SYSEM LEVEL DESIGN OF BASEBAND OFDM FOR WIRELESS LAN Ciprian Comşa, Ion Bogdan echnical Universiy Gh. Asachi elecommunicaions Deparmen 11 Carol I Boulevard, Iasi, Romania ABSRAC Mulicarrier or Orhogonal Frequency Division Muliplexing (OFDM) has gain recenly an increased ineres wih he developmen of faser signal processing componens and echnologies. OFDM has been shown o be a very efficien scheme for miigaing he adverse effecs of iner-symbol inerference, squeezing muliple modulaed carriers ighly ogeher bu keeping he modulaed signals orhogonal so hey do no inerfere wih each oher s. his paper describes he sysem level model of he OFDM baseband and uses i o evaluae he BER performance. 1. INRODUCION he new demand for wireless broadband access neworks is imposed by he emergence of mulimedia applicaions and high speed wireless access. Orhogonal Frequency Division Muliplexing has been proven suied for his kind of applicaions, being a mehod of daa modulaion which miigaes he effecs of iner-symbol inerference (ISI) caused by mulipah propagaion encounered in high-speed wireless communicaions. OFDM is used in wireless environmen such as mobile communicaion sysems, bu also in oher applicaions such as European digial audio broadcas (DAB). OFDM based on discree mulione (DM) sysems are also employed for broadband digial communicaion on he exising copper neworks, being exploied for high-bi-rae and asymmeric digial subscribers lines (HDSL and ADSL) [1], [2]. In wireless applicaions, OFDM can be found in several exising wireless local area nework (WLAN) sandards, like IEEE 82.11 in he Unied Saes, ARIB MMAC in Japan, or HIPERLAN/2, defined by he European elecommunicaion Sandards Insiue Projec on Broadband Radio Access Neworks (ESI BRAN). his sysem provides high-speed communicaions up o 54Mbi/s beween porable compuing devices and access poins, aached o an Eherne, AM or UMS backbone nework [2], [7]. he main idea behind OFDM is o spli daa sream o be ransmied ino N parallel sreams of reduced daa rae and o ransmi each of hem on a separae subcarrier. hese carriers are made orhogonal by appropriaely choosing he frequency spacing beween hem. herefore, specral overlapping among subcarriers is allowed, since he orhogonaliy will ensure ha he receiver can separae he OFDM subcarriers, and a beer specral efficiency can be achieved han by using simple frequency division muliplex. OFDM combas frequency selecive fading and randomizes he burs errors caused by he wideband radio frequency channel. o preven iner-symbol inerference, a cyclic prefix is appended o each OFDM symbol a he ransmier and hen removed a he receiver, before he deecion process. However, here are proposed some echniques and algorihms, as in [11], of nonconvenional OFDM sysems wihou cyclic prefix. he cyclic prefix, which is a repeiion of he las chips of he OFDM symbol, can be exploied also for boh iming and frequency synchronizaion [13]. he synchronizaion echnique based on he cyclic prefix exension is paricularly suied o racking or blind synchronizaion in a circui-swiched connecion, when no special raining signals are available. For packe ransmission may be used several special OFDM raining symbols for which daa conen is known a he receiver. Channel esimaion a he receiver is achieved using he raining symbols provided in he preamble. A priori knowledge of he ransmied preamble faciliaes he generaion of a vecor defining he channel sae informaion. his is used o remove he channel disorion by muliplying he received OFDM vecor by he pre-compued channel esimaion. Anoher mehod o compensae for he flucuaion of ampliude and phase due o fading is he inserion of pilo chips a fixed ime inervals a he ransmission, used a receiver o esimae he channel characerisics [5]. he key advanages of he OFDM ransmission scheme, according o [16], are: OFDM is an efficien way o deal wih mulipah; for a given delay spread, he implemenaion complexiy is significanly lower han ha of a single carrier sysem wih an equalizer. In relaively slow ime-varying channels, i is possible o significanly enhance he capaciy by adaping he daa rae per subcarrier according o he signal-o-noise raio of he paricular subcarrier. OFDM is robus agains narrowband inerference, because such inerference affecs only a small percenage of he subcarriers. Neverheless, OFDM has also some negaives associaed compared wih single-carrier modulaion: OFDM is more sensiive o frequency offse and phase noise. he orhogonal naure leads o signals wih a large dynamic range, imposing a relaively large peak-oaverage power raio, which ends o reduce he power efficiency of he RF amplifier.
In he following we give a mahemaical descripion of he OFDM signal and presen ypical OFDM sysem. Finally, we show he resuls obained by simulaing an OFDM sysem in a slighly modified HIPERLAN/2 conex. 2. SYSEM MODEL he following descripion of he OFDM signal is based on [4] and [6]. In order o give a mahemaical descripion of an OFDM sysem we assume a sysem wih N subcarriers, a bandwidh of B Hz and an OFDM symbol lengh of S seconds, of which is he lengh of he cyclic prefix. he spacing beween subcarriers is given by (1), as in Figure 1. 1 N = = = S (1) f B symbols ransmied is obained by juxaposiion of he individual ones. N 1 n k, nφk S n= n= k= (4) s() = s () = d ( n ) Assuming he impulse response ch(;) τ of he physical channel (possibly ime varian) is resriced o he lengh of cyclic prefix τ [, ), he received signal becomes (5), where n ( ) is complex, addiive and whie Gaussian (AWGN) channel noise. () ( * ) r = ch s() = ch( τ;)( s τ) + n () (5) d n, d k nn, 1 IFF φ () φn () 1 s s () n, () nn, 1 ch (;) τ n () e n, k S FF ψ () r () n r () n enn, 1 r () n ψ N () 1 Figure 1. Individual subchannels for an OFDM sysem. Figure 2 illusraes he baseband OFDM model mahemaically described bellow. Every n h OFDM symbol of he ransmission sream can be wrien as a se of modulaed carriers ransmied in parallel. Relaions (2) express he waveforms used in modulaion. 1 j2 π fk( ) e, [, S ) φk () = S, where, oherwise N 1 1 (2) fk = fc+ k, k =,..., N 1, for passband or 2 k fk =, k =,..., N 1, for baseband echivalen Noe ha nonzero erm of φ k () has he period [, S ) and φk() = φk( + N ), for [, ) (3) B If dn,,..., dn, N 1 denoes he complex symbols, obained by QAM mapping of he inpu daa sream, he n h OFDM symbol sn () is expressed by (4) and he infinie sequence of OFDM Figure 2. Baseband OFDM sysem model. he filer from he receiver is mached o he las par [, ) of he ransmier waveform (6), he cyclic prefix being his way effecively removed in he receiver. Since he cyclic prefix conains he ISI, he sample oupu from he receiver filer bank conains no ISI. Also, we can ignore he ime index n when calculaing he sampled oupu a he k h mached filer (7). [ ) φ * ( ),, ψk() =, oherwise k S S ek = ( r* ψk)( ) = r( ) ψk( S ) d = (7) S Considering he channel o be fixed over he OFDM symbol inerval, denoing i by ch( τ ) and aking ino accoun he orhogonaliy condiion expressed by (8), we obain afer some mahemaical operaions he oupu daa, given by (9). * φ l() φ k() = δ ( k l) (8) e = h d + n, where k k k k B j2πkτ ( ) N k τ S * k = ( S ) φk( ) h = ch e dτ and n n d S (6) (9)
By sampling he low-pass equivalen signal of (2) and (4) a a rae N imes higher han he subcarrier symbol rae 1/, we can obain he discree model of he baseband OFDM sysem, where he modulaion/demodulaion wih waves φ / ψ can be replaced wih idf/df (or pracically wih IFF/FF) and he channel model wih discree-ime convoluion. In figure 3, a block diagram of an OFDM sysem is presened, based on [9], [16], and he pracical way of generaing he OFDM signal is described bellow. he binary inpu daa are encoded using a FEC block. his is realized by using a single convoluional code or a concaenaed code. Usually i implies an ouer block code wih hard decision, which may be a shorened Reed-Solomon [17], followed by a convoluional code wih a rae of ½ or higher by puncuring. he encoders are accompanied by bi inerleaving blocks and some imes by a scrambler. A he recepion, he inverse operaions are made, using as pair for he convoluional encoder, a Vierbi decoder wih sof decision. Pilo Inserion Serial o o Serial Channel Correcion Baseband Modulaion IFF FF Baseband Demodulaor o Serial Serial o Coding & Inerleaving Add Cyclic Prefix & Windowing Removing Cyclic Prefix Deinerleaving & Decoding Binary inpu daa Symbol iming Binary oupu daa Channel iming & Frequency Sync. Figure 3. Block diagram of an OFDM sysem. he baseband modulaion performed can be from BPSK o 256 QAM. Conforming [16], in fading channels is preferable o use high-order consellaions in combinaion wih low-rae coding schemes. he usage of rellis srucures as convoluional encoders designed for specific consellaions requires Grayencoded QAM. In order o esimae he fading channel s effecs on he received signal, especially suied for coninuous ransmissions is he inserion a fixed ime inervals of pilo subcarriers wih polariy generaed by a pseudoaleaory sequence. he FF block s hardware is very similar o IFF and i may be used he same block for boh if he ransmier and he receiver does no have o work simulaneously. According o [16], an IFF can be efficienly buil using a radix-4 buerfly algorihm. he cyclic prefix is imporan for synchronizaion, especially in coninuous ransmissions, and for ISI caused by mulipah propagaion avoidance. he ou-of-band specrum decreases raher slowly, so ha o accelerae i, windowing is applied o he OFDM signal. I can be used convenional windows, such as raised cosine, Hamming, Blackman, Kaiser, or special designed windows, such as Lawrey window [1]. 3. SIMULAION RESULS he main parameers of he HYPERLAN/2 sandard are expressed in able 1 [8]. We chose o simulae a sysem a 8Mbps rae, wih 64QAM modulaion. he guard inerval () has o be 3-5 imes greaer han he delay spread, in order o miigae he ISI. Assuming a olerable delay spread of 2ns for boh indoor and microcellular oudoor [16], a guard ime of = 8ns mees he requiremen. Also, he SNR loss inroduced by he and given by (1) is SNR =.9691dB, which is an accepable value, being smaller han 1dB. SNR = 1 log1 1 S (1) Daa rae 6, 9, 12, 18, 24, 36, OFDM symbol 48, 54 Mbps duraion 4µ s Modulaion BPSK, QPSK, 16QAM, 64QAM Guard inerval 8ns Coding rae 1/2, 2/3, 3/4 Subcarrier spacing 312.5 khz Number of subcarriers 52-3dB Bandwidh 16.56 MHz Number of pilos 4 Channel spacing 2 MHz able 1. Main parameers of he HYPERLAN2 sandard. Because he number of subcarriers is 52, he FF lengh will be 64, mached by he subcarrier spacing (2MHz/64 = 312.5kHz = 1/3.2µs). o obain a 48Mbps bi rae wih a symbol period of S =4µs, he number of bis per OFDM symbol should be 192. aking ino accoun ha he modulaion level is 6 (2 6 =64), we used a coding rae of 2/3, mached by he number of daa subcarriers 52-4=48 (2/3 = 192/288 = 32/48). We can use an ouer shorened Reed-Solomon(36,32) encoder and an inner rellis encoder wih consrained lengh 7 and generaor polynomials 133 (6) and 171 (6), wih a ½ rae and puncured o ¾. Figure 4. Received signal consellaion for 64QAM and E b /N =19.5dB.
he sysem was modeled wih Mahworks Simulink using frame based signals, which speeds up he compuaion [12], [15]. Using Simulink blocks, daa raes, power of he signal, signal waves, QAM symbol consellaion, as in figure 4, signal specrum, as in figure 5, and insananeous BER can be explored. In order o obain a BER versus E b /N for AWGN channel we used a malab scrip ha auomaically modifies he E b /N parameer of he AWGN block and runs he simulaion a specified simulaion ime. he resul may be observed in figure 6. Figure 5. ransmied signal specrum. 4. CONCLUSIONS AND FUURE WORK According o [5] and [14], BER performance in convenional 64QAM scheme and AWGN channel is given by (11). 7 1 E 49 2 1 b E BER b h = erfc erfc 24 7 N 384 7 N (11) siuaion and he heoreical one agains he bi energy-o-noise raio (E b /N ) has o be observed. I mus no be forgoen he.9691db SNR loss caused by cyclic exension as compared o he heoreical resuls. As fuure work we inend o exend firs he Simulink model in order o simulae he mulipah fading effec; second, o inroduce as channel model, he exended Suzuki model [3] and hird, o parameerize he simulaion model. 5. REFERENCES [1] Abdelkefi F., Duhamel P., Alberge F., A poseriori conrol of complex Reed Solomon Decoding wih applicaions o impulse noise cancellaion in Hiperlan2, ICC Proceedings, New York 22 [2] Ben Slimane, S., Channel Esimaion for HIPERLAN/2 wih ransmier Diversiy, ICC Proceedings, New York 22 [3] Comsa C, Alecsandrescu I., Bogdan I., Maiorescu A., Simulaion Model for Mobile Radio Channels, ECI Iasi, 22 [4] Edfors O., Sandell M., Van de Beek J. J., An Inroducion o Orhogonal Frequency-Division Muliplexing, 1996 [5] Harada H., Prasad R., Simulaion and Sofware Radio for Mobile Communicaions, Arech House, 22 [6] Hazy L., Iniial Channel Esimaion and Frame Synchronizaion in OFDM Sysems for Frequency Selecive Channels, hp://www.sce.carleon.ca/ ~hazyl/meng/, 1997 [7] HIPERLAN/2 sandard, defined by ESI BRAN, www.esi.org [8] IEEE 82.16 Broadband Wireless Access Working Group, OFDM proposal for he IEEE 82.16a PHY draf sandard, hp://ieee82.org/16 [9] Inini A. L., Orhogonal Frequency Division Muliplexing for Wireless Neworks, Sana Clara Universiy of California, 2 [1] Lawrey E. Ph., Adapive echniques for Muliuser OFDM, hesis submied in December 21 for he degree of PhD, James Cook Universiy, Ausralia [11] Lee Y., Huang P., Channel Inerpolaion and MMSE Muli- Inpu Muli-Oupu Frequency-Domain DFE for Wireless Daa Communicaions Using OFDM, ICC Proceedings, New York 22 [12] Mahworks Malab and Simulink Official Websie, www.mahworks.com [13] OFDM Forum websie, hp://www.ofdm-forum.com [14] Proakis J. G., Salehi M., Communicaion Sysems Engineering - Second Ediion, Prenice Hall, 22 [15] horpe Ch., OFDM Wireless Simulaion Using Simulik, Inernaional DSP Conference, Sugar, May, 21 [16] Van Nee R. and Prasad R., OFDM for Wireless Mulimedia Communicaions, Arech House Publishers, Boson, 2 [17] Zaghoul H., Knudsen S., Faouche M., Reed Solomon FEC for OFDM ranceiver, hp://www.wi-lan.com, Wi-Lan, 1998 Figure 6. BER for 64QAM and AWGN. In figure 6, i can be observed he shape of BER for AWGN channel for he heoreical siuaion and he simulaing one wih and wihou coding. he difference beween he simulaed