Simulation of Frequency, Timing Acquisition, and Cell Search Algorithms for OFDMA Based Mobile WiMAX

Transcription

1 2011 Iteratioal Coferece o Commuicatio Egieerig ad Networks IPCSIT vol.19 (2011) (2011) IACSIT Press, Sigapore Simulatio of Frequecy, Timig Acquisitio, ad Cell Search Algorithms for OFDMA Based Mobile WiMAX Fakher Eldi M. Sulima, Nuha M. Elhassa ad Terteil A. Ibrahim Departmet of Electroics Egieerig, College of Egieerig,Suda Uiversity of Sciece ad Techology, Khartoum, Suda Abstract Mobile WiMAX is based o orthogoal frequecy divisio multiple access techique. It, therefore, iherited the frequecy ad timig offset problems which cotribute to the loss of the trasmitted data. To overcome these problems, the trasmitter ad receiver must be well sychroized. This paper addresses the Mobile Wimax cocept ad itroduces sychroizatio algorithms for frequecy, timig acquisitio, ad cell search. These algorithms have bee simulated uder adaptive white Gaussia oise ad fadig chael for differet values of sigal to oise ratio. The simulatio results obtaied show that most of the errors have bee successfully illumiated. Keywords- mobile WiMAX; orthogoal frequecy divisio multiple access sychroizatio algorithms 1. Itroductio Curret wireless commuicatio stadards fail to provide sufficiet data rate, whe the user is movig at high speed. I view of this requiremet for future mobile wireless commuicatio systems, the Istitute of Electrical ad Electroic Egieers (IEEE) has proposed the IEEE e stadard to achieve a high speed broadbad wireless access etwork that ca cover a complete city [1]. The stadard is widely kow as WiMax, which is a acroym for Worldwide Iteroperability for Microwave Access. The WiMAX etwork is cosidered as a Wireless Metropolita Area Network (WMAN) ad is oe of the Broadbad Wireless Access (BWA) techiques that have emerged as a promisig solutio for last mile access techology. Fig.1 shows positios of differet existig wireless access techologies i terms of mobility ad data rate. Figure 1. Positioig of differet wireless access techologies i terms of mobility ad data rate. Mobile WiMAX systems are based o the IEEE e-2005 specificatios which defie the physical (PHY) ad the medium access cotrol (MAC) layers for mobile ad broadbad wireless access systems operatig at microwave frequecies below 6 GHz [2]. Actually, three differet PHY layers specificatios were defied by IEEE e They are sigle-carrier trasmissio, orthogoal frequecy-divisio multiplexig (OFDM), ad orthogoal frequecy divisio multiple access (OFDMA). WiMAX systems are based o OFDMA PHY layer specificatios [3],[4]. 39

2 A OFDM system is highly sesitive to timig ad frequecy offsets. Demodulatio of a OFDM sigal with a offset i the frequecy ca lead to a high bit error rate. Mobile WiMAX dowlik (DL) sychroizatio ivolves sychroizatio of carrier frequecy ad timig as well as idetificatio of the preamble idex. Carrier frequecy offset (CFO) may arise from the differece i atural oscillator frequecies betwee the base statio (BS) ad the mobile statio (MS). With OFDMA based systems, effective, reliable, ad efficiet techiques are required to allow sychroizatio of remote termials. So, sychroizatio algorithms are the major desig problem that has to be solved to build a successful product. 2. Wimax frame ad Symbol Structure 2.1. Time Domai OFDM Cosideratios The OFDM theory requires the additio of a Cyclic Prefix (CP) at the begiig of the OFDM symbol to allow the receiver to absorb the delay spread due to the multipath much more efficietly ad to maitai frequecy orthogoality. The CP occupies a duratio called the guard time ad is a temporal redudacy that must be take ito accout i data rate computatios. The stadard idicates that, for OFDMA ad OFDMA PHY layers, a substatio (SS) iitially searches for all possible values of the CP util it fids the CP beig used by the base statio (BS). The SS the uses the same CP o the uplik. Oce a specific CP duratio has bee selected by the BS for operatio o the dowlik, it caot be chaged. Chagig the CP would force all the SSs to resychroize to the BS Frequecy Domai OFDM Cosideratios I order to create the OFDM symbol i the frequecy domai, the modulated symbols are mapped o to the subchaels that have bee allocated for the trasmissio of the data block. A subchael is a logical collectio of subcarriers. The umber of subchaels allocated for trasmittig a data block depeds o various parameters, such as the size of the data block, the modulatio format, ad the codig rate. As illustrated i Fig. 2, the umber ad exact distributio of the subcarriers that costitute a subchael deped o the subcarrier permutatio mode. I WiMAX, the subcarriers that costitute a subchael ca either be adjacet to each other or distributed throughout the frequecy bad, depedig o the subcarrier permutatio mode. A distributed subcarrier permutatio provides better frequecy diversity. Observig Fig. 2, it ca be oted that there are four types of subcarriers. Data subcarriers are for useful data trasmissio. Pilot subcarriers are maily for chael estimatio ad sychroizatio. For OFDM PHY, there are eight pilot subcarriers. Null subcarriers are frequecy guard bads ad there is o trasmissio o them. The DC subcarrier is the subcarrier whose frequecy is equal to the RF cetre frequecy of the trasmittig statio ad its fuctio is to simplify digital-to-aalogue ad aalogue to digital coverter operatios [5]. 3. Frequecy ad Timig Sychroizatio Algorithms This paper focuses o the sychroizatio part of the mobile WiMAX trasceiver which cosists of packet detectio, symbol timig, cell search, ad frequecy offset estimatio Packet Detectio ad Symbol Start Packet detectio is the task of estimatig the start of the preamble of a icomig data packet. It is the first sychroizatio algorithm to be performed ad the rest of the sychroizatio process depeds o its success [5], [6]. The algorithm evaluatio deped the probability of detectio, which is the probability of correctly detectig a existig packet ad the probability of false alarm, which is the probability of detectig a packet give that it does ot exist. Both probabilities deped o the used algorithm. For example, i double slidig widow packet detectio algorithm, the eergy of two cosecutive slidig widows is calculated from the received sigal. The basic priciple is to form the decisio variable m as a ratio of the total eergy cotaied iside the two widows as show i Fig

3 Figure 2. Subchael ad subcarrier permutatios. Figure 3. The respose of the double slidig widow packet detectio algorithm. To explai this, let r be the received complex data after the ADC, ad let M ad L be the widow legths for the first ad the secod widow, respectively. The the eergy of the two widows ad the decisio variable may be defied as: (1) M M = M 0 m m = = M= 0 m a r r r (2) L L 2 = l 0 + l + l = = l= 0 + l b r r r m a = (3) b Where a is the eergy cofied i the th widow for the widow A, ad b is the eergy cofied i the th widow for the widow B. This algorithm does ot deped o the sigal atteuatio or eve the iterferece at the receiver as it measures the ratio of two quatities ot a absolute quatity. Symbol timig refers to the task of fidig the idividual OFDM symbol start ad ed. The symbol timig result defies the set of samples used to calculate the DFT of each received symbol. The DFT result is the used to demodulate the subcarriers of the symbol. After the packet detector has provided a estimate of the start edge of the packet, the symbol timig algorithm refies the estimate to sample level precisio. If L is the legth of the correlatio sequece, the calculatio for the cross-correlatio is obtaied by: tˆ = r t (4) L 1 * s arg max k= k The value of that correspods to maximum absolute value of the cross-correlatio is the symbol timig estimate. I mobile WiMAX there are 114 differet preamble shapes ad storig a referece for each requires may correlators. This is the reaso why the above techique fails whe applied o mobile WiMAX [7] Frequecy Offset Estimatio ad Correctio Carrier frequecy offset due to oscillators mismatch ad Doppler frequecy has a great effect o OFDMA systems sice the OFDMA symbol totally depeds o the subcarriers beig orthogoal. So it s importat to detect ay frequecy offset that occurs o the OFDM sigal. If the carrier frequecy sychroizatio is perfect, the receiver samples at the peak of each subcarrier where the amplitude is maximum ad the iter carrier iterferece (ICI) is zero. However, if the carrier frequecy is misaliged by some amout, some of the desired eergy is lost ad more ICI is itroduced. The frequecy offset-shift- ca be fie or coarse. I fie frequecy offset, the shift is withi oe subcarrier spacig while i coarse frequecy offset, the shift is withi multiple iteger umber of subcarrier spacig [8] [9]. The process of timig ad frequecy acquisitio takes place i both time ad frequecy domais as illustrated i Fig. 4. If the spacig of the ozero subcarriers i the preamble is much smaller tha the coherece badwidth of the chael, the the chael resposes at eighborig preamble subcarriers are approximately equal. Mathematically, this ca be give by: H( K + 1) = H( K) +Δ H( K) (5) 41

4 Where, Δ H( K) << H( K) { ( ) ( 1) } { ( ) j ( ) ( 1) ( 1) } R Q k Q k = R H k P k + H k P k + (6), j 2 Δ H( K) Dj ( k + ) (7) N p 1 ( ) { ( ) ( 1) } (8) k + 0 j M = D k + R Q k Q k Dj( k) + Pj ( k) Pj( k 1) K is a idex for ozero preamble subcarriers Pk ( ) j is the stored preamble of idex (j) Q(k) is the received preamble i the frequecy domai. is the ormalized frequecy offset RQkQk { ( ) ( 1) } is the differetial sigal The, the estimated itegral carrier frequecy offset (CFO) ad the preamble idex are give by: (, j)=argmax M, j, j (9) Figure the proposed algorithms Timig ad frequecy iitial acquisitio. The proposed symbol timig techique depeds o the CP ature of the OFDMA symbols. The icomig packet slides over two widows separated by fixed distace. The size of each widow is the same as the used CP. Whe the packet is detected, the estimated start of the packet is shifted back ad a correlatio betwee the fixed widows is tured o for certai period withi which the maximum correlatio gives a estimate for the true symbol timig. Fig. 5 shows the illustratio of this techique. The received sigal is correlated with a delayed versio of itself where is the distace betwee the two widows. ( t )=arg(max L s r r ) K = 1 + k + m+ k (10) The value of that correspods to a maximum correlatio is the symbol timig estimate; where is the CP legth. The symbol timig estimate has a Probability Desity Fuctio (PDF) that makes it impossible to fix the symbol timig poit perfectly to the first sample of the OFDM symbol. Fig. 6 shows the PDF effect o the symbol timig. If the mea value of this PDF is the ideal symbol start, the ISI ad ICI problems arise. But, as show i Fig. 7, the mea value of the symbol timig poit ca be shifted iside the CP sice early symbol timig does ot create sigificat problems. 42

5 Figure 5. Symbol timig techique. Figure 6. Effect of symbol timig PDF o DFT widow estimatio. Figure 7. Symbol timig PDF correctio. To estimate the frequecy offset, the CP samples are correlated i time domai to their repeated part of the preamble OFDMA symbol. The umber of samples used is chose startig from the begiig of the secod quarter of the guard bad iterval to avoid the trasiet part affected by the chael. The estimated frequecy offset is proved by: r = S.exp( j2 πδ fts) (11) Z L 1 = rr ( ) ( + D ) (12) = 0 L 1 ( )exp( 2 π )[ ( )exp( 2 π ( ) )] (13) = 0 Z = S j Δ fts S + D j Δ f + D Ts Z = exp( j2 πδfts) S (14) Where is the umber of compared time samples, which must be lower tha the guard time ad is the idex time sample. The estimated frequecy offset takes the form: 1 Δ f = agle( Z) (15) 2π DTs The use of this correlatio based algorithm allows the hardware reuse sice it is the same correlatio eeded for symbol start algorithm. After estimatig the fie frequecy offset through the agle of maximum correlatio, compesatig the offset is through multiplyig the preamble samples by ( 2 Δ ). The limitatio i this estimator is the agle (Z) which has the rage from to Simulatio Results ad Disscusio The proposed algorithms are simulated uder AWGN ad dispersive fadig chael with fixed poit aalysis assumptio. The simulatio results for the packet detectio ad symbol start algorithm are show i Fig. 8. The correlatio for the multiplicatio is fixed at 12 bit/operatio ad the additio is fixed at 6 bit/operatio. Results are obtaied after 250 rus at three differet SNR values. L 1 N =

6 I the case of multipath fadig uder fixed poit, 250 rus were performed for differet frames. It was oticed that the performace is eve better whe applyig a back off algorithm of 10 samples as a safety factor. The simulatio results of this algorithm are give i Fig. 9. Packet detectio ad symbol start fixed at 12bit ad SNR=0dB Number of rus Shift i samples (a) Packet detectio ad symbol start fixed at 12bit ad SNR=5dB Number of rus Figure 8. Shift i samples (b) Packet detectio ad symbol start fixed at 12 bits obtaied at SNR of (a) 0 db ad (b) 5 db. Packet detectio ad symbol start fixed at 12bit ad fadig poit at 0dB Shift i samples (a) Packet detectio ad symbol start fixed at 12bit ad fadig poit at 5dB Number of rus Number of rus Figure 9. Shift i samples (b) Packet detectio ad symbol start fixed at 12 bits with fadig of (a) 0 db ad (b) 5dB. 44

7 To compute the percetage of errors for the CP based fie frequecy offset estimatio, 1000 umber of rus has bee carried for both axes. The area of cosideratio is estimated 500 times for each db. The upper lie at 2% represets the ed rage of error stated by the stadard for frequecy offset error i estimatio. The simulatio results for the fie frequecy offset estimatio are show i Fig. 10 for differet SNR values. (a) (b) Figure 10. Fie frequecy offset estimatio uder: (a) AWGN (b) 16 b fixed poit aalysis ad (c) 20 bit fixed poit aalysis. Preambles of differet segmets have bee cosidered for the coarse frequecy offset to make sure it works for all 114 preambles. Uder 0dB fadig, the estimated coarse frequecy shift is 6 ad preamble umber is 90 at 240 rus. This meas that the algorithm was accurate at 240 rus; these are illustrated i Fig. 11a ad Fig. 12a, respectively. Whe the algorithm was applied uder 5dB fadig, the performace icreased to 250 rus as give i Fig. 11b ad Fig. 12b. (c) Itegral frequecy offset estimatio uder fadig at 0dB Number of rus Estimated coarse frequecy shift (a) 45

8 Itegral frequecy offset estimatio uder fadig at 5dB Number of rus Estimated coarse frequecy shift (b) Figure 11. Itegral frequecy offset estimatio uder fadig obtaied at SNR of ( a) 0 db ad (b) 5dB Cell search uder fadig at 0dB Preamble umber (a) Cell search uder fadig at 5dB Number of rus Number of rus Preamble umber (b) Figure 12. obtaied at (a) 0 db ad (b) 5 db To compute the probability of error the umber of rus is 1000 ad the chael model used is the ITUchael model profile-4 with the parameters specified i TABLE 1. FFT output is fixed at 12-bit for additio. The widow size of power calculatio is 30 cotiguous samples. The results are show i Fig. 13 ad Fig. 14. To reach high performace, the legth of the widow ca be icreased by usig the power calculatio i packet detectio. Also a iterleaved power widow ca be used to ehace the performace agaist arrow bad iterferece. 46

9 TABLE I. ITU CHANNEL MODELS Parameter Fd Ns Ts Tc Profile Fs PSYM PShape Descriptio Doppler Number of chael sample fuctios Symbol period i micro secods Chip duratio or observatio rate Profile choice Oversamplig factor of the pulse shape Pulse trucated to +/- PSYM symbol periods Use sic pulse shape Value Figure 13. The probability of error usig the secod method with widow size of 30 samples. Figure Coclusio ad Future Work The probability of error usig the secod method with widow size of 64 samples. Frequecy, timig acquisitio, ad cell search algorithms for OFDMA based mobile WiMAX have bee proposed ad simulated. The timig OFDM symbol boudaries idetificatio was doe by the packet detectio ad symbol start algorithms. The performace uder AWGN icreases with the icrease of sigal power. Uder multipath fadig the performace is good ad most of the errors are illumiated. The fie ad coarse frequecy offset estimatio approaches are used to alig the carrier frequecies of the trasmitter ad the receiver. Joit detectio of the coarse frequecy offset ad the cell search uder fadig ad AWGN was obtaied by these algorithms. Simulatio provided accurate results ad the frequecy offset i the received frame was successfully estimated. I the future, the system ca be hardware implemeted with FPGA architecture for all the WiMax trasceiver system. It would also be iterestig to cosider the desig of a graphical user iterface for the system. 47

10 7. Ackowledgmet We would like to thak the Departmet of Electroics Egieerig, Faculty of Egieerig, Suda Uiversity of Sciece ad Techology where this work has bee carried. 8. Refereces [1] C. Ball, LTE ad WiMax Techology ad Performace Compariso, Nokia Siemes Networks, EW2007 Pael, [2] B. Sidhu, H. Sigh, ad A. Chabra, Emergig Wireless Stadards WiFi, ZigBee ad WiMax, WASET.ORG, pp , 2007 [3] M. Morelli ad M. Pu, Sychroizatio Techiques For Orthogoal Frequecy Divisio Multiple Access (OFDMA) A Tutorial Review", Proc. IEEE, July 2007, Vol. 95, o. 7. pp , doi: /JPROC [4] M. Ali, Simulatio ad implemetatio of the frequecy sychroizatio ad Viterbi decodig for the OFDMAbased Mobile WiMax e, a thesis submitted to the Faculty of Egieerig at Cairo Uiversity, [5] IEEE broadbad wireless access workig group, Chael models for fixed wireless applicatios, IEEE c-01/29r4, 16 July [6] K. Che, J. Roberto, ad B. Marco, Mobile WiMax, Joh Wiley & Sos. Ltd, [7] K. Che, Itroductio to Mobile WiMax, Taiwa Uiversity, [8] L. Nuaymi, WiMax techology for broadbad wireless access, Joh Wiley ad Sos Ltd, [9] J. Adrews, A. Ghosh, ad R. Muhamed, Fudametals of WiMax: uderstadig broadbad wireless etworkig, Pretice Hall,