The Application of Interpolation Algorithms in OFDM Channel Estimation

Transcription

1 The Applcaton of Interpolaton Algorthms n OFDM Estmaton Xjun ZHANG 1,, Zhantng YUAN 1, 1 School of Electrcal and Informaton Engneerng, Lanzhou Unversty of Technology, Lanzhou, Gansu , Chna School of Computer and Communcaton, Lanzhou Unversty of Technology, Lanzhou, Gansu , Chna Abstract In ths paper we propose algorthms for system channel estmaton usng Orthogonal Frequency Dvson Multplexng, OFDM. Based on the latest hgh speed transmsson technology, there are two ways to mplement the technques: usng frequency doman or tme doman channel estmaton. In OFDM the known plot sgnal s nserted to gve a channel approxmate estmate, and then the channel full response s obtaned by nterpolaton algorthms. Ths paper proposes three nterpolaton algorthms and studes ther characterstcs qualtes n channel estmaton by smulaton. We can use the concluson to choose the correct nterpolaton algorthms n OFDM channel estmaton. Keywords-OFDM; nterpolaton algorthms; channel estmaton I. INTRODUCTION As we all know, multmeda and nformaton technology plays an ncreasngly mportant role n human socal lfe and development wth the proposed personal communcatons concept. The need of personal hgh data rate wreless access s to promote wreless broadband multmeda communcatons development. The multpath delay caused nter-symbol nterference whch severely lmts the data transfer rate on the rado channel, and then Orthogonal Frequency Dvson Multplexng (OFDM) technology can effectvely suppress nter-symbol nterference, so t s wdely used. OFDM s an effcent technque used n hgh-speed dgtal transmsson over multpath fadng channels. An OFDM system requres an accurate estmate of the channel mpulse responses for sgnal detecton, and as a result, channel estmaton becomes a key problem for OFDM systems. Its man dea s: The channel s dvded nto a number of orthogonal sub-channels. It changes hgh-speed data sgnals nto parallel low speed sub-data streams modulated to each sub-channel. In the recever we can separate the orthogonal sgnal and reduce nterference between the sub-channels. Multple antennas can be used n orthogonal frequency dvson multplexng (OFDM) system to mprove the communcaton capacty and qualty of moble wreless systems. parameters are requred for dversty combnng, coherent detecton, and decodng. In OFDM systems the multple transmt antennas, such as permutaton and space-tme codng based transmt dversty, dfferent sgnals are transmtted from dfferent transmt antennas smultaneously. Consequently, the receved sgnal s the superposton of these sgnals, whch gves rse to challenges for channel estmaton. In ths paper, we nvestgate tranng-sequence desgn and parameter estmaton smplfcaton technques for OFDM wth multple transmt antennas. for channel estmaton. A common conjecture s to use orthogonal sequences at dfferent transmt antennas [1-3]. Tranng sequences are used n wreless communcaton systems to obtan ntal estmaton of channel parameters, tmng, and frequency offset. For multple transmt antenna systems, tranng sequences should be desgned to decouple the nter-antenna nterference for channel estmaton. estmaton based on plot n OFDM system s nvestgated whch s based on the channel modelng and parametrc selecton. In OFDM system because the entre system band s dvded nto a number of ndependent subchannel bandwdth whch has the same bandwdth, each subchannel s to transmt ther modulated sgnals. estmaton purpose s to get the channel state nformaton through the plot sequence. The common way s to drectly estmate the channel frequency response [4-6]. There are three ways n OFDM channel estmaton whch are blnd channel estmaton, sem-blnd channel estmaton and tranng sequence channel estmaton. The method based on tranng sequence channel estmaton s most wdely used and has a more stable performance [7-8]. II. THE OFDM SYSTEM MODEL A. The OFDM system model The OFDM system model s shown n Fg.1. OFDM s a block transmsson system where data symbols are transmtted n parallel on a large number of sub-carrers. The complex data symbols are modulated on N subcarrers by an nverse dscrete Fourer transform (IDFT). To form the OFDM symbol the last L samples are coped and put nto a preamble staton usually referred to as the cyclc prefx. The data vector s dgtal-to-analog converted and transmtted over a channel, whose mpulse response we assume s shorter than the length of the cyclc prefx. One OFDM symbol thus has duraton (N+L) Ts where Ts s the system s samplng perod. In the recever the sgnal s sampled, the cyclc prefx s removed, and the resultng data vector s demodulated by a dscrete Fourer evaluate system performance. DOI /IJSSST.a ISSN: x onlne, prnt

2 modulaton Demodulaton Fg. 1 OFDM system model. The sgnal transmsson s as follows: frstly the bnary nformaton data bts are mapped. Then X[k] s got accordng to the sub-carrer number N whch s through the s/p transformaton n accordance wth the structure of the plots and nsert plots. Fnally we can use the Fourer nverse transform (IDFT or IFFT), whch s expressed as N 1 1 ( ) kn j N x n X [ k ] e, n 0,1,, N 1 N k 0 (1) Where n s the n tme doman samples, k s the subcarrer. In order to elmnate the nter-symbol nterference to mantan orthogonalty among sub-carrers, every two groups OFDM symbol nsert cyclc guard nterval (CP), whch s the last symbols of each OFDM coped to the frst part. Guard nterval s greater than the length of the channel mpulse response or s equal to the maxmum delay. It s expressed as: x( N n), n Ng 1,, 1 x( n) () x( n), n 0,1,, N 1 Complex base-band moble wreless channel mpulse response can be expressed as ( ) ( h ( t, ) ) t (3) Where s the path s delay tme, (t) s the complex fadng. Usng the model of wde-sense statonary complex random process and supposng each track s ndependent, where the dscrete forms s shown n formula (4). h ( n, ) ( n) ( ) S/P S/P Plot Inserton Sgnal Detecton Estmaton X[k] (4) The sgnal x g (n) affected by fadng n recever s expressed as yg ( n) xg ( n)* h( n, ) w( n) (5) Where w (n) s the AWGN. IFFT FFT x[n] OFDM modulaton Insert cp Delete cp OFDM demodulaton P/S Nose P/S x(t) B. The summary of OFDM channel estmaton The nterpolaton algorthms are very popular n OFDM channel estmaton. Known the channel transmsson characterstcs of the plot poston, we can use the varous nternal algorthms to estmate the channel characterstcs of data locaton. At present the common plot plan are block plot and comb plot. The block plot s perodcally nserted plot n tme doman. The plot s nserted n all the subcarrers [7]. Because ths method that the plot on the frequency doman s contnuous, t s not senstve to frequency selectve fadng; the Plot on the tme doman s not contnuous, t usually requres the channel has a lttle change wthn a perod of tme or t even remans unchanged. So the block plot suts to the constant reference channel and WLAN channel. The comb plot s that the plot s all nserted n some subcarrer accordng to the ntervals. Because the plot s contnuously nserted n the tme doman, t has a good effect to the fast fadng. Thus the comb plot suts to the flat fadng channel. In OFDM systems we generally use plot symbol to estmate the channel. Today there are many estmaton methods we have got. OFDM system channel estmaton method s summarzed n Fg.. Fg. The summary of OFDM channel estmaton. In OFDM systems we generally use plot symbol to estmate the channel. Today there are many estmaton methods we have used. Now the tranng sequence based on the channel estmaton methods s wldly used. The channel estmaton model can be defned as follows. If H ( s the estmaton of H (,we can get the X ( s the estmaton of X ( : DOI /IJSSST.a ISSN: x onlne, prnt

3 Y( N( X ( X( e(,0 k N1 (6) The e ( s the error components caused by nose. It s can be proved that f H ( s an unbased estmaton and N ( s the zero mean whte nose process, X ( wll be the unbased estmaton. At the same nose condtons the estmated varance of H ( X ( s determned by the estmated varance of, so how to get accurate channel estmaton s very mportant. III. THE STUDY OF INTERPOLATION IN OFDM CHANNEL ESTIMATION Ths paper s manly studed the channel estmaton based on the plot. The common nterpolaton methods are: lnear nterpolaton, second-order nterpolaton method, cubc splne nterpolaton method, low-pass flter nterpolaton method and etc. A. Lnear nterpolaton Lnear nterpolaton method s to use before and after the adjacent two plot sub-channel channel response to calculate the other data sub-channels channel response whch s located between them. For the k-th channel, usng a lnear nterpolaton to obtan a channel frequency response s: K) mll) ml) l L ( ( m1) L) ml)) l H p( m) ( H p( m1) H p( m)) L k ml l, 0 l L (7) Where L<k<(m+1)L, L s the nterval between the plot sub-channel, m s the relatve poston of the plot. B. Second order nonlnear nterpolaton (Gauss nterpolaton) Gauss nterpolaton s a knd of second order nonlnear nterpolaton. It uses the current and the three plot symbols to estmate the performance whch s better than the lnear nterpolaton. The nterpolaton algorthm n frequency doman s descrbed as follows: ml l) C1 HP ( m1) C0 HP ( m) C 1HP ( m1) (8) ( 1) C1, C 0 ( 1)( 1) ( 1) l C 1, L In the same way, the nterpolaton algorthm can be obtaned n tme doman. For several locatons of the start, the algorthm s degenerated nto the lnear nterpolaton. C. Cubc splne nterpolaton Each sub-carrer channel transfer functon s approxmately l/l to a cubc polynomal n ths method. Where s expressed as H ( AH ( km) BH ( km 1) CZ( km) DZ( km 1) (9) Where A,B,C,D s determned by a d / D f s lnear '' combnaton constant. Z( H ( s the second order dervatve of the subcarrer k on the channel frequency. D. Low-pass flter nterpolaton Ths method s added zeros to the sequence of the plot sub-carrer channel response before usng the low-pass nterpolaton. Then we can get all the sub-carrer channel frequency response. IV. THE SIMULATION OF INTERPOLATION ALGORITHMS In the paper we choose MATLAB software to smulate the nterpolaton algorthms n OFDM system. The smulaton parameter s shown n the Table 1. TABLE 1. THE SIMULATION PARAMETER Parameter Modulaton Doppler shft Value QPSK 00MHz Number of multpath 6 Number of plot 6 Plot nserton nterval 4 Raylegh model Number of sub-carrer 96 IFFT and FFT ponts 18 In ths smulaton we choose 6 plots and use Raylegh channel model. In ths System, the Doppler frequency shft fm s 00MHz, multpath number s 6 dameters. The QPSK modulated technology s used n ths smulaton. The IFFT and FFT ponts are 18. To get the hgh qualty of smulaton, the dfferent Doppler shts are used n ths smulaton. DOI /IJSSST.a ISSN: x onlne, prnt

4 The comparaton of the dfferent nterpolaton methods lnear nterpolaton second-order nterpolaton cubc splne nterpolaton Fg.3 The Maxmum Doppler shft s 00 The comparaton of the dfferent nterpolaton methods lnear nterpolaton second-order nterpolaton cubc splne nterpolaton Fg.4 The Mnmum Doppler shft s 30 The comparaton of the dfferent nterpolaton methods lnear nterpolaton second-order nterpolaton cubc splne nterpolaton Fg.5 The Maxmum Doppler shft s 1500 We can use the propagaton model to smulate the characterstc of the dfferent nterpolaton methods. Thus the results can be seen n the Fg.3, Fg.4, Fg.5. From the fgures we can see that the cubc splne nterpolaton performance s the best n the three nterpolaton algorthms. The Doppler shft affects the communcaton qualty. The performance of the nterpolaton s better when the maxmum Doppler shft s low. Wth the ncreasng of the SNR, the better performance n OFDM channel estmaton can be got usng Low-pass nterpolaton method and cubc splne nterpolaton method. Lnear nterpolaton algorthm s smple, but the estmaton error s large; Gauss nterpolaton algorthm has a slghtly mproved performance; splne Cubc nterpolaton s a knd of hgh order nterpolaton, hgh precson, but polynomal structure s more complex. In vew of the threshold effect, we can use the method of low pass flterng after nterpolaton to elmnate the nfluence of nose and reduce the nose threshold. The nterpolaton error caused by the lnear nterpolaton accuracy s much larger than the nose. In Fg. (3) the Maxmum Doppler shft s 00. The hgher of the SNR, the better of the cubc splne nterpolaton. The computaton of FFT has nothng to do wth the nterpolaton multple rrelevant because the FFT computaton s only related to the number of FFT ponts. To the lnear nterpolaton because the data volume wll be the recprocal relatonshp wth the nterpolaton multple, the amount of computng s a lnear declne. V. CONCLUSIONS In ths paper several nterpolaton algorthms based on the plot channel estmaton n OFDM system are compared and analyzed through the numercal smulaton. The concluson can be got through the smulaton. The lnear nterpolaton algorthm s not used for estmaton n OFDM system. The nterpolaton accuracy s decreasng wth ncreasng of the multpath effects and the deducton of the plot number based on nterpolaton flter method. The FFT method calculaton has nothng to do wth the nterpolaton multples, whle the nterpolaton flter method s ncreasng along wth the exponental growng. For smplfyng the smulaton analyss, we made some necessary concluson, whch are gven below: The lnear nterpolaton algorthm s effectve only for a functon wth a rough slope, and can not be used for channel estmaton of OFDM system dscussed n ths paper or smlar system; Based on the nterpolaton flter the nterpolaton precson s gradually degraded wth the ncrease of the multpath effect and the reducton of the number of plot n the wreless channel; The nterpolaton precson of FFT method s only related to the computaton precson under the condton of no nose, and the error power s equal to the nose power under the condton of nose system. FFT method must strctly ensure that the number of FFT ponts s the nteger multple relatons wth the plot number and must be equal nterval dstrbuton. Based on the nterpolaton flterng method has not the lmt DOI /IJSSST.a ISSN: x onlne, prnt

5 ; Under certan sgnal to nose rato condton, the error performance of the FFT method s equal to that of the nterpolaton flter. Even n low sgnal to nose rato the FFT method s low to that of the nterpolaton. To sum up n the hgh sgnal-to-nose rato the FFT method s better than any other nterpolaton algorthm, but n some low sgnal-to-nose rato condtons t s lower than the nterpolaton flterng method. The FFT method s not always optmal. We must decde to adopt what knd of nterpolaton method and reasonable plot pattern desgn accordng to the system of sgnal envronment. In addton to the algorthm ntroduced n ths paper, there are many other algorthms. For example, wth the applcaton of dversty technology research, dversty estmaton of OFDM system s also an mportant research drecton, and the blnd channel estmaton s performed usng plot symbols. In short, the contnuous development of OFDM channel estmaton technology wll provde a new generaton moble communcaton system based on OFDM. ACKNOWLEDGEMENT Ths work was fnancally supported by the Natonal Natural Foundaton(NO ) of chna. REFERENCES [1] Snem Coler, Mustafa Ergen, A study of channel estmaton n OFDM systems, IEEE Vehcular Technology Conference, Vancouver, Canada, 00,vol., pp [] J.-J. var de Beek, O.Edfors, M.Sandell, S.K.Wlson, and P.O. Borjesson, On channel estmaton n OFDM systems, n Proceedngs of IEEE Vehc. Techno. Conf, vol., pp ,1995. [3] Suh C, Hwang C S, and Cho H, Comparatve study of tme-doman and frequency-doman channel estmaton n MIMO-OFDM systems, IEEE 14th Proceedngs on PIMRC 003 Bejng, 003, pp ,. [4] M Jankraman,Ramjee Prasad, Performance Evaluaton of Hybrd OFDM/CDMA/SFH aproach for wreless multmeda, IEEE Trans. Commun, vol., pp [5] V. Taronkh, N. Seshadr, AR. Calderbank, Space-tme codes for hgh data rate wreless communcaton: Performance crteron and code constructon, IEEE Trans. Inf. Theory, vol. 44, no., pp ,1998. [6] Yan yan, Lu Xudong, Content-based herarchcal authentcaton watermarkng algorthm based on mage quad-tree decomposton, Journal of Informaton and Computatonal Scence, vol.8, no.8, pp , 011. [7] Zhang quyu, The study on unversal steg analyss method based on dct doman for jpeg mages, Internatonal Journal of Dgtal Content Technology and ts Applcatons, pp , 011. [8] Zhao, Fuqng, Tang Janxn, Wang, Jzhe, We, Chunmao, An Improved PSO Algorthm wth Declne Dsturbance Index, Journal of computers, vol. 6, no.1, pp , 011 DOI /IJSSST.a ISSN: x onlne, prnt