Minimum Normalized Transmit Rate Based Fair Scheduling Algorithm in Orthogonal Frequency Division Multiplexing (OFDM)

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1 Iteratioal Joural of Electroic Egieerig Research ISSN Volue 1 Nuber 4 (009) pp Research Idia Publicatios Miiu Noralized Trasit Rate Based Fair Schedulig Algorith i Orthogoal Frequecy Divisio Multiplexig (OFDM) *1 Sageeta Moga ad Sukhdev Sigh 1, Assistat Professor 1, Departet of Electroics & Couicatio Egieerig 1 Adesh Istitute of Egieerig & Techology, Faridkot 1103 GTB halsa Istitute of Egieerig & Techology, Malout. *E-ail: sageetagadhi78@gail.co Abstract The dead o high rate ultiedia iforatio has pushed the developet of wireless couicatio systes i a uprecedeted pace. Syste desig of fourth geeratio (4G) techology has already begu, which seeks to support a wide rage of services with highest data rates reachig 0Mbps. OFDM is a iportat cadidate techique for the future wireless trasissio. It is a ulticarrier odulatio ad access techique which ca support high data rates ad perfor well i wireless eviroet. However this ca be esured oly through good schedulig algorith to allocate the coo resources. The proble is to allocate resources aog users fairly. I this paper Miiu Noralized Trasit Rate Based Fair Schedulig Algoriths based o Throughput is discussed also the perforace of this algorith is evaluated through siulatio results. ey words: Multicarrier odulatio, OFDMA, Fair Schedulig. Itroductio Orthogoal Frequecy Divisio Multiplexig (OFDM) has bee cosidered as a very proisig solutio for supportig high-data-rate trasissio i future broadbad wireless couicatio systes. The basic idea of OFDM is to divide the available spectru ito several sub-carriers so that the iforatio sybols are trasitted i parallel o the sub- carrier over the wireless chael. This allows us to desig a syste supportig high data rates while aitaiig sybol duratios uch loger

2 338 Sageeta Moga ad Sukhdev Sigh tha the chael delay spread. By doig so, each sub-carrier experieces alost a flat fadig ad the detrietal effects of the ulti-path chaels are reduced. OFDM is also attractive fro a ulti-user perspective. Sice the badwidth is divided ito orthogoal sub-carriers, it is possible to schedule differet users siultaeously o differet frequecy bads. The ost beeficial properties with the OFDM odulatio are: Each tras-receiver will have access to all sub-carriers with i a cell layer (this eables very high bit rates) There is ore or less o eed of frequecy plaig with i cell layer (it is perfored with ad adaptive allocatio algorith) Sub-carrier odulatio is perfored with a FFT (easy to ipleet) The divisio of sigal ito a large uber of ore or less idepedet subchaels will provide the flexibility eeded for all future ultiedia services (variable bit-tare with differet quality of services) Schedulig i OFDM The process of selectig a user out of ay users i order to access the coo resources of a chael is called schedulig [3]. The fuctio of a schedulig algorith is to select the user whose data is to be trasitted ext. This selectio process is based o the QoS requireets of each user. It is desirable for a schedulig algorith to possess the followig features: Efficiet lik utilizatio, Fairess, Delay boud, Throughput, ad Isolatio. I ulti-user OFDM syste (OFDMA), the chael coditios of obile users vary i the tie doai ad differet sub carriers experiece differet chael gais because of frequecy selective fadig chaels. Wireless lik capacity is geerally a scarce resource that eeds to be used efficietly. Therefore, it is iportat to fid a efficiet way of supportig Quality of Service (QoS) for each user. Specifically, it is iportat to axiize the syste throughput while providig fairess aog users i.e. the resources ust be fairly allocated aog the users. The criterio for fairess ay be latecy, throughput or QoS. To axiize the throughput of the syste best sub carrier is allocated to each user. Of course, the procedure is ot siple sice the best sub carrier of the user ay also be the best sub carrier of aother user who ay ot have ay other good sub carriers. As already said, that at all the tie the user with the best chael is selected to axiize the throughput. But i this case, if a user is at a great distace fro the base statio or its chael is i deep fade, the it will ever get a chace to access the chael. Hece there is eed to provide fairess aog users [], [4]. Algorith Developet Multicarrier Aalysis [1] I case of ulticarrier trasissio such as OFDMA where uber of user is M ad the uber of sub carriers is. Let SNR k be the SNR correspodig to th user ad k th sub carrier the for adaptive OFDM syste, the axiu uber of bits assiged to the k th subcarrier of the th user is decided by the followig forula:

3 Miiu Noralized Trasit Rate Based Fair Schedulig Algorith 339 SNRk bk = log ( M ) = log 1+ (1) Γ Where Γ represets the sigal-to- oise ratio (SNR) gap ad for QAM odulatio, Γ is writte as: l( BER t arg et ) Γ = () 1. Where BER target is the required Bit Error Rate (BER).Let p ad σ deote the trasit power of each carrier ad variace of additive white guassia oise, respectively. Let g k be the chael gai correspodig to th user ad k th sub carrier. The g k p SNRk = (3) σ Substitutig (3.3) i (3.1), we get g k p bk = log ( M ) = log 1+ (4) Γσ The above equatio tells axiu how ay bits a user ca allocate o a sub carrier. Here it is assued that P e is aitaied costat i all the sub carriers ad hece SNR gap is the sae for all the sub carriers. The total uber of bits trasitted i oe OFDM sybol is give by, b = b k k = 1 Matheatical Model for Algorith As per [1], a k = l deotes that the sub carrier k is allocated to user ad a k = 0 if sub carrier k is ot allocated to user. Assue that a sub carrier ca ot be used by ore tha oe user, thus M = 1 a k 1, k For each user the total grated trasit rate is calculated as W = k = 1 a k b k ad the oralized trasit rate is W / Φ, where () (6) (7) Φ is the rate weight of user. Service Fairess Idex (SF1), the axiu differece betwee the oralized trasit rates, is usually used to easure the fairess of schedulig algorith, which is represeted as: SFI = axw / Φ W / Φ, SFI = 0 idicates the ideal fairess, which is ufeasible i real systes. For real systes there a upper boud B is used to easure the fairess, i.e. (8)

4 340 Sageeta Moga ad Sukhdev Sigh axw, / Φ W / Φ B A efficiet fair resource schedulig algorith should axiize the total throughput while satisfyig the fairess requireet. The optiizatio proble ca be expressed as: M ax a b (10) { 0,1} ak = 1 k = 1 k k Subjected to: akbk akbk k = k = 1 ax 1 i B (11) Φ Φ ad M = 1 a 1 (1) k Miiu Noralized Trasit Rate Based Fair Schedulig Algorith I this algorith, the user with the least oralized trasit rate is allowed to choose a sub carrier. This guaratees the fairess aog all users. The, the sub carrier with the highest utilizatio efficiecy to that user is selected. Thus, a high efficiecy ca be achieved. This algorith is divided ito steps where is the uber of sub carriers. The ai algorith is give below: Step 1: Iitialize a k = 0, W = 0 for = l,,.. M ad for k= l,... Set S = {l,,..k}. Step : Select = arg i( W / Φ ) for all k S calculate the utilizatio efficiecy M u* k = b* k / bk. Let k = arg k ax{ u * k } ad set a * k* = 1. Update = 1 W * = W * + b * k* ad S = S \{ k } Step 3: If S = Φ the stop. Otherwise, go to Step. (9) Siulatio & Results A throughput based fair schedulig algorith [1] has bee siulated i MATLAB 7.1 cosiderig oly dowlik (base statio users) resource schedulig i OFDM cellular syste. The siulatio odel cosidered i [1] is used oly differece is i BER which is ow take 10 - i siulatig the dowlik resource schedulig for OFDMA.

5 Miiu Noralized Trasit Rate Based Fair Schedulig Algorith 341 Siulatio Paraeters 7 odulatio schees, viz, BPS, QPS, 8 PS, 16 QAM, 3 QAM, 64 QAM AND 18 QAM, are eployed i this siulatio. The siulatio paraeters are give i table 4.1. Table 4.1: Siulatio Paraeters. Paraeter Value No. of users (M) No. of sub carriers () 64 Carrier frequecy (fc) GHz Bit rate SNR (P/ σ ) 10 bps 0 db BER 10 - Doppler frequecy (f d ) 100 Hz Results ad Discussio I the siulatio, for the sae odel, throughputs of iiu oralized trasit rate based fair resource schedulig algorith (FRS), axiu resource schedulig algorith (MRS.) ad rado resource schedulig algorith (RRS) have bee easured. Fig. 4.1 shows the throughput of each user i case of FRS, MRS ad RRS. The average chael gai ad rate weight of d user is set to1. It is clear fro the figure that axiu throughput is achieved i case of MRS because it allocates 100% of the subcarriers to the best user whose average chael gai is higher but it is ufair because zero throughputs are achieved for the users whose gais are less or who are i deep fade. I case of RRS, although the throughput of each user is sae ad, therefore, it is a fair algorith, but throughput is less aroud % because it allocates the sub carriers to each user radoly. FRS provides a coproise betwee the above two algoriths. I this case, the throughput of each user is sae ad is 0%. This is higher tha that i case of RRS, sice each user i the FRS algorith selects a best subcarrier istead of rado subcarrier i RRS case. The relatioship betwee average uber of loaded bits with φ for differet values σ is show i fig.4..i this case whe average chael gai of fifth user is greater tha 0.4, the average uber of loaded bits icreases with icrease i φ,because i this case ore badwidth is allocated to the user which has good chael coditio.fig.4.3 ad fig.4.4 show the relatioship betwee average uber of loaded bits per subcarrier versus φ for SNR=db ad SNR=30db.Figures shows that as the SNR icreases, average uber of bits loaded icreases, so perforace of algorith

6 34 Sageeta Moga ad Sukhdev Sigh iproves with icreasig SNR. I this case the results obtaied through siulatio are ot exactly atchig as results obtaied by [1] but the ature of result is sae. Figure 4.1: Achieved Throughput of each user with chael has axiu gai. Figure 4.: Average loaded bits per subcarrier versus φ for SNR=0db.

7 Miiu Noralized Trasit Rate Based Fair Schedulig Algorith 343 Figure 4.3: Average loaded bits per subcarrier versus φ for SNR=db. Figure 4.4: Average loaded bits per subcarrier versus φ for SNR=30db. Coclusio The perforace of iiu oralized trasit rate based fair schedulig algorith has bee evaluated through siulatio. The perforace of this algorith is copared with that of axiu resource scheduler (MRS) ad rado resource scheduler (RRS). It is evidet fro the siulatio results that the fair schedulig

8 344 Sageeta Moga ad Sukhdev Sigh algorith provides alost 0% throughput with fairess aog the users. Siulatio results show that the perforace of algorith iproves with icreasig SNR. Refereces [1] Dig Y.G., Zhao-yag Z., Pei-Iiag Q. ad Peg C. (00), Fair Resource Schedulig Algorith for Wireless OFDM Systes, Proceedigs of Iteratioal Coferece o Couicatios, Circuits ad Systes 7-30 May 00, vol. 1, pp [] Erge M., Coleri S. ad Varaiya P. (003), QoS Aware Adaptive Resource Allocatio Techiques for Fair Schedulig i OFDMA Based Broadbad Wireless Access Systes, IEEE Trasactios o Broadcastig 003, vol. 49.4, pp [3] Fattah H. ad Leug C. (00), A Overview of Schedulig Algoriths i Wireless Multiedia Networks, IEEE Wireless Couicatios, 00, pp [4] Zhao E. ad Yao J (006), Data Traffic Fair Schedulig for Multi-user OFDM Syste Based o Heuristic Geetic Algorith, Iteratioal Coferece o Coputatioal Itelligece ad Security, 3-6 Nov, 006, vol.. pp