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590 The Internatonal Arab Journal of Informaton Technology, Vol., No. 6, November 04 A Real Tme Adaptve Resource Allocaton Scheme for OFDM Systems Usng GRBF-Neural Networs and Fuzzy Rule Base System Atta

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590 The Internatonal Arab Journal of Informaton Technology, Vol., No. 6, November 04 A Real Tme Adaptve Resource Allocaton Scheme for OFDM Systems Usng GRBF-Neural Networs and Fuzzy Rule Base System Atta Rahman, Ijaz Quresh, Aqdas Mal, and Muhammad Naseem School of Engneerng and Appled Scences, ISRA Unversty, Pastan Department of Electrcal Engneerng, Ar Unversty, Pastan Abstract: Adaptve Resource Allocaton s a promnent and necessary feature of almost all future communcaton systems. The transmsson parameters le power, code rate and modulaton scheme are adapted accordng to the varyng channel condtons so that throughput of the OFDM system may be maxmzed whle satsfyng certan constrants le Bt Error Rate (BET) and total power at the same tme. For real tme systems, t s requred that the adaptve process should be fast enough to synchronze wth Channel State Informaton (CSI) and Qualty of Servce (QoS) demand that change rapdly. So n ths paper, we have a real tme system n whch once CSI and QoS s fed n as nput, t gves us optmal Modulaton Code Pars (MCPs) and power vectors for dfferent subcarrers. Usng a Fuzzy Rule Base System (FRBS) we obtan MCP by gvng CSI and QoS and by usng Dfferental Evoluton (DE) the power vector s obtaned. Ths becomes an example. A Gaussan Radal Bass Functon Neural Networ (GRBF-NN) s traned n offlne mode usng suffcent number of such examples. After tranng, gven QoS and CSI as nput GRBF-NN gves Optmum Power Vector (OPV) and FRBS gves optmum MCP mmedately. Proposed scheme s compared wth varous other schemes of same doman and supremacy of the proposed scheme s shown by the smulatons. Keywords: DE, OFDM, FRBS, GRBF-NN, adaptve modulaton and codng, MCP. Receved January 3, 03; accepted July 4, 03; publshed onlne March 3, 04. Introducton and Related Wor Use of evolutonary computng, soft-computng and hybrd ntellgent algorthm for soluton of optmzaton problems n varous felds of engneerng s an emergng area of research nowadays. These algorthms are attractve due to ther nonlnear nature, fast convergence and easy mplementaton. Adaptve Orthogonal Frequency Dvson Multplexng (AOFDM) s one of the successful canddates for many 3 rd Generaton (3G) and 4 th Generaton (4G) Systems. In ths technque a sngle very hgh data rate stream s dvded nto several equvalent low data rate streams by usng Inverse Fast Fourer Transform (IFFT). Then, these streams are modulated over dfferent orthogonal subcarrers. Addton of sutable Cyclc Prefx (CP) maes the system Inter Symbol Interference (ISI) free. Fuzzy system based adaptve modulaton scheme for OFDM system was proposed n [4]. Turbo coded adaptve modulaton was nvestgated by Lew et al. [8] and also dfferent adaptaton schemes were analyzed [5]. For sngle antenna OFDM systems, coded bt and power loadng problem was addressed by L et al. [7] usng Low Densty Party Chec (LDPC) codes orgnally motvated by [7]. Many Bt Interleaved Coded Modulaton (BICM) systems have been proposed le [7, 6, 7]. Le et al. [6] nvestgated adaptve communcaton usng turbo codes. An adaptve codng and modulaton scheme s proposed by Bocelmann et al. [6], n whch a bsecton method was used to adapt the transmt rate. A Genetc Algorthm (GA) based adaptve resource allocaton scheme was proposed by Reddy [3], to ncrease the user data rate, where water-fllng prncple was used as a ftness functon. A subchannel allocaton based on aucton algorthm was proposed by [], where throughput was sustaned at the cost of user data rates. A novel effcent resource allocaton algorthm for multuser OFDM system usng a proportonal farness based algorthm among users and to acheve good performance even wth low SNR was proposed by []. Another nterestng paper adaptve resource allocaton based on modfed GA and Partcle Swarm Optmzaton (PSO) for multuser OFDM system was proposed by []. An approach an to the prevous one, Ant Colony Optmzaton (ACO) evolutonary technque for subcarrer allocaton n OFDMA-based wreless system was proposed by [8]. Adaptve subcarrer and power allocaton wth farness for mult-user Space-Tme Bloc-Coded (STBC) OFDM system was nvestgated n contrast to Greedy algorthm as well as water-fllng prncple [9]. An optmzaton problem for power constrants usng GA to maxmze the sum capacty of OFDM system A Real Tme Adaptve Resource Allocaton Scheme for OFDM Systems Usng GRBF-Neural Networs wth the total power constrant was nvestgated n [0]. Also, t was shown that GA performs better than conventonal methods. A scheme for resource allocaton n downln Multple Input Multple Output (MIMO) OFDMA wth proportonal farness was proposed n [] where domnant Egen channels obtaned from MIMO state matrx are used to acheve low complexty. Ths scheme provdes much better capacty gan than statc allocaton method. A PSO based Adaptve multcarrer cooperatve communcaton technque whch utlzes relay node for subcarrer n deep fade to mprove the bandwdth effcency was proposed by [9] where centralzed and dstrbuted versons of PSO were nvestgated. A low complexty subcarrer and power allocaton technque based upon GA to maxmze the sum of user data rates n MIMO-OFDMA system was proposed n [5]. Al-Janab et al. [], proposed a bt and power allocaton strategy for Adaptve Modulaton Codng (AMC) based MIMO-OFDMA WMAX system. Another GA based effcent real-tme subcarrer and bt allocaton for multuser OFDM transmsson technque was proposed n whch overall transmt power was mnmzed under user constrant [0]. A subcarrer-chun based technque n whch resource allocaton problem for the downln of OFDMA wreless systems was proposed n []. A Qualty of Servce (QoS) based performance and resource management scheme n 3G wreless networ for realstc envronments s presented by [30]. An ntellgent approach for data collecton n Wreless Sensor Networ (WSN) was presented by [9]. Adaptve codng and modulaton scheme wth fxed transmt power by Atta-ur-Raman et al. [3] proposed a Fuzzy Rules Base System (FRBS) for fndng sutable Modulaton Code Pars (MCPs) for subcarrers gven the QoS demand and Channel State Informaton (CSI) of all subcarrers. Same strategy whle usng Product Codes as codng scheme was proposed n [5]. A combned approach to adaptve codng, modulaton and power was proposed by Atta-ur-Rahman et al. [4] n whch FRBS was used for choosng modulaton code par whle power vector for subcarrers was optmzed by usng two dfferent algorthms, Water fllng algorthm and GA. In ths paper, we have a real tme system n whch once we feed n CSI and QoS as nput, the system gves us optmal MCP for dfferent subcarrers and the power vector. Usng the FRBS suggested n [3, 4], we frst fnd out the MCP after feedng n CSI and QoS requred. Then, usng Dfferental Evoluton algorthm, we get power vector for partcular stuaton. Ths gves us one example. We buld up many examples for varous values of CSI and QoS. Havng formulated these examples, we tran a Gaussan Radal Bass Functon Neural Networ (GRBF-NN) wth dfferent CSI and QoS as nput and ther correspondng power vectors as desred output. All ths tranng s done offlne. Now, once tranng s over, gven CSI and QoS for subcarrers, we mmedately get MCP from FRBS and power vector from traned GRBF-NN. The remander of ths paper s organzed as follows: In secton, system model s ntroduced. Performance of dfferent codes n conjuncton wth dfferent modulatons s presented n secton 3. The results of secton 3 are used n secton 4 to formulate a constraned optmzaton problem. In secton 5 a bref ntroducton to FRB s gven that s used to solve the optmzaton problem formulated n prevous secton. Secton 6 contans the ntroducton to Dfferental Evoluton (DE) algorthm; Secton 7 contans the proposed GRBF-NN scheme, performance comparson of ths scheme wth varous other famous adaptve schemes wth and wthout FRBS s gven n secton 8 whle secton 9 concludes the paper.. System Model The system model consdered s OFDM equvalent baseband model wth N number of subcarrers. It s assumed that complete CSI s nown at both transmtter and recever. The frequency doman representaton of system s gven by: Where r, h, r,,..., N = h. p.x + z ; = () p, x and z denote receved sgnal, channel coeffcent, transmt ampltude, transmt symbol and the Gaussan nose of subcarrer =,,..., N, respectvely. The overall transmt power of the OFDM system s N Ptotal = = p and the nose dstrbuton s complex Gaussan wth zero mean and unt varance. It s assumed that sgnal transmtted on the th subcarrer s propagated over an ndependent non-dspersve sngle-path Raylegh Fadng channel and where each subcarrer faces a dfferent amount of fadng ndependent of each other. Hence, the channel coeffcent of th subcarrer can be expressed as: h jθ,,..., N = α e ; = () Where α s Raylegh dstrbuted random varable of th subcarrer, and the phase θ s unformly dstrbuted over [0, π]. OFDM PHY Transmtter Feedbac Channel OFDM Channel New Modulaton Code and Power PHY layer Recever Sub-channel Estmates Qualty of Servce Demand per Subcarrer Fuzzy Rule Base System (FRBS) Gaussan Radal Bass Functon Neural Networ (GRBF-NN) Fgure. Bref dagram of proposed system. 59 The Internatonal Arab Journal of Informaton Technology, Vol., No. 6, November 04 A bref dagram of proposed system s gven n Fgure. Once the sgnal s receved from OFDM channel, channel estmates CSI and QoS demand per subcarrer s fed nto adaptaton bloc whch suggests the parameters for the next transmsson nterval. These parameters are sent to PHY layer transmtter va a feedbac channel. compensated easly. Some of these graphs are depcted n the Fgures 3, 4 and 5 wth rate /4, /3 and / respectvely. Each curve n these fgures represents performance of a specfc modulaton and code par. Ths nformaton wll be used n FRBS rule base n subsequent sectons. These graphs are plotted n MATLAB Codng and Modulaton Components of the proposed system model are descrbed below. Bt Bt loadng Loadng FEC FEC Encoder QAM Modulator AWGN Channel 3.. Codng Schemes Non recursve convoluton codes are used for codng scheme n ths paper. The code rates taen from the set C = {/4, /3, /, /3, 3/4} wth constrant length 3. For decodng, standard Soft Output Vterb Algorthm (SOVA) decoder s used [4] whle proposed FRBS s used for adaptng optmal code rate. 3.. Modulaton Schemes As modulaton scheme for adaptve modulaton Quadrature Ampltude Modulaton (QAM) s used, wth rectangular constellaton. The modulaton symbols are taen from the set M = {, 4, 8, 6, 3, 64, 8}. FRBS s used for adaptng optmal modulaton symbol Power Dstrbuton Power dstrbuton or the loadng algorthm s the man contrbuton of ths paper. For ths purpose a GRBF-NN s proposed. Moreover, the proposed scheme s compared wth other loadng algorthms le Water-fllng and GA etc., and also wth fxed power case. For expermentaton the sequence of operatons s carred out n same way as gven n the Fgure. The transmtted sgnal s frst encoded usng standard feed-forward convolutonal encoder havng code rate from the set C and then the encoded sgnal s modulated usng the elements of QAM from the set M. In ths way we have followng possble pars of codng and modulaton by cross product of sets C and M, whch yelds: P = Cx M = {( c, m j ) c C m j M } (3) Then, graph for each par s obtaned over an Addtve Whte Gaussan Nose (AWGN) channel. The selecton of ths channel s sutable n a sense that t reflects the proper relatonshp between Sgnal to Nose Rato (SNR) and data rate achevable under a specfc target Bt Error Rate (BER). And other channel characterstcs le fadng types etc., can be Bt Bt Recevng BER FEC FEC Decoder QAM QAM Demodulator Fgure. Bref dagram of smulatons. QAM wth rate /4 SNR[dB] Fgure 3. BER comparson of dfferent QAM modulatons usng rate /4 convolutonal codes. BER BER QAM wth rate /3 SNR[dB] Fgure 4. BER comparson of dfferent QAM modulatons usng rate /3 convolutonal code. QAM wth rate / SNR[dB] Fgure 5. BER comparson of dfferent QAM modulatons usng rate / convolutonal code. A Real Tme Adaptve Resource Allocaton Scheme for OFDM Systems Usng GRBF-Neural Networs Rate Optmzaton In order to maxmze the data rate for OFDM systems, the constraned optmzaton problem may be stated as, Maxmze the overall data rate of OFDM system such that BER and transmt power remans constraned. Mathematcally: m ax R T o tal = r N = s.t, B E R B E R Q o S an d N P T o tal = p PT = (4) Where r = (log (M)) R C, s bt rate of th subcarrer, whch s a product of code rate R C, and modulaton order (log (M)) used at th subcarrer, P T s the avalable transmt power and BER QoS, s target BER that depends upon a specfc QoS request or applcaton requrement over th subcarrer, whle N s number of subcarrers n OFDM system. From the results obtaned n secton 3, those codemodulaton pars that fulfll dfferent BER demands dependng upon dfferent QoSs.e., BER T = 0-5, 0-4, 0-3, 0 - etc., are obtaned. Ths s done by drawng straght lnes on the graphs as shown n Fgures 3-5 on certan BER ponts QoS le 0-5, 0-4, 0-3, 0 -. Ths s shown n Fgure 6. The mappng shown n Equaton 5 s a non-convex functon that cannot be optmzed usng convex optmal technques unless t s made convex accordng to [9]. However, ths functon s optmzed by the proposed FRBS descrbed n next secton. The steps nvolved n creaton of FRBS are descrbed n the flowchart gven n Fgure 7. The bref descrpton of each phase of the flowchart s gven below: Data Acquston: Data s obtaned from the graphs obtaned n secton 3 n the form of Input/Output (IO) pars. Rule Formulaton: Rules for each par are obtaned by the approprate fuzzy set used. That s by puttng complete par n IO set and a rule generated for each par. Elmnaton of Conflctng Rule: The rules havng same IF part but dfferent THEN parts are nown as conflctng rules. Ths appears when more than one MCP s avalable for gven specfcaton. Completon of Looup Table: Loo up table s complete n a sense that there exsts a rule for every stuaton. Obtanng Graphs for standard Codng/ modulaton schemes Elmnatng the Conflctng rules Data Acquston from Graphs n terms of IO pars Obtanng rules from IO pars (one rule from each par) QAM wth rate /4 Completon of Fuzzy Loo-up table usng heurstcs Creaton of Fuzzy Rule Base System usng Loo-up table BER SNR[dB] Fgure 6. Process of obtanng modulaton code par under specfc QoS. Then, the ponts of ntersecton of these lnes and the curves (representng a code and a modulaton) are noted that gves the approprate SNR value. So, the nformaton obtaned can be expressed as for a gven SNR and specfc QoS whch modulaton code par can be used. In order to obtan more granularty BER ponts are even quantzed. In ths way there are about fve hundred pars are obtaned from the graphs. Ths table after completon s used as a startng pont for generaton of loo-up table for the FRBS. Wthout loss of generalty we can say that ths table represents a functon (mappng) n whch the throughput can be expressed n terms of BER, transmt power and SNR: R = MCP = f(snr, BER, P) (5) Fgure 7. Fuzzy rule base system flowchart. 5. Fuzzy Rule Base System A FRBS s used to optmze the cost functon gven n Equaton 4. It wll be decded that whch modulaton code par s sutable for a specfc subcarrer based upon the ndvdual CSI at the subcarrers and the QoS demand. The rules are of the form: p p p ( x, x ; y ); p =,,3... N (6) Where x represents receved SNR, x represents requred BER QoS and y P represents the output MCP suggested by FRBS, so a rule can be narrated as: p {If (x s L and x s Q7) Then y s P} Followng s the bref descrpton of dfferent components of FRBS used. Desgn of the FRBS s carred out n MATLAB standard Fuzzy System Toolbox. 5.. Fuzzy Sets and Fuzzfer Suffcent numbers of fuzzy sets are used to cover the nput output spaces. There are two nput varables receved SNR and Mnus Log Bt Error Rate (MLBER) p 594 The Internatonal Arab Journal of Informaton Technology, Vol., No. 6, November 04 that represents a QoS. The reason tang MLBER s because BER of a requred QoS s gven by 0 -, 0-3, 0-4 etc., whle the range of fuzzy varable should be equally spaced and quantfable. So, to get ths, followng operaton s done frst: M LBER = -log(ber ) -q BER = 0 -q M LBER = -log(0 ) = q There s one output varable that s MCP. Standard trangular fuzzfer s used wth AND as MIN and OR as MAX. 5.. Rule Base Rule base contans rules aganst all the IO pars. As there are thrty-one sets (L0 to L30) for frst nput varable named SNR and about sxteen sets (Q to Q6) for nput varable MLBER, hence there are 496 rules n rule base. Rule base s complete n the sense that rules are defned for all possble combnatons of nput space Inference Engne and De-Fuzzfer Famous Mamdan Inference Engne (MIE) s used that wll nfer whch nput par wll be mapped onto whch output pont. Standard Center Average Defuzzfer (CAD) s used for defuzzfcaton. 6. Dfferental Evoluton Algorthm (7) DE s an evolutonary algorthm orgnally proposed by [8]. In many aspects t s comparable to GA, but the man features that maes t superor than GA, s ts fast convergence rate and less vulnerablty to stuc n the local mnma problem whch s nherent n many varants of GA. There are four man operatons n DE namely ntalzaton, mutaton, crossover and selecton. A flowchart of the algorthm s gven n Fgure 8. Descrpton of each step pertanng to our problem s gven below: a. Intalzaton: The frst power vector taen n the scheme would be taen as flat power for all subcarrers. Power vector length s equal to number of subcarrers N. Then, ntal populaton s generated randomly around the ntal vector, so that the power constrant remans satsfed. b. Mutaton: Standard mutaton operaton s used as descrbed orgnally n the algorthm,.e., a weghted dfference of two power vectors s added to thrd vector. c. Crossover: Standard crossover method s used to generate the tral vector. d. Selecton: Whether to eep a vector or not s based upon a ftness value used n greedy crteron. We have employed FRBS for ths purpose, as shown n Fgure 9. That s ftness equal to sum rates after applyng the chosen vector to the system. Mathematcally, t can be wrtten as: R = r N = = (log ( M )) RC, N = = FRBS ( SNR, QoS ) N = = FRBS ( pα, QoS ) = MCP N = = End Decson Taen Yes Start Intalzaton Mutaton Crossover Selecton based upon FRBS Crtera met? Fgure 8. Dfferental evoluton algorthm flowchart. Transmt power vector (p) Fgure 9. Ftness bloc for selecton phase n DE. 7. Gaussan Radal Bass Functon Neural Networ GRBF-NN are consdered the most powerful networs for hghly nonlnear systems. They are also proven to be the unversal approxmators [3]. In our scenaro, GRBF-NN are well suted because our problem s hghly non-lnear, n whch we need to see the approprate power vector based upon the gven channel condtons and QoS demand per subcarrer, wth a constraned overall transmt power. The schematc dagram for the proposed networ s gven n Fgure 0. Input n x R Qualty of servce vector Q α α α N Gaussan Hdden Layer ( x c ) δ e Fuzzy Rule Base System (FRBS) (MCP) (MCP) (MCP) N No Lnear Combner Fgure 0. Bloc dagram of the GRBF-NN. W r N = Output n y R Throughput (8) A Real Tme Adaptve Resource Allocaton Scheme for OFDM Systems Usng GRBF-Neural Networs Followng are the steps nvolved n constructon of the networ. 7.. Example Set In order to tran the networ, a large number of examples are generated by Fuzzy Rule Base System wth Dfferental Evoluton (FRBS-DE). Ths s done n followng manner: Randomly pc set of channel coeffcents and QoS demands per subcarrer. For ths set fnd the MCP and then Optmum Power Vector (OPV) usng FRBS-DE as descrbed n secton 6. It becomes an example that s for a certan channel coeffcent vector and QoS vector whch power vector s optmum[ x, x ;d ]. Add example to mae an example set of S n total, S.e., [ x,x ;d ] =. About 50,000 examples are generated n ths fashon, n order to mae the system robust. 7.. Tranng The networ s traned by the supervsed learnng technque usng famous Least Mean Square (LMS) algorthm. The tranng process s shown n Fgure. In ths process an example s ntroduced to the networ the output s compared wth the desred output, consequently the error s fed bac to LMS algorthm that updates the weghts. Then the change n weghts s updated n th

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