LMS Beamforming Using Pre and Post-FFT Processing for OFDM Communication Systems

Transcription

1 B LMS Beamformng Usng Pre and Post-FFT Processng for OFDM Communcaton Systems Mohamed S. Heae (), Mohab A. Mangoud () and Sad Enoub (3) () Teecomm Egypt Co., Aexandra Sector, e-ma: () Dept. of Eectroncs & Comm., Coege of Engneerng, AAST, Aexandra Egypt, e-ma: (3) Dept. of Eect. Eng., Fac. of Eng., Aexandra Unversty, Aexandra 544, Egypt, Abstract- the adaptve array antenna s combned wth OFDM "orthogona frequency dvson mutpexng" as mutcarrer technque to combat the fat and frequency seectve fadng effects at hgh speed wreess communcaton. In ths paper an optmum weght sets beamformer at tme and frequency doman were obtaned based on LMS agorthm. Dfferent aspects of these systems were nvestgated such as dfferent vaues of deay spread, ange of arrva of nterferng sources and number of array eements. Keywords- LMS beamformng, adaptve array antenna, OFDM. I. Introducton The demand for hgh data rate where very wdeband waveforms s needed, requred the study of three major topcs, whch are mutpath fadng, deay spread and co-channe nterference []. To mtgate nter symbo nterference (ISI) found n hgh speed data rate, arge deay spread and mutpath propagaton OFDM s used as a mutcarrer scheme n whch the bandwdth of the channe s dvded nto subcarrers and data are moduated and transmtted on each sub carrer [], By nsertng guard tme onger than the deay spread of the channe the system can mtgate nter symbo nterference. By addng adaptve array at the recever the system can separate the desred sgna from nterferng sgnas whch orgnate from dfferent spata ocatons. Therefore, system capacty s ncreased. For OFDM-Adaptve array system beamformng can be apped to ether n tme-doman or frequency-doman [3]. Tme-doman beamformng s caed Pre-FFT because the array processng s done before the FFT step n tme doman and frequency-doman beamformng can be caed Post-FFT because the array processng s done after the FFT step n frequency doman. The Post-FFT requres a set of weghts for each array branch. So that the tota number of weghts processed s equa to the number of array eements tmes the number of subcarrers, whch requres a hgh computatona compexty. On the other hand, the Pre-FFT array antenna requres ony one weght set so t can reduce the computatona compexty [4], [5].In ths paper, east mean square (LMS) adaptve agorthm s apped to OFDM system and the performance s nvestgated n mutpath envronment wth presence of mutuser nterference. Ths paper combnes a Pre-FFT and a Post-FFT wth adaptve beamformng agorthm based on the east mean square. The paper s organzed as foows: Secton II descrbes the system mode of the Pre-FFT and Post-FFT OFDM adaptve antenna array. Secton III presents the anayss of the system ncudng the recever, the transmtter and the channe. Secton IV descrbes the east mean square adaptve agorthm whch s used n beamformng. Secton V demonstrates the computer smuaton resuts and dscusses them n detas. Fnay, Secton VI concudes ths paper.

2 B II. System Mode and parameters In ths mode the nterferng users are subject to the same condtons and parameters of the desred sgna to be more reastc and to prove that the combnng of OFDM and adaptve array beamformng can separate the desred user from other users n the presence of fat and frequency seectve fadng channe. In that mode 8 unform near array eements haf wave spacng ength s used. Fgure () The boc dagram of the OFDM recever. III. Post-FFT and Pre-FFT Mode At the transmtter the data bts are mapped usng the QAM moduaton and the mapped symbos are feed to the sera to parae (S/P) boc to perform IFFT. The m-th tme doman sampe at the n-th subcarrer at the output of IFFT s gven by: x = exp πmn m Xn {j }, m n= () where s the number of subcarrers and X n s the data symbo on the n-th subcarrer. Assumng that the resutng OFDM symbo s transmtted through a mut path channe wth L dscrete paths. At the recever wth unformy spaced near antenna array consstng of K eements the m-th sampe at the -th antenna eement can be wrtten as: L π r = h x exp{ j( ( )d snθ)} + n, m = m, m () m, λ m, where d s the antenna spacng, λ s the wave ength of the carrer, θ s the ange of arrva (AOA), h m, s the compex random varabe for the -th path of the channe mpuse response at tme m and n m, s the adaptve whte Gaussan nose at the -th antenna eement at tme m. The tota moduated sgna on the n-th subcarrer at the output of FFT at the -th antenna eement can gven by [6] : Y n, = L X m H ( n m ) exp{ m= = π m j( + ω ( θ ))} + n, (3)

3 B 3 where π ω ( θ ) = ( ) d sn( θ ) (4) λ where n, s the AWG on the n-th subcarrer at the -th antenna eement, and H (n-m) s the FFT of tme varant mutpath channe h m,,whch s defned as foows : H ( n m) = π ( n m) h exp{ j } = m, (5) If we assume the mutpath channe s tme nvarant over OFDM symbo duraton H (n-m) n equaton (3) becomes Zero except at n=m. The tota sgna of desred and nterferng users can be gven by: [7] t L πn Y = [ H () exp{ j( + ω ( θ ))}] X n, n = R L n X [ π + H () exp{ j( + ω ( θ))}] n + = = n, (6) where R s the number of co-channe nterferng users. In case of usng Post-FFT whch s ocated after the FFT stage so we can steer the beam to the desred user whch s gven by: Y, s passed to beamformer t n D n = K W = * Y t n, n, (7) where W n, s the weght on the -th antenna eement for the n-th beamformer. Parae to sera converson s performed at the output of beamformers foowed by symbo demoduaton.in case of usng Pre-FFT r m, n equaton () w pass to beamformer whch s ocated before the FFT stage and the channe effects and nterferng users w be emnated before passng the sgna to FFT. IV. Least mean square adaptve agorthm Snce the channe n wreess communcatons s tme varant, the weght vector must be updated perodcay, so t s not desrabe to sove the beamformer equatons n mnmum mean square error (MMSE) or east square (LS) technque. Thus, an update technque, whch uses prevous soutons to cacuate the next weght set, s used. There are many types of adaptve agorthms; LMS whch s teratve and maes use of past nformaton to mnmze the computatons requred at each update cyce w be used n the smuaton. The gradent approach, whch provdes an teratve update souton for the MMSE crtera, s gven by [8]: W, = W µ j(w ) +,, (8) where j(w ) s the gradent of functon j(w) whch s gven by

4 B 4 j(w ) H = E[ W x d ] (9), The functon j(w) s the cost functon. By sovng the gradent of the cost functon n equaton (9) and we can get the approxmated souton for the nstantaneous squared error and Sub. In equaton (8) the Least Mean Square agorthm s found by: W = W + x e *,, µ, + () where e, = s the error between the array output and the desred sgna. W H x d,, V. Computer smuaton and resuts Computer smuatons are performed for mpementng the Pre and Post-FFT LMS beamformrer n 8 subcarrers OFDM system; 4-QAM moduaton s used n the system wth eght unform near array eements antenna wth haf-waveength spacng s empoyed. The channe has three paths consstng of unfaded LOS path and two Rayegh components, and the channe transfer functon whch modeed as n [9] s gven by: H ( f ) = a + a R + a R exp( j π f τ ) where R and R are two ndependent Rayegh paths and τ s the deay between the two Rayegh components. a, a, a are the reatve power eves of the three mutpath components. The desred sgna s corrupted by the pervous mutpath mode and AWG and four nterferng users. The system has fve users, the sgna of the desred user s transmtted from the spata ocaton of 4 and the four nterferng sgnas at [, -8, 4, 55 ].When appyng the pervous channe condtons (fadng, AWG and nterferng) to adaptve array OFDM system, the recever separated the desred user from the nterferng users, the beam pattern for the beamformer s ustrated n fgure () nus s formed at nterferng users. The effects of changng the number of antenna eements on the performance of the receved sgna s studed n fgure (3) where the number of eements s changed from 8 eements more than the number of users=5) to 4 eements (ess than the number of users=5). The beam pattern for 8 eements steer toward the desred user (-4 ) perfecty and nus to the nterferng users ( ). However, the case of 4 eements the beamformer was not abe to cance a the nterferng users, there s no nu at the spata ocaton 55. Fgure (4) ustrates the symbos at the recever wth 4 eements and 8 eements, the consteaton for 8 eements s better than that for 4 eements. For 4 eements the recever can not be abe to recover the symbos. Fgure (5) ustrates the bt error rate of adaptve array antenna wth 4 eements and 8 eements. The BER wth 8 eements s ower than that one at 4 eements and the gap between the two curves ncrease as S/ rato ncrease. As descrbed before there are two types to formng the beam n OFDM system, tme doman beamformng (Pre- FFT) and frequency doman beamformng (Post-FFT) The umber of weghts n the (Pre-FFT) equa to the number of antenna eements (8 weghts) and the umber of weghts n the (Post-FFT) equa to the number of antenna eements mutpy by the number of carrers (8*8= 4 weghts) []. A comparson between the two types s ustrated n fgure (6,7,8).In fat fadng channe the performance of the two types (Pre and Post-FFT) appears to be the same as shown n fgure (6) no arge gap between the BER curves. Fgure (7) descrbes the performance of Pre

5 B 5 and Post-FFT n frequency seectve fadng channe wth deay spread equa to 4 sampes, the performance of Post- FFT s better than Pre-FFT and Post-FFT mtgated the channe effects than Pre-FFT dd. When the nterferng users change ther spata ocatons coser to the desred user as [ ] where the desred user at 4, the Post-FFT separated the desred users from the nterferng user better than Pre-FFT dd as shown n fgure (8) the BER curve s mproved by usng Post-FFT. VI. Concuson By combnng the adaptve array antenna wth OFDM most of channe effects and errors can be emnated, through dvdng the band nto sub bands wth orthogona carrers one for each sub band. Wth combnng LMS beamformer of adaptve array wth OFDM n ts both types (Pre-FFT and Post-FFT) the nterferng was canceed and the desred user at the recever s detected wth ow bt rate.the Post-FFT needs more cacuatons and compexty but t has better performance than Pre-FFT especay at hoste channe and nterferng condtons. References [] Hdehro Matsuoa and Hro Sho, "Comparson of pre-fft and post-fft processng adaptve arrays for OFDM systems n the presence of co-channe nterference", Persona, Indoor and Mobe Rado Communcatons, Vo., o., pp , Sept 3. [] Henr Schuze and Chrstan Luders, Theory and appcatons of OFDM and CDMA wdeband wreess communcaton, Wey, 5. [3] Zhongdng Le and FrancosP.S. Chn, "Post and Pre-FFT Beamformng n an OFDM System", Vehcuar Technoogy Conference, Vo., pp , May 4. [4] Shnsue Hara and Yoshtaa Hara, "Smpe u-steerng OFDM Adaptve Array Antenna for Dopper- Shfted Sgna Suppresson",IEEE Transacton on vehcuar Technoogy, Vo. 54, o., pp. 9-99, January 5. [5] Shnsue Hara, Montree Budsabathon, and Yoshtaa Hara, "A Pre-FFT OFDM Adaptve Antenna Array wth Egenvector Combnng", 4 IEEE Internatona Conference on communcaton, Vo. 4, pp. 4-46, June 4. [6] Fahru Aam, B.L. Patrc Cheung, Raqbu Mostafa, W.G. ewha, B.D. Woerner and J.H. Reed, "Sub-band Beamformng for OFDM System n Practca Channe Condton", Vehcuar Technoogy Conference, 4, Vo., pp , Sept. 4. [7] Yunhu Lu and Yuhang Yang, "Effcent Adaptve Array Recever for OFDM based Wreess Loca Area etwors (WLA)", IEEE Transactons on Consumer Eectroncs, Vo. 5, pp. - 6, ov. 4. [8] Joseph C. Lbert, Theodore S. Rapaport, Smart Antennas for Wreess Communcatons, Prentce Ha, 999. [9] Wam H. Tranter, K. Sam Shanmugan, Theodore S. Rappaport, Kurt L. Kosbar, Prncpes of Communcaton Systems Smuaton wth Wreess Appcatons, Prentce Ha, 4. [] Y.L and D.Kenyon, "An Examnaton of the Processng Compexty of an Adaptve Antenna System (AAS) for WMax", The nd IEE/EURASIP Conference on DSP enabed Rado, 5, pp. - 7, Sept. 5.

6 B 6 Fgure () The beam pattern n the output of the beamformer we can observe the deep us at the drectons at the nterferng users [ ] degree. 4 eements array antenna 8 eements array antenna Fgure (3) The beam pattern n the output of the beamformer of adaptve array antenna wth 4 eements and 8 eements. 4 eements array antenna 8 eements array antenna Fgure (4) Symbos at the recever at adaptve array antenna wth 4 eements and 8 eements.

7 B 7 Fgure (5) the bt error rate of adaptve array antenna wth 4 eements and 8 eements Fgure (6) Pre-FFT and Post-FFT n fat fadng. Fgure (7) Pre-FFT and Post-FFT n frequency seectve fadng. Fgure (8) Pre-FFT and Post-FFT n coser nterferng users.