An Efficient Adaptive Modulation Scheme for Wireless OFDM Systems

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1 A Efficiet Adaptive Modulatio Scheme for Wireless OFDM Systems Chag Wook Lee ad Gi Joo Jeo A adaptive modulatio scheme is preseted for multiuser orthogoal frequecy-divisio multiplexig systems. The aim of the scheme is to miimize the total trasmit power with a costrait o the trasmissio rate for users assumig kowledge of the istataeous chael gais for all users usig a comied it-loadig ad sucarrier allocatio algorithm. The sucarrier allocatio algorithm idetifies the appropriate assigmet of sucarriers to the users while the it-loadig algorithm determies the umer of its give to each sucarrier. The proposed it-loadig algorithm is derived from the geometric progressio of the additioal trasmissio power required y the sucarriers ad the arithmeticgeometric meas iequality. This algorithm has a simple procedure ad low computatioal complexity. A heuristic approach is also used for the sucarrier allocatio algorithm providig a trade-off etwee complexity ad performace. umerical results demostrate that the proposed algorithms provide comparale performace with existig algorithms with low computatioal cost. Keywords: Bit loadig sucarrier allocatio trasmit power adaptive modulatio OFDM. Mauscript received Sept ; revised July This work was supported y the Korea Sciece ad Egieerig Foudatio (KOSEF grat fuded y the Korea govermet (MOST o. R Chag Wook Lee (phoe: cw0407@samsug.com was with the School of Electrical Egieerig ad Computer Sciece Kyugpook atioal Uiversity Daegu S. Korea ad is ow with Moile Commuicatio Divisio Samsug Electroics Gyeoguk S. Korea. Gi Joo Jeo (phoe: gjjeo@ee.ku.ac.kr is with the School of Electrical Egieerig ad Computer Sciece Kyugpook atioal Uiversity Daegu S. Korea. I. Itroductio Orthogoal frequecy-divisio multiplexig (OFDM is a attractive techique for high-speed data trasmissio over idoor ad outdoor wireless commuicatio systems due to its aility to comat itersymol iterferece (ISI. Moreover it has already ee widely adopted y the Europea digital audio/video roadcastig (DAB DVB-T stadards highspeed modems over digital suscrier lies (DSL roadad wireless local area etworks such as the IEEE 80.11a as well as Hiperla ad the roadad wireless access stadard IEEE 80.16a [1]. To further improve performace OFDM systems also use adaptive modulatio [] which is composed of a itloadig algorithm ad a sucarrier allocatio algorithm. The former allocates the optimum umer of its to sucarriers accordig to istataeous chael trasfer fuctios so that each sucarrier ca e modulated with a differet modulatio scheme while the latter assigs the sucarriers to users ased o istataeous chael iformatio i a multiuser frequecy selective fadig eviromet. Previous research o adaptive modulatio schemes has essetially ee carried out i two differet directios amely: 1 margi adaptive (MA ad rate adaptive (RA. The ojective of MA is to miimize the overall trasmit power uder a data rate costrait [3]-[5] while the ojective of RA is to maximize the data rate uder a power costrait [6] [7]. Rhee ad Cioffi [6] proposed a dyamic sucarrier allocatio scheme which assures that all users achieve a similar data rate y maximizig the worst user s capacity. However this scheme has high computatioal complexity. Jag ad Lee [7] formulated the rate maximizatio prolem ad proved that the sum capacity is maximized whe each sucarrier is assiged to the user with the est suchael gai ad the power is the ETRI Joural Volume 9 umer 4 August 007 Chag Wook Lee et al. 445

2 distriuted usig a water-fillig algorithm. However fairess is ot cosidered i [7]. Thus whe the path loss differeces amog users are large the users with higher average chael gais ca e allocated most of the resources. I geeral wireless systems without prioritized services all users should e offered equal data rates as with the MA approach. I [3] a Lagragia-ased algorithm has ee proposed to achieve power efficiecy uder a data rate costrait. However although suoptimal the prohiitively high computatioal complexity reders it almost impractical. Fially a efficiet it-loadig algorithm for DMT applicatio [8] ad a multiuser it-loadig algorithm for multicarrier systems [9] have ee proposed where the former adds or removes oe it at a time ased o a two-dimesioal look-up tale while the latter seeks a solutio y iteratios which is optimal for certai chael coditios. Accordigly this paper proposes a ew adaptive modulatio scheme which comies a it-loadig algorithm ad a sucarrier allocatio algorithm ased o the MA approach. The proposed it-loadig algorithm is derived from a simple mathematical derivatio ad does ot require ay iteratios to adjust the power level i cotrast to covetioal water-fillig approaches [7] [10] [11]. I additio a heuristic approach is used for the sucarrier allocatio algorithm creatig a trade-off etwee speed ad performace. Sice the proposed adaptive modulatio scheme has a comparale performace ad low computatioal complexity it would appear to e practical. The orgaizatio of this paper is as follows. Sectio II descries the system model ad formulates the miimum overall trasmit power prolem. I sectio III the it-loadig algorithm is derived for a sigle-user system from a geometric progressio ad the arithmetic-geometric meas iequality. The sucarrier allocatio algorithm is preseted i sectio IV ad sectio V compares the performace of the proposed method with other approaches. Fially some coclusios are give i sectio VI. II. Prolem Descriptio I this paper it is assumed that the system has K users ad the k-th user has a data rate equal to B k its per OFDM symol. Usig the chael iformatio the trasmitter applies the comied it-loadig ad sucarrier allocatio algorithm to assig each sucarrier to differet users ad determie the umer of its/ofdm symols to e trasmitted y each sucarrier. Depedig o the umer of its assiged to a sucarrier the adaptive modulator uses a correspodig modulatio scheme to adjust the trasmit power level. Whe cosiderig the prolem of miimizig the total trasmitted power for a fixed umer of trasmitted its per OFDM symol B k for the k-th user for oe momet the trasmissio power allocated to the -th sucarrier for k its is equal to f ( k Pk = (1 k where k is the umer of its allocated to the -th sucarrier y the k-th user k is the magitude of the chael gai of the -th sucarrier as see y the k-th user ad f( k is the received power required per symol y the sucarrier for the reliale receptio of k iformatio its per symol. With respect to the total trasmitted power P T the prolem ca e formulated as T K k P = mi P. ( k D = 1 k = 1 k k Moreover the miimizatio is uder the costrait that Bk = =1 k where D = { 0 1 L J} is the set of all possile values of k ad more tha oe user sharig a sucarrier is ot allowed. III. Bit-Loadig Algorithm for Sigle-User System A ew it-loadig algorithm is preseted which is faster tha covetioal methods ad completes the computatio withi a defiite time. The proposed algorithm is ased o the geometric progressio of the additioal trasmissio power required y the sucarriers ad the arithmetic-geometric meas iequality. I this sectio the it-loadig algorithm is derived for a sigle-user eviromet. The optimizatio prolem i ( is rewritte for the case of a sigle user as T P = mi P (3 D = 1 ad the miimizatio is uder the costrait B = = 1. The trasmissio power allocated to the -th sucarrier ca P e expressed as the sum of the additioal trasmissio power required to successively allocate up to its oe it at a time to the -th sucarrier; P ΔP 1 + ΔP + + ΔP = L (4 where ΔP l = { f ( l f ( l 1}/. ΔP l deotes the additioal power eeded to trasmit oe additioal it through sucarrier whe the umer of its loaded o the sucarrier is l 1. The power required to satisfy the desired performace depeds o the umer of allocated its. As such the 446 Chag Wook Lee et al. ETRI Joural Volume 9 umer 4 August 007

3 trasmissio power required y the -th sucarrier for its to e trasmitted i the case of rectagular M-ary quadrature amplitude modulatio (MQAM sigal costellatios ( is eve ca e determied as i [1] as 0 p e ( ( Q f where 0 / is the variace of additive white Gaussia oise (AWG p e is the proaility of a symol error ad ( t Q x = e dt x costellatios ( { 357L} (5 1 π. For o-rectagular QAM sigal the required trasmissio power ca also e expressed as (5 without the equal sig [1]. Meawhile i the case of iary phase shift keyig =1 the required trasmissio power f(1 ca e approximated as 1 { O[ Q ( p e ] }/ which is kow to e slightly larger tha the right-had side of (5. However for simplicity ad practicality whe derivig the it allocatio algorithm to miimize the total trasmitted power f( from (5 with the equality sig is used as the trasmissio power required y the -th sucarrier for { 1 3 L} its to e trasmitted. For the prolem of miimizig the it allocatio (3 ca e rewritte as P T = mi D 1 < [( ΔP + L+ ΔP + ( ΔP + L+ ΔP 11 + L+ ( ΔP + L+ ΔP ] It ca e easily show that if the sum of the last additioal trasmissio power required y sucarriers ΔP 1 +ΔP + L + ΔP 1 is the miimum the P T is the miimum value. Also from (4 ad (5 it is uderstood that the sequece Δ P 1 Δ P L ΔP is the geometric progressio i which the iitial term is f ( 1 ad the commo ratio is. To fid the miimum value of ΔP 1 + ΔP P + L + Δ 1 advatage is take of the arithmetic-geometric meas iequality: Δ P +Δ P + L+ΔP 1 1 f(1 f(1 f(1 = + + L { f (1} 1+ + L+. 1 L 1 Whe each term o the left side of (7 is equal the sum is the miimum. Therefore if each term o the left side has the same value as (6 (7 f ( 1 { f ( 1 } 1 = for L L+ = 1 L (8 the the total trasmitted power P T is the miimum value. From (8 the optimal umer of its for the -th sucarrier is otaied as B = log + log ( 1 L for = 1 L. (9 Thereafter (9 is used to calculate the its allocated to the sucarriers where = 1 L must e itegers ad the sum of these its must e equal to B. Thus for actual modulatio/demodulatio is rouded-off as a iteger such that ˆ = roud ( for = 1 L. Whe the sum of ˆ coicides with B the it allocatio procedure is fiished. Otherwise as may its as the umer of B ˆ should e added to or sutracted from the appropriate sucarriers. Let s deote B ˆ y R. If R is positive R sucarriers are selected i a descedig order of ˆ ad oe more it is allocated to each of these sucarriers. I cotrast if R is egative oe it is sutracted from each sucarrier amog R sucarriers i the ascedig order of ˆ. The total umer of added or sutracted its is o more tha /. The followig is a summary of the proposed it-loadig algorithm: Step 1. Compute the umer of its for each sucarrier usig (9. Step. Calculate ˆ = roud( ad R = B ˆ. Step 3. Adjust ˆ to satisfy the costrait B = ˆ : If R=0 the the procedure is fiished. If R>0 the select R sucarriers ased o the descedig order of the value of ˆ ad add oe it to each of these sucarriers. If R<0 the select R sucarriers ased o the ascedig order of the value of ˆ ad sutract oe it from each of these sucarriers. Figure 1 shows a example of the allocated its ad power for a test chael with 18 sucarriers 51 its to e trasmitted ad a 10-3 target BER. The proposed algorithm does ot require ay iteratios i cotrast to a water-fillig approach regardless of the chael eviromet ad its computatioal complexity is O(+log. The computatio complexity of Lai s algorithm [13] used i [3] is O((J 1 ETRI Joural Volume 9 umer 4 August 007 Chag Wook Lee et al. 447

4 Chael gai umer of its Power (db Sucarrier umer (a Sucarrier umer ( Sucarrier umer (c Fig. 1. Simulatio results of the it ad power allocatio for 18 sucarriers: (a chael gai ( it allocatio ad (c power allocatio. Tale 1. Complexity of it-loadig algorithms. Bit-loadig algorithm Order of operatio Hughs-Hartogs algorithm [10] O ( B log Chow s algorithm [11] O ( k + log Lai s algorithm[13] (( J 1 B + log O Proposed algorithm O ( + log B: total umer of loaded its : umer of sucarriers k: required umer of iteratios J: maximum umer of iformatio its per symol. B+log where J is the maximum umer of iformatio its per symol. The order of operatios for the proposed ad other algorithms is taulated i Tale 1. Clearly the proposed algorithm requires far fewer operatios tha the other algorithms. IV. Sucarrier Allocatio Algorithm I multiuser OFDM systems ay of the multiple user sigals ca udergo idepedet fadig as the users may ot all e i the same locatios. Thus sucarriers that appear i deep fade to oe user may ot e i deep fade for other users. Hece each user should e allocated suitale sucarriers ased o cosideratio of the chael gais for all users ad fairess amog all users which is the essetial purpose of the sucarrier allocatio algorithm. The oce all the sucarriers are allocated to the users usig the sucarrier allocatio algorithm the sigle-user it-loadig algorithm give i sectio III is applied to each user of the allocated sucarriers. As such this sectio presets a heuristic method which provides a trade-off etwee swiftess ad performace. The proposed sucarrier allocatio algorithm specifically focuses o utilizig chaels with high gais. Thus i the case of two or more users with higher chael gais tha threshold th selected y trial ad error i a certai sucarrier the selectio of that sucarrier is waived. After the rest of the sucarriers are allocated to the users with the highest gai the waived sucarriers are the allocated. Thus users with a lower chael gai have a fair chace whe iddig agaist more powerful users. I the secod iteratio if there are still two or more uallocated users with a high chael gai i a waived sucarrier the user throughput C k is employed as a criterio of selectio: w f( avg k Ck = log 1 + w 0 (10 where deotes the waived sucarriers w is the total adwidth ad f( avg is the calculated power assumig that the average umer of its is allocated to each sucarrier. I a K-user OFDM system with -sucarriers each user is assumed to e allocated s k sucarriers where S k = /K. The followig is the proposed sucarrier allocatio algorithm: Step 1. Every user s average chael gai is ormalized to oe. Step. First iteratio for sucarrier =1: if the umer of sucarriers with k > th is or more waive allocatio else k arg max( k k allocate the -th sucarrier to user k if the umer of selected sucarriers is s k stop allocatio for user k ed if ed if ed for 448 Chag Wook Lee et al. ETRI Joural Volume 9 umer 4 August 007

5 Step 3. Secod iteratio for waived sucarrier if the umer of sucarriers with k > th is or more k arg mi( Ck k allocate the -th sucarrier to user k if the umer of selected sucarriers is s k stop allocatio for user k ed if else k arg max( k k allocate the -th sucarrier to user k if the umer of selected sucarriers is s k stop allocatio for user k ed if ed if ed for The order of operatios for the proposed algorithm ad other algorithms is taulated i Tale. As the umer of sucarriers icreases the computatioal urde of the proposed algorithm decreases compared to that of other algorithms. Tale. Complexity of sucarrier allocatio algorithms. Sucarrier allocatio algorithm Order of operatio Kivac s RCG algorithm [5] O ( K + log Rhee s algorithm [6] O ( K log Kivac s ACG algorithm [5] O (K Wog s algorithm [3] O ( Proposed algorithm O ( K ote: K: umer of users : umer of sucarriers V. Simulatio Results To demostrate the performace of the proposed algorithm for oth sigle-user ad multiuser OFDM computer simulatios were carried out i a frequecy selective Rayleigh fadig chael with additive Gaussia oise. It was assumed that the sigle-sided power spectral desity level 0 was equal to oe ad o chael codig scheme was used. The it error rate (BER ad the average trasmit power were adopted as the performace measures of the it allocatio algorithms. Figure shows the BER versus the it SR i a sigle-user OFDM system with 18 sucarriers. I this simulatio the total trasmissio rate B was equal to 51 its/symol ad 768 its/symol respectively ad the target BER was set at The average it SR was defied as the ratio of the average trasmit power to the oise power spectral desity BER Hughes-Hartogs algorithm (B=51 Proposed algorithm (B=51 Chow's algorithm (B=51 Hughes-Hartogs algorithm (B=768 Proposed algorithm (B=768 Chow's algorithm (B= Average it SR (db Fig.. BER performace compariso of it-loadig algorithms i a sigle-user OFDM system with 18 sucarriers. Tale 3. Average trasmit power for various target BERs (p e. (db Bit-loadig algorithm p e=10-3 p e=10-4 p e=10-5 Hughs-Hartogs algorithm [10] Chow s algorithm [11] Proposed algorithm level 0. The BER for the proposed algorithm was slightly higher tha that for Hughes-Hartogs algorithm [10] as expected yet it was lower tha that for Chow s algorithm [11]. Tale 3 shows the average trasmit power allocated to all sucarriers i the sigle-user OFDM system with 18 sucarriers ad 51 its to trasmit for various target BERs. The average trasmit power for the proposed algorithm was withi 0.7 db of that of Hughes-Hartogs algorithm. The proposed algorithm outperformed Chow s y aout 5.1 db. To compare the performace of the sucarrier allocatio algorithms computer simulatios were performed i which a equal umer of its were allocated to all the sucarriers. Figure 3 shows the BER versus the average it SR i a 16-user OFDM system with 18 sucarriers. The BER performace of the proposed sucarrier allocatio algorithm lay etwee that of Wog s algorithm ad Kivac s ACG algorithm. The performace of a multiuser OFDM system usig the proposed it-loadig ad sucarrier allocatio algorithm was also compared with that usig Wog s algorithm. After the same umer of sucarriers was selected for each user usig the sucarrier allocatio algorithms the sucarriers allocated for each user were loaded with the appropriate umer of its ETRI Joural Volume 9 umer 4 August 007 Chag Wook Lee et al. 449

6 BER Kivac s ACG algorithm Proposed algorithm Wog s algorithm Average it SR (db Fig. 3. BER performace compariso of sucarrier allocatio algorithms i 16-user OFDM system with 18 sucarriers. algorithm for multiuser OFDM systems. The proposed itloadig algorithm is derived from the fact that the sequece of the additioal trasmissio power required y each sucarrier is a geometric progressio ad the miimum total trasmitted power is otaied whe the additioal trasmissio power required y each sucarrier is the same accordig to the arithmetic-geometric meas iequality. As such the proposed algorithm does ot require ay iteratio; rather it ivolves calculatig the umer of its for each sucarrier ased o a formula followed y a addig or sutractig procedure for the remaiig its which are o more tha /. The proposed sucarrier allocatio algorithm is a heuristic method which alaces the trade-off etwee speed ad performace. Simulatio results i sigle-user ad multiuser OFDM systems show that the proposed algorithms ca achieve a similar BER performace to existig algorithms with low computatioal cost. As a result the proposed adaptive modulatio scheme is efficiet ad feasile for practical implemetatio. BER K=16 =18 Wog s algorithm (B=51 Proposed algorithm (B=51 Wog s algorithm (B=1536 Proposed algorithm (B=1536 K=3 = Average it SR (db Fig. 4. Compariso of BER performace i multiuser OFDM system. y the it-loadig algorithms. Figure 4 shows the BER versus the average it SR i the multiuser OFDM system for the case of a 16-user OFDM system (with = 18 ad B = 51 ad a 3-user OFDM system (with =56 ad B = 1563 respectively. The BER of the proposed algorithm was slightlyhigher tha that of Wog s algorithm as expected. VI. Coclusio This paper preseted a ew adaptive modulatio scheme cosistig of a it-loadig algorithm ad a sucarrier allocatio Refereces [1] ETSI Broadad Radio Access etwork (BRA: HIPERLA Type II Tech. Spec. Part I Physical Layer DTS/BRA [] B. Capolat ad Y. Taik Performace Aalysis of Adaptive Loadig OFDM uder Rayleigh Fadig IEEE Tras. Veh. Techol. vol. 53 o. 4 July 004 pp [3] C.Y. Wog R.S. Cheg K.B. Letaief ad R.D. Murch Multiuser OFDM with Adaptive Sucarrier Bit ad Power Allocatio IEEE J. Select. Areas Commu. vol. 17 o. 10 Oct pp [4] C.Y. Wog C.Y. Tsui R.S. Cheg ad K.B. Letaief A Real- Time Su-carrier Allocatio Scheme for Multiple Access Dowlik OFDM Trasmissio Proc. VTC 99 Amsterdam etherlads 1999 pp [5] D. Kivac G. Li ad H. Liu Computatioally Efficiet Badwidth Allocatio ad Power Cotrol for OFDMA IEEE Tras. Wireless Commu. vol. o. 6 ov. 003 pp [6] W. Rhee ad J.M. Cioffi Icrease i Capacity of Multiuser OFDM System Usig Dyamic Suchael Allocatio Proc. VTC 000 Tokyo Japa 000 pp [7] J. Jag ad K.B. Lee Trasmit Power Adaptatio for Multiuser OFDM Systems IEEE J. Select. Areas Commu. vol. 1 o. Fe. 003 pp [8] R.V. Soalkar ad R.R. Shively A Efficiet Bit-Loadig Algorithm for DMT Applicatios IEEE Commu. Lett. vol. 4 o. 3 Mar. 000 pp [9] J. Lee R.V. Soalkar ad J.M. Cioffi Multiuser Bit Loadig for 450 Chag Wook Lee et al. ETRI Joural Volume 9 umer 4 August 007

Multicarrier Systems IEEE Tras. Commu. vol. 54 o. 7 July 006 pp. 1170-1174. [10] D.

ow J.M. Cioffi ad J.A.C. Bigham A Practical Discrete Multitoe Trasceiver Loadig Algorithm for Data Trasmissio over Spectrally Shaped Chaels IEEE Tras. Commu. vol. 43 o. /3/4 Fe./Mar./Apr. 1995 pp.

7 Multicarrier Systems IEEE Tras. Commu. vol. 54 o. 7 July 006 pp [10] D. Hughes-Hartogs Esemle Modem Structure for Imperfect Trasmissio Media US Patet (July (March 1988 ad (May [11] P.S. Chow J.M. Cioffi ad J.A.C. Bigham A Practical Discrete Multitoe Trasceiver Loadig Algorithm for Data Trasmissio over Spectrally Shaped Chaels IEEE Tras. Commu. vol. 43 o. /3/4 Fe./Mar./Apr pp [1] J.G. Proakis Digital Commuicatio 4th ed. McGraw-Hill ew York 001. [13] S.K. Lai R.S. Cheg K.B. Letaief ad R.D. Murch Adaptive Trellis Coded MQAM ad Power Optimizatio for OFDM Trasmissio Proc. VTC 99 Housto Texas USA 1999 pp Chag Wook Lee received the BS MS ad PhD degrees i electrical egieerig from Kyugpook atioal Uiversity Daegu Korea i ad 007 respectively. Sice March 007 he has ee with Samsug Electroics Korea. His curret research iterests iclude wireless commuicatio CDMA ad OFDM. Gi Joo Jeo received the BS degree from Seoul atioal Uiversity Korea i He received the MS ad PhD degrees i systems sciece ad egieerig from the Uiversity of Housto Texas USA i 1978 ad 1983 respectively. Sice 1983 he has ee with the School of Electrical Egieerig ad Computer Sciece Kyugpook atioal Uiversity Daegu Korea. His mai research iterests are curretly itelliget cotrol sesor etworks ad resource cotrol i OFDM systems. ETRI Joural Volume 9 umer 4 August 007 Chag Wook Lee et al. 451

Adaptive Resource Allocation in Multiuser OFDM Systems

Adaptive Resource Allocation in Multiuser OFDM Systems Adaptive Resource Allocatio i Multiuser OFDM Systems Fial Report Multidimesioal Digital Sigal Processig Malik Meherali Saleh The Uiversity of Texas at Austi malikmsaleh@mail.utexas.edu Sprig 005 Abstract