Packet Access (HSDPA) [2], cdma2000 1x Evoluton for Data and Voce (1xEVDV) [3], IEEE 802.16 [4], and 3GPP Long Term Evoluton (LTE) [5], n order to offer hgh data rate n tme-varyng fadng channels. The AMC mechansm usually requres channel condton feedback from the recever to the transmtter. Hence t may not perform well f the channel vares too rapdly compared to the feedback rate. Ths problem can be allevated wth the use of hybrd automatc repeat request (HARQ) whch provdes tme dversty to mprove transmsson robustness [6]. In fact, the use of HARQ allows AMC to operate more aggressvely and further boosts the system throughput [7]. Ths work was supported by the Natonal Scence Councl, Natonal Tawan Unversty, and Intel Corporaton under Grants NSC99-2911-I-002-201, NSC99-2219-E-002-019, 99R70600, and 10R70500. Although the HARQ mechansm can enhance the robustness of the system and hence boost system performance, t suffers from the problem of ncreased latency due to the round trp delay of the acknowledgement (ACK) sgnalng. In conventonal HARQ systems, durng the transmsson perod of each data frame, the system does not change the modulaton and codng scheme (MCS) used untl the frame s successfully receved or the maxmum number of the retransmsson rounds s reached. One mportant reason why the latency ncreases s that the transmtter does not select the MCS whch best fts the channel condton n retransmsson rounds. Therefore, n the lterature, there are a varety of works developed to handle ths ssue. A straghtforward dea to decrease the number of retransmsson rounds of HARQ, whch s called adaptve HARQ, s to vary the MCS used n each retransmsson round n order to select a best ft MCS n fast fadng channel and hence the number of retransmsson rounds can be mnmzed [8]. In addton, n practcal system mplementaton, the thresholds of AMC mechansm for swtchng the MCSs are generally determned under some smplfed channel assumptons and stored n the systems. If the channel statstcs were fxed and the transmsson system always swtched the MCSs wth correct thresholds, the optmal throughput could be obtaned. However, n realty, the communcaton channel may vary wth tme, and the optmal thresholds wll vary wth the channel statstcs. As a result, the pre-determned thresholds wll not be optmal for swtchng MCSs, and there wll be a great performance loss. In [9], [10], and [11], the problem was dscussed and analyzed for non-adaptve HARQ wth constant transmsson tme nterval (TTI). In these studes, methods to adaptvely adjust thresholds were proposed, but these methods can not be appled to adaptve HARQ. In ths paper, a novel and smple algorthm s proposed to mprove the system throughput for AMC systems wth adaptve HARQ. II. SYSTEM MODEL In ths study, the system consdered ncludes a transmtter, a recever, a sngle-nput sngle-output (SISO) forward channel, and an error-free feedback channel between transmtter and recever. The recever keeps measurng the receved sgnalto-nose rato (SNR), and reportng t back to the transmtter va the feedback channel wth a constant feedback delay. It s
C T nformaton bts Informaton Source C T /R C coded bts Channel Encoder R C Modulator Fg. 1. Smplfed transmtter block dagram. R M C T /R C R M symbols assumed that the transmtter does not have the knowledge of the long term channel statstcs and the transmsson power s constant. It s also assumed that the system s equpped wth both the AMC and the HARQ mechansms. To llustrate the transmsson process, the smplfed block dagram of the wreless transmtter n Fg. 1 s consdered. When the transmsson starts, there s a data frame of nformaton bts wth length C T generated from the nformaton source block and buffered to be transmtted. If the transmtter decdes to transmt t wth the MCS of nomnal rate R, the nformaton bt frame s frstly encoded by channel codng and rate-matchng processes wth codng rate R C, and then modulated wth modulaton rate R M. The relatonshp among the rates R, R C, and R M s R (nf ormaton bts per symbol) (1) = R C (nformaton bts per coded bt) R M (coded bts per symbol). When AMC s consdered, the transmtter has to select an MCS whch fts the current channel condton best and can get maxmum throughput. That s, the transmtter has to select an MCS ˆθ such that ˆθ = arg max η(θ(ˆρ)), (2) θ where ˆρ s the nstantaneous receved SNR value measured and reported by the recever, θ s the MCS ndex and s a functon of ˆρ, and η s the system throughput and s a functon of θ. For mplementaton smplcty, practcal system usually keeps a pre-determned lookup table for decdng MCS. It s assumed that there s a set S M of M possble MCSs wth nomnal rates R 1, R 2,, R M, denoted as S M = {MCS : = 1, 2,, M}, and the MCS lookup table contans a set S T of M 1 threshold values, denoted as S T = {Γ : = 1, 2,, M 1}. The MCS selecton strategy then can be expressed as θ(ˆρ) = 1, ˆρ (, Γ 1 ); m, ˆρ [Γ m 1, Γ m ); M, ˆρ [Γ M 1, ). When HARQ s consdered, after the frame s receved, the recever decodes the frame and checks f the frame s correct by cyclc redundant check (CRC). If the frame s correctly decoded, the recever sends an ACK sgnal to the transmtter to ask for next data frame. If the recever fals to correctly decode the frame, t sends a NAK sgnal to the (3) transmtter to ask for retransmsson of the same coded frame (or ts redundancy verson) untl the frame s successfully decoded or the maxmum transmsson lmt L s reached. If the frame s stll not correctly decoded after the maxmum L transmssons, the recever wll clam the frame to be erroneous and ask for next data frame. For HARQ wthout frame combnng or wth Chase combnng [6], the same coded frame s transmtted at each retransmsson round. If frame combnng s not mplemented, the recever only uses the most recent retransmsson of the frame n the decodng. For Chase combnng, the recever softly combnes all transmssons of the data frame and utlzes the accumulated sgnal n the decodng. Through frame combnng, the faled transmssons of the data frame are not wasted because the recever uses them to ncrease the decodng SNR. If ncremental redundancy (IR) HARQ [6] s adopted n the system, the transmtter sends a dfferent redundancy verson of the coded frame n each retransmsson round. After the recever combnes these redundancy versons, not only the decodng SNR s ncreased, the codng rate s also reduced. In summary, compared to HARQ wthout frame combnng, Chase combnng mproves the system performance va accumulated SNR n decodng, whle IR further enhances the performance by reducng the codng rate. The HARQ protocol adopted n the system n ths study s adaptve HARQ, whch means that the MCS used n each retransmsson round can be changed and can be dfferent from the MCS used n the ntal transmsson. The recever combnes the transmssons of the frame wth frame combng. For the adaptve HARQ n consderaton, t s assumed that the system mantans a lookup table for decdng the MCS used n each transmsson. In each transmsson and retransmsson, the transmtter decdes whch MCS s adopted by lookng up the MCS lookup table only accordng to the nstantaneous receved SNR ˆρ measured and reported by the recever. The target of ths study s to adaptvely adjust the values of the SNR thresholds {Γ 1, Γ 2,, Γ M 1 } n the MCS lookup table. III. PROPOSED ALGORITHM From the ntroducton and dscusson above, the purpose of the proposed algorthm s to select an MCS whch best fts the current channel condton and s able to adaptvely adjust the MCS swtchng thresholds, so that the system throughput can always be maxmzed for any gven channel statstcs. For adaptve HARQ, t should be noted that the cases of the ntal transmsson round and the retransmsson rounds of the data frame should be consdered separately. For the ntal transmsson round, not only the expected throughput but also the nomnal rate should be consdered n the selecton of the MCS. For the retransmsson rounds of the frame, the nomnal rate, whch means the amount of nformaton bts need to be transmtted, has been determned n the ntal round, and hence the only concern s to select an MCS whch can complete the transmsson of the data frame as fast as possble. Therefore, the algorthm s also separated nto two
parts to ft the dfferent goals of the two types of transmssons. The detal dscusson s stated n the followng subsectons. A. Intal Transmsson Round To analyze the problem, frst of all, we defne the event A as the event that the transmtter gets an ACK sgnal when MCS s selected n the ntal transmsson round. Then the average throughput η of the transmsson when the MCS wth nomnal rate R s selected n the ntal transmsson round under the condton that the nstantaneous receved SNR measured (for determnaton of the ntal MCS) beng ˆρ can be expressed as R N A (ˆρ) η (ˆρ) = lm N N (ˆρ) = R p A (ˆρ), where N s the number of tmes MCS s selected n the ntal transmsson round, N A s the number of tmes A occurs, and p A s the probablty the event A occurs and can be defned as N A (ˆρ) p A (ˆρ) = lm N (ˆρ) N (ˆρ). (5) Snce the optmal thresholds cannot be known before the data communcaton takes place, the transmtter only ntalzes a lookup table wth a pre-determned set of threshold ponts S T. The condton for the threshold Γ to be optmal and maxmzng the throughput s that the MCS on ether sde of the threshold yelds the same throughput (4) η (Γ ) = R p A (Γ ) (6) =η (Γ ) = R p A (Γ ). Usng the method proposed n [11], we defne a threshold band as [Γ γ, Γ + γ + ), (7) where γ and γ + defne the lower and upper ranges of the threshold band, respectvely. If γ and γ + are small enough, (6) can be approxmated by P r(a R ) P r(b ) R P r(a ) P r(b (8) ), where the notaton P r(x) means the probablty of the event X, B m means the event that the MCS m s selected when the measured SNR ˆρ falls n threshold band, and A m means the event that the ACK sgnal s receved when MCS m s used n threshold band. To smplfy (8), we force the followng assumpton for each threshold band: P r(a ) = P r(a ), (9) whch can be acheved by alternatng the MCS selecton when the measured SNR falls n a threshold band as: If A happens, select MCS the next tme ˆρ [Γ γ, Γ + γ + ). If A happens, select MCS the next tme ˆρ [Γ γ, Γ + γ + ). Otherwse, when ˆρ [Γ γ, Γ + γ + ), the MCS s kept the same as the prevous transmsson. Then we have: R P r(b ) R P r(b (10) ). Note that when the SNR does not fall n any threshold band, the MCS selecton s regular,.e., selectng MCS when the SNR s between Γ 1 and Γ. Consderng the problem how to adaptvely adjust the thresholds, we may adjust the threshold Γ hgher by δ B when B happens. Ths s because, wth (9), more frequent B means lower throughput of MCS than MCS at Γ. Thus Γ s lower than ts optmal value. Smlarly, we may adjust the threshold Γ lower by δ B when B happens. When Γ s at ts optmal value, the up-adjustments and down-adjustments should balance up, so Γ does not move on average. Therefore, we need P r(b )δ B = P r(b )δ B. (11) Comparng (10) and (11), the relatonshp for step-sze values can be derved as B. Retransmsson Round δ B δ B = R R. (12) In the retransmsson rounds, because the nomnal rate and the number of the nformaton bts to be transmtted were already fxed n the ntal transmsson round, the transmtter only needs to decde whch MCS s best for transmttng the equvalent number of nformaton bts left so that the number of the retransmsson rounds can be mnmzed. Hence, the consderaton for the selecton of MCS s transformed to the condton how to arrange the resources for each remanng nformaton bt to be effectvely transmtted. In ths study, t s assumed that the only ndcaton of the avalable resources for MCS selecton s the receved SNR. Therefore, the MCS selecton problem s now transformed to selectng a sutable MCS to transmt nformaton bts accordng to the SNR avalable for each nformaton bt,.e., the normalzed SNR. To calculate normalzed SNR n the retransmsson round j, frstly the equvalent number of nformaton bts left to be transmtted n ths round should be measured. The nformaton bt effectvely receved by the recever n the transmsson round l can be computed at the recever as C l R = log 2 (1 + ˆρ l ), (13) where ˆρ l s the actual receved SNR at round l. Then the estmated equvalent number of the nformaton bts left to be transmtted at retransmsson round k can agan
be computed at the recever as C (k) T = R k 1 CR l (14) l=1 = R k 1 log 2 (1 + ˆρ l ), l=1 where R s the nomnal rate n nformaton bts per symbol (computed as n (1)) selected n the ntal transmsson round. Therefore, the normalzed SNR value ρ j the retransmsson round j can provde per remanng nformaton bt s ρ j = ˆρ C (j) T, (15) where ˆρ s the measured nstantaneous SNR at round j used to derve the normalzed SNR ρ j to be fed back to the transmtter. To select an MCS n the retransmsson round, a set of normalzed threshold values S T = { Γ : = 1, 2,, M 1} s defned. Then the MCS s selected accordng to the normalzed SNR feedback nstead of the nstantaneous receved SNR feedback used n the ntal round. That s, smlar to the formulaton n (2), the MCS selecton n retransmsson round s θ( ρ j ) = 1, ρ j (, Γ 1 ); m, ρ j [ Γ m 1, Γ m ); M, ρ j [ Γ M 1, ). (16) Thereafter, to adaptvely adjust the thresholds n retransmsson rounds, a normalzed threshold band s defned as [ Γ γ, Γ + γ + ). (17) If the ρ j value falls n any normalzed threshold band, the adaptve adjustment algorthm n retransmsson round s trggered. For any nomnal rate n the ntal round, and for any gven round j, the optmal threshold should make the remanng nformaton bts successfully transmtted equally fast no matter usng MCS or MCS. In other words, the normalzed throughputs (normalzed to the same number of remanng nformaton bts) on both sdes of the optmal threshold should be the same. Thus, η ( Γ ) = R p (j) A ( Γ ) (18) = η ( Γ ) = R p (j) A ( Γ ), where A (j) means the event that the ACK sgnal s obtaned when MCS s used n j-th retransmsson round, and p (j) A s the probablty of A (j) defned smlarly as n (5). Based on smlar dervatons as n Secton III-A, the MCS selecton strategy n normalzed threshold band can be derved and summarzed as: If A (j) happens, then select MCS the next tme ρ j [ Γ γ, Γ + γ + ). If A (j) happens, then select MCS the next tme ρ j [ Γ γ, Γ + γ + ). Otherwse, when ρ j [ Γ γ, Γ + γ + ), the MCS s kept the same as the prevous transmsson. Note that when the SNR does not fall n any threshold band, the MCS selecton s regular,.e., selectng MCS when the normalzed SNR feedback s between Γ 1 and Γ. And the adaptve threshold value adjustment algorthm n retransmsson round s: If B (j) happens, then update Γ wth Γ + δ B, If B (j) happens, then update Γ wth Γ δ B, where δ B and δ B are the step-sze values for up and down adjustments, respectvely, and the relatonshp between s the same as (12). IV. SIMULATION RESULTS To verfy the performance of the proposed algorthm, a smulaton was done on a CDMA based system. The multplexng technque used s code dvson multplexng (CDM), the channel codng adopted here s turbo code (TC), and the HARQ type s IR. Four MCSs wth nomnal rates 1.0, 2.0, 3.0 and 4.5 are used n ths system. The channel s generated usng Jakes model [12]. The detal parameters used n ths smulaton are summarzed n Table I. All the smulatons are run for 10000 frames and the the smulaton tme s enough to have convergence for all schemes. The smulaton results under dfferent moble speed condtons are shown n Fg. 2 and Fg. 3. In both fgures, the curve wth trangular mark sketches the performance of the system wth fxed MCS thresholds for the ntal transmsson, and the curve wth cross mark presents the result of the system wth adaptve thresholds for the ntal transmsson of each data frame. Both these curves are for non-adaptve HARQ, meanng, the MCS for the retransmsson rounds s the same as that of the ntal transmsson. In addton, the curve wth damond mark s the result of the system wth adaptve HARQ protocol and fxed thresholds, and the curve wth crcle mark s the result of the proposed method whch adapts thresholds n both ntal and retransmsson rounds wth adaptve HARQ protocol. The smulaton results wth moble speed 10km/hr are shown n Fg. 2. From the results shown n Fg. 2, t can be seen that the proposed adaptve threshold adjustment algorthm n HARQ retransmsson rounds mproves the throughput n most SNR regon, and can get maxmum about 0.5dB gan over the performance of the system only adaptng MCS threshold n ntal transmsson whle gettng 2dB and 2.2dB gan over those of the fxed-threshold systems wth adaptve and non-adaptve HARQ, respectvely. Smlarly, the smulaton results wth moble speed 60km/hr n shown n Fg. 3. From the results shown n Fg. 3, t can be seen that the proposed adaptve threshold adjustment algorthm n HARQ retransmsson rounds also mproves the throughput n most SNR regon wth 1dB gan over the performance of the system only adaptng MCS threshold n ntal transmsson whle gettng 2dB and 2.5dB gan over those of the fxed-threshold
TABLE I PARAMETERS FOR SINGLE CARRIER CDM SIMULATION. Parameter Multplexng Carrer Frequency Symbol Tme Duraton Channel Model Moble Speed HARQ Type ACK/NACK Feedback delay SNR Feedback delay MCS Value CDM 2GHz 0.667ms Jakes Model 10km/hr, 60km/hr IR 3 frames 6 frames QPSK/ 1 2 TC 16QAM/ 1 2 TC 16QAM/ 3 4 TC 64QAM/ 3 4 TC 7 rounds 2dB, 5dB, 10dB Maxmum Retransmssons Intal Thresholds Step-sze n Intal Transmsson 0.75 Step-sze n Retransmsson 0.0025 Throughput (bps) 3.5 3 2.5 2 1.5 4 x 105 1 Non adaptve HARQ, fxed thresholds Non adaptve HARQ, adaptve thresholds Adaptve HARQ, fxed thresholds Adaptve HARQ, adaptve thresholds 0.5 0 2 4 6 8 10 SNR (db) Fg. 2. Throughput of CDMA based system wth moble speed = 10km/hr. systems wth adaptve and non-adaptve HARQ, respectvely. By comparng the results n Fg. 2 and Fg. 3, t can be seen that the proposed algorthm provdes better performance gan under the condton of hgher moble speed. It s because that the channel varaton s not so severe when moble speed s slow, and therefore most of the data frames are receved successfully at the ntal transmsson. On the other hand, f the moble speed s fast, the proposed algorthm s able to trace and adapt the varyng channel condton better. In addton, t can be seen that, n hgh SNR regon, the curves seem to be merged. Ths s because only the MCS wth hghest rate s selected and the retransmssons seldom take place n hgh SNR regon. From the results and dscussons above, t s clear that the proposed threshold adaptaton algorthm ndeed mproves the system throughput when compared wth the other two systems. V. CONCLUSION In ths paper, we nvestgated the throughput maxmzaton problem for AMC systems wth HARQ. We frst dscussed the condtons for throughput maxmzaton, and then proposed a novel algorthm capable of adaptvely fulfllng these Throughput (bps) 2.5 2 1.5 1 0.5 3 x 105 Non adaptve HARQ, fxed thresholds Non adaptve HARQ, adaptve thresholds Adaptve HARQ, fxed thresholds Adaptve HARQ, adaptve thresholds 0 0 1 2 3 4 5 6 7 8 SNR (db) Fg. 3. Throughput of CDMA based system wth moble speed = 60km/hr. condtons. To generalze our dscusson, t s assumed that adaptve HARQ protocol s used. Smulaton results show that the proposed algorthm s very effectve and has sgnfcant performance gan. Ths algorthm s very easy to mplement, and can releve the operators of dfferent knds of wreless communcaton systems usng AMC and HARQ from havng to perform offlne optmzaton each tme the channel statstcs change. REFERENCES [1] A. J. Goldsmth and S.-G. Chua, Varable-rate varable-power MQAM for fadng channels, IEEE Transactons on Communcatons, vol. 45, no. 10, pp. 1218 1230, October 1997. [2] Hgh Speed Downlnk Packet Access: Physcal Layer Aspects. 3GPP TSG RAN WG1 Std. TR 25.858 V5.0.0, 2002-2003. [3] Physcal Layer Standard for cdma2000 Spread Spectrum Systems. 3GPP2 Std. C.S0002-D V1.0, 2004. [4] Ar Interface for Fxed Broadband Wreless Access Systems. IEEE Std. 802.16-2004, 2004. [5] Evolved Unversal Terrestral Rado Access (E-UTRA); LTE Physcal Layer-General Descrpton (Release 8). 3GPP TSG RAN TS 36.201 Verson 8.3.0, September 2009. [6] S. Kallel and D. Haccoun, Generalzed type II hybrd ARQ scheme usng punctured convolutonal codng, IEEE Transactons on Communcatons, vol. 38, no. 11, pp. 1938 1946, November 1990. [7] A. Das, F. Khan, A. Sampath, and H.-J. Su, Adaptve asynchronous ncremental redundancy (A 2 IR) wth fxed transmsson tme nterval (TTI) for hsdpa, n Proc. 2002 IEEE 13th Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons (PIMRC 2002), Lsboa, Portugal, September 15-18 2002, pp. 1083 1087. [8] F. Khan, LTE for 4G Moble Broadband: Ar Interface Technologes and Performance. Cambrdge Unversty Press, 2009. [9] H.-J. Su, On adaptve threshold adjustment wth error rate constrants for adaptve modulaton and codng systems wth hybrd ARQ, n Proc. 2005 IEEE 5th Internatonal Conference on Informaton, Communcatons and Sgnal Processng (ICICS 2005), Bangkok, Thaland, December 6-9 2005, pp. 786 790. [10] H.-J. Su and T.-N. Ln, Adaptve throughput maxmzaton for adaptve modulaton and codng systems, n Proc. 2005 Ass-Pacfc Conference on Communcatons (APCC 2005), Perth, Australa, October 5-5 2005, pp. 406 410. [11] H.-J. Su and L.-W. Fang, A smple adaptve throughput maxmzaton algorthm for adaptve modulaton and codng systems wth hybrd ARQ, n Proc. 2006 2nd Internatonal Symposum on Communcatons, Control, and Sgnal Processng (ISCCSP 2006), Marrakech, Morocco, March 13-15 2006. [12] W. C. J. (Edtor), Mcrowave Moble Communcatons. New York: John Wley and Sons Inc., February 1975.