Using EM algorithm as a new method for Synchronization and channel estimation of MIMO-OFDM systems

Transcription

1 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 9, Issue 3, o 2, May 2012 ISS (Onlne): Usng EM algorthm as a new method for Synchronzaton and channel estmaton of MIMO-OFDM systems avd daryasafar, Babak ehyaee, Aboozar lashkar 1 Department of Communcaton, Bushehr Branch, Islamc Azad Unversty Bushehr, Iran 2 Department of Communcaton, Bushehr Branch, Islamc Azad Unversty Bushehr, Iran 3 Department of Communcaton, Bushehr Branch, Islamc Azad Unversty Bushehr, Iran Abstract In ths paper, a new algorthm has ntroduced the most estmaton smlarty, channel coeffcents fadng and movng the carrer frequency n MIMO-OFDM systems. The purpose of ths paper provdes an algorthm to synchronze and estmate channel coeffcents whch has low computatonal complexty. The proposed algorthm usng the process sequence contanng the tranng symbols, carrer frequency offset and channel coeffcents fadng, estmate n two consecutve stages. Consequently, low computatonal complexty and havng easy mplementaton. Moreover, the algorthm can be used n a varety of STC-OFDM systems. Keywords: Mult-Input Mult-Output systems, Synchronzaton, Channel Estmaton, EM algorthm 1. Introducton MIMO-OFDM systems are one of the systems whch have become the bass of many communcaton researches nowadays. A system wth several hgh speed nputs and outputs n sendng nformaton or sutable dversty between transmtter and recever; however the estmaton of the channel n ths connecton s complex. In order to reveal the coherent of receved sgnals, dgtal communcaton systems must have an exact estmaton of the stuaton of exchange channel between transmtter and recever. Snce ncreasng the number of transmtter and recever antennas causes an ncrease n the number of unknowns (coeffcents of the channel between both antennas of transmtter and recever) the estmaton of channels n mult-antenna systems s a lot more challengng than n one-antenna ones. [1] A mult carrer orthogonal modulaton system by usng the mmedate Fourer dverson technque creates nterest range and changes the swtch frequency to several flat sub channels; however smultaneously, lack of source and target and outbreak of delay by the channel, hardly decreases the functon of ths system. In other words, ths knd of system has a hgh senstvty toward tme and frequency delays. More n the second secton, the MIMO-OFDM systems are ntroduced. In the thrd secton synchronzng methods, n fourth secton estmatng methods of coeffcents of channel, and n ffth secton proposed algorthm for estmatng coeffcents of fadng channel and carrer frequency offset n MIMO-OFDM systems are descrbed, and at the end the results of accomplshed smulatons are presented. 2. Introducton of MIMO OFDM systems In a tradtonal wreless communcaton system, provded that the bandwdth s constant, there s no possblty of ncreasng the sendng rate of nformaton. In ths knd of stuaton, only dversty methods can be used to mprove the qualty of revealng. In desgnng communcaton systems, bandwdth, nformaton sendng rate and software-hardware complextes are the mportant parameters. To expand the new generaton of communcaton systems, methods such as MIMO, OFDM or ntegratng them together as MIMO- OFDM, are suggested. 2.1 MIMO-OFDM systems The hgh ntrnsc resstance of OFDM aganst the ISI event and ts sutable functon aganst fadng destructve event, besdes the hgh rate of nformaton sendng of MIMO, creates a very effcent complex n accesson toward the fourth generaton of wreless communcaton s demands. Lke OFDM systems, the MIMO-OFDM systems have a great deal of senstvty toward synchronzaton errors. Besdes, accordng to the ncrease n number of unknowns, estmatng the n these systems are a lot more complex than estmatng channel n one antenna systems [2]. Dagram block of one knd of MIMO-OFDM systems, s shown n the fgure1.

2 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 9, Issue 3, o 2, May 2012 ISS (Onlne): Fg. 1 Dsplayng a MIMO-OFDM system. [3] Accordng to the fgure, the nformaton n each antenna s sent after IDFT actons and addton of (CP) cyclc prefx. Each recever antenna receves the sum of nose and sgnals sent by the transmtter s antenna. In each recever antenna the revealng s done after removng CP and DFT actons. 3. Synchronzaton methods The most mportant ntrnsc restrcton of the OFDM technque s ts hgh senstvty toward synchronzng errors. The frst creator factor s called the asynchronousty of carrer frequency offset (CFO). Ths causes the loss of orthogonalty between subcarrers and outbreak of nterference between carrers. Another factor of asynchronousty s nequalty of sendng and recevng rate of samples precsely, whch s ntroduced as samplng frequency delay. The proposed synchronzng algorthms for OFDM based systems are categorzed to the followng two man groups [4]: A. Before FFT algorthms The above-mentoned algorthms are dvded to two groups of nput based algorthms and non nput based algorthms as follows: on nput based algorthms: ths group of algorthms estmates the synchronzaton parameters usng the specal structure of OFDM symbols. Ths group s also called cyclc prefx based methods [5] and [6]. Input based algorthms: ths group of algorthms uses the educatonal symbols sent n nformaton frames to estmate synchronzaton parameters [7], [8], [9] and [10]. B. After FFT algorthms Ths algorthms of ths group are also categorzed n two groups of plot based algorthms and drect decson algorthms. In comparng the two algorthms, although before FFT algorthms are faster than after FFT algorthms, but after FFT algorthms has a hgher throughput spectral. 4. Channel estmaton methods n MIMO OFDM systems The major consdered estmatng channel methods are as follows: A. Usng educatonal sequence methods By puttng samples n the sent symbol whch are known by the recever, we can reach the channel s doman whch s multpled by sum symbol and shft results. ow by usng the channels reached coeffcents, we can reveal the rest of symbol samples whch are the desred nputs and the recever s unaware of them [11]. B. Blnd methods In ths method whch has no need of educatonal samples, usng the covarance matrx, the recever estmates the coeffcents of channel and reveals the sent nputs by usng them [12]. C. Half blnd methods In ths method the between up between propertes of the two prevous methods are used [13]. 5. Channel s coeffcents estmaton algorthm and the presented carrer frequency offset A MIMO-OFDM system s supposed, wth transmtter antennas and M recever antennas and K sub carrer whch has the followng dagram block. Fg. 2 Dagram block of MIMO-OFDM system s transmtter. Fg. 3 Dagram block of MIMO-OFDM system s recever. Wth the assumpton of the total synchronzaton of transmtter and recever n tme we have: ( ) j kn s n X ( k) e ; n 0,1,..., 1 (1) k 0 It changes to followng by addng the s( cyclc prefx:

3 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 9, Issue 3, o 2, May 2012 ISS (Onlne): j k( ncp) 1 cp 1 S ( X( k) e ; n 0,1,... cp1 (2) k 0 Wth a few calculatons and removng the cyclc prefx, the r( vector s calculated as follows: r( e j2f ( n cp ) X ( ) H ( ) e 2 j n v( In whch the v s the complex Gaussan nose wth a zero average. At the end what s receved n the recever s as follows: y( e, w 2 f 1 jwcp 0 (3) X ( ) H( ) v( ) (4), k k 5.1 Estmatng the carrer frequency offset and channel s coeffcents By studyng the equaton (4) agan, we can observe that ths relaton has two unknown parameters of w and h(). Snce v s supposed the whte Gaussan nose wth a zero average, estmatng the maxmum smlartes of w and h unknown parameters, equals estmatng ther mnmum squares. Estmatng the maxmum smlartes of w and h can be obtaned from the followng cost functon [14]: mn M 2 r w h w Ah. 1, jw jw( k1) w dag1, e,, e jw 8 jw 8 A n e, A1 (,, e A (., k L (5) Step 1 (estmatng the carrer frequency offset): the queston of estmatng maxmum smlarty of carrer frequency offset can be presented as follows: max M w 1 w, h ph ˆ arg log p r dh (6) There are some estmators n two lmt modes of (DA, DA) and one mddle mode of (CA), separated from what s used as scale for estmaton, related to the amount of recever knowledge of assumed densty functon. The DA ML estmator does not explot all the nformaton avalable about the channel because t makes use of the datafree observaton samples only.to mprove the channel estmate qualty,the channel can be estmated on the bass of the whole receved burst,ncludng both the tranng sequence and the data. However,when the transmtted sequence s unknown and encoded,the lkelhood functon explotng the code s much more dffcult to compute. The EM algorthm enables teratvely solvng ths problem.the EM algorthm has been exploted prevously to estmate the channel,but t has usually been used to estmate the channel taps only. In order to reduce the hgh calculatons of estmatng maxmum smlarty, EM repetton based algorthm s used. The EM algorthm estmates carrer frequency offset n two followng steps: Step E: Expectaton: ( k) M ( k) Q w \ w E log p r,, 1 w h r w (7) Step M: Maxmaton: k1 max ( k) w argw Qw \ w (8) In above relatons, w(k) show the estmated carrer frequency offset n the k th repetton of EM. At the end Equaton 8 after a seres of calculatons becomes lke the followng: M k1 k1 max * k jwp w argw Re r V. e 1 p0 (9) Wth the assumpton of S (k) (p)=r * (p)v (k) (p), relaton number 9 s rewrtten lke the followng: ( k) k1 max M w arg Re R 1 w (10) The above relaton can be calculated usng FFT. Thus the proposed method has a sutable calculaton speed. Step 2 (estmatng the coeffcents of fadng channel): after the estmaton of rate of carrer frequency offset, t s tme to estmate the maxmum smlartes of coeffcents of fadng channel h ( =1,...,M ). Thus the estmaton of maxmum smlartes of channel s coeffcents can be obtaned from the followng relaton: ˆ H 1 H h ( A A) A ( ˆ). r, 1,, M H (11) 5.2 Smulaton results Smulaton for MIMO-OFDM system wth 32 sub carrers and dfferent number of transmtter and recever antennas s repeated n swtch frequency fadng channels. The bandwdth has been assumed 1 MHz and ts modulaton QPSK and L s the tap of channel. In the followng fgures, mean square error s shown accordng to sgnal to nose rato. The carrer frequency offset s assumed a stable amount n smulatons ( f=0.1). Fg.4 Mean square error accordng to SR for MIMO-OFDM system wth 32 sub carrers, whch uses 2 transmtter antennas and one recever antenna wth EM algorthm.

4 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 9, Issue 3, o 2, May 2012 ISS (Onlne): Fg. 5 Mean square error accordng to SR for MIMO-OFDM system wth 32 sub carrers, whch uses 2 transmtter antennas and 2 recever antennas wth EM algorthm Fg. 8 Synchronzaton for SISO OFDM system channel estmaton BER SR Fg. 6 Channel estmaton n 2*2 MIMO-OFDM systems L=4 wth synchronzaton. MSE (CIR) Channel Estmaton n 2*2 MIMO OFDM Systems L= SR [db] Fg. 9 Jont channel estmaton and synchronzaton for SISO-OFDM systems. Fg.10 reports the normalzed MSE obtaned after 10 teratons of the whole recever,as a functon of the average E b /0 per receve antenna.the curve labeled CRB s the Cramer-Rao bound when all the symbols of the frame are known,that s to say the DA CRB.The MSE of the UEM- HEM estmator,.e.,the UEM channel estmator wth the HEM nose-varance estmator,reaches that bound for E b / 0 above 5-6 db.the DD estmator s also close to the CRB.The MSEs of the three other EM-based estmators are between those of the DD and DA estmators.all the teratve algorthms seem to perform better than the DA one,whose estmates are not teratvely refnd.regardng the nose varance,the EM estmator overestmates t more than the HEM one,as expected.for a E b / 0 =7dB,the bas of the EM- EM and UEM-EM estmators s 3dB at teraton 2 and around db at teraton 10,whereas the bas of the EM-HEM and UEM-HEM estmators s only 2 db at teraton 2 and around 0.05 db at teraton 10[15]. Fg. 7 Channel estmaton n 2*2 MIMO-OFDM systems L=4 wthout synchronzaton.

5 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 9, Issue 3, o 2, May 2012 ISS (Onlne): Fg. 10 ormalzed MSE of the channel-tap estmates after 10 teratons for a 4*4 flat Raylegh-fadng channel. 6. Conclusons Estmaton of channel coeffcents and synchronzaton parameters are two man challenges n realzaton of MIMO- OFDM systems whch are practcal. In almost all publshed references tll no, estmaton of cannel coeffcents s done wth the assumpton of total frequency synchronously of transmtter and recever. The created frequency synchronously between transmtter and recever, n practce, s always exposed to rsk due to presence of factors such as Doppler phenomenon and phase nose. Therefore for exact estmaton of fadng channel status, t s necessary to keep the created frequency synchronously between transmtter and recever, unnterrupted. The presented algorthm estmates the carrer frequency offset and fadng channel coeffcents n two sequental steps, usng the header sequence at the begnnng of sent frames. The aforementoned algorthm s also extendable to dfferent STC-OFDM systems. References [1] X. Ma, M.K. Oh, G. B. Gannaks, and D.J.Park, "Hoppng Plots for Estmaton of Frequency-Offset and Multantenna Channels n MIMO- OFDM", IEEE Trans. On commun., vol. 53, no. 1, pp , Jan [2] G. J. Foschn and M. Gans, On lmts of wreless communcatons n a fadng envronment when usng multple antennas, Wreless Pers. Commun., vol. 6, pp , March [3] Gao Fefe PhD thess, " Robust Synchronzaton and Channel estmaton for MIMO-OFDM Systems ",2007. [4] M. Speth, S.A. Fechtel, G. Fock, and H. Meyr, Optmum Recever Desgn for Wreless Broadband Systems Usng OFDM, Part I, IEEE Trans. Communcatons, vol. 47, o. 11, pp , ov [5] F. Classen, and H. Meyr, Synchronzaton algorthms for an OFDM system for moble communcaton, n Coderung f ur Quelle, Kanal und U bertragung: ITGFachbercht 130, Mu nchen. Berln Offenbach: VDE-Verlag, ITG, pp , Oct [6] F. Daffara, and O. Adam, A novel carrer recovery technque for orthogonal multcarrer systems, Eur. Trans. Telecommun., vol. 8, no. 4, pp , July [7] ETSI, Rado broadcast systems; dgtal audo broadcastng (DAB) to moble, portable and fxed recevers: Fnal draft pr ETS , European Telecommuncatons Standards Insttute, Tech. Rep., ov [8] T. Keller, and L. Hanzo, Orthogonal frequency dvson multplex synchronzaton technques for wreless local area networks, n Proc. IEEE Int. Symp. Personal, Indoor, and Moble Rado Communcatons, pp , [9] U. Lambrette, M. Speth, and H. Meyr, OFDM burst frequency synchronzaton based on sngle carrer tranng data, IEEE Commun. Lett., vol. 1, pp , Mar [10] T. Schmdl, and D. Cox, Robust frequency and tmng synchronzaton for OFDM, IEEE Trans. Commun., vol. 45, pp , Dec [11] Jn-Goog Km and Jong-Tae Lm," MAP-Based Channel Estmaton for MIMO OFDM Over Fast Raylegh Fadng Channels ", [12] Fefe Gao, Yonghong Zeng, Arumugam allanathan, Tung- Sang g,, " Robust Subspace Blnd Channel Estmaton for Cyclc Prefxed MIMO OFDM Systems: Algorthm,Identfablty and Performance Analyss ", [13] Feng Wan, W.-P. ZhuM.. S. Swamy, " A Semblnd Channel Estmaton Approach for MIMO OFDM Systems ",2008. [14] M. O. Pun, S. H. Tsa, and C. C. Jay Kuo, An EM-Based Jont Maxmum Lkelhood Estmaton of Carrer Frequency Offset and Channel for Uplnk OFDMA Systems, IEEE Transactons on communcatons, Vol. 2, no. 3, pp , [15] Xaver Wautelet, Cédrc Herzet, Antone Dejonghe, Jérôme Louveaux, Comparson of EM-Based Algorthms for MIMO Channel Estmaton, IEEE Transactons on communcatons, VOL. 55, O. 1, JAUARY avd Daryasafar was born n Bushehr,Iran.He receved Bachelor and Master degrees n Electrcal-Telecommuncaton engneerng from Islamc Azad Unversty, Bushehr, Iran. Babak Ehyaee was born n Bushehr,Iran.He receved Bachelor and Master degrees n Electrcal-Telecommuncaton engneerng from Islamc Azad Unversty, Bushehr, Iran. Aboozar Lashkar was born n Bushehr,Iran.He receved Bachelor and Master degrees n Electrcal-Telecommuncaton engneerng from Islamc Azad Unversty, Bushehr, Iran.