Iterative Doppler Shift Estimation in Radio propagation

Transcription

1 Iterative Doppler Shit Etimation in Raio propaation AMIRHOSSEIN FEREIDOUNTABAR,GIAN CARLO CARDARILLI Department o Electronic Enineerin Univerity o Rome (Tor Verata ITALY Fereiountabar@in.uniroma.it,.cararilli@uniroma.it Abtract:Thi paper analye the bia o a Doppler hit etimator bae on aaptive autocorrelation unction (ACF computation an propoe a proce or reuction the bia o etimation at hih pee movement. Furthermore, a inaltonoie ratio (SNR etimator i propoe accorin to the varyin bia in the iteration, where the etimate o the Doppler hit in the irt an the inal tae o iteration are mere to contruct a bia ratio relate to the SNR. Simulation how the propoe alorithm achieve accurate etimation within a wie rane o velocitie an SNR. KeyWor: Iterative Etimation; Sinal to Noie Ratio; Doppler Shit; Hih Vehicle Spee; Raio Propaation; Hih Spee Approximation Introuction In raio communication ytem, multipath ain in channel caue power luctuation in ranom amount an thereore ecreae the perormance o the receiver []. Unertanin o the ain proce ha been important reearch iel in raio communication. Amon comprehenive conieration on channel ain, accurate etimation o channel parameter, uch a inaltonoie ratio (SNR an Doppler hit (, play important role in communication ytem. For intance, in raio ytem, accurate SNR an Doppler hit etimation are critical or ynamic channel parameter etimation [3]. More than the SNR an Doppler hit, there are many channel parameter to be coniere, uch a the time elay [4].However, our ocu i only on the SNR an Doppler hit etimation in thi paper. For etimation o the Doppler hit, lot o technique have been employe, uch a the level croin rate [3], the channel autocorrelation unction (ACF [5] an the phae ierence [6]. Unortunately, the perormance o thoe technique will ecreae by aitive white Gauian noie (AWGN iniicantly. In [7] a metho, can reuce the AWGN inluence i propoe. But, when the AWGN i mall (i.e. the hih SNR reion, metho o [7] uer rom lare etimation bia uner the cae o hih pee (pee that uually ue by plane, ince it erieapproximation error i lare in thi ituation. For olvin thi problem, a linear curve ittin i propoe to reine the etimate o the Doppler hit, which i bae on the act that the proce o [7] metho how almot the ame etimation curve or ierent SNR. Monte Carlo imulation conirm the accuracy o the propoe metho. Conventionally, tuy o the receiver i uner thi conition that SNR i nown. Thereore, only a ew metho or the SNR etimation, uch a the momentbae SNR etimator in [8, 9, ] an the correlationunctionbae SNR etimator are exit []. Alo both in o metho uer rom lare etimation biae at hih SNR reion in hih pee. Furthermore, a pointe out in [5], the SNR an Doppler hit mut be etimate by two inepenent etimator, which obviouly increae the implementationcot. Thereore, it i beneicial to combine the two etimator toether, which impliie the implementation. In [7], author oun the etimation bia o ierent iteration were relate to the SNR thereore, it i poible to etimate the SNR accorin to thee varyin bia. In act, when the iterative proce en, the inal etimate o Doppler hit i cloe to EISSN: Volume 4, 5

2 the actual Doppler hit. Then, the Doppler hit etimation ratio o noiy cenario to noieree cenario, i.e., the ratio between the etimate o the Doppler hit in the irt roun o iteration an that in the inal roun o iteration, can be approximately obtaine. Moreover, the analytical expreion o thi ratio can be iven by a polynomial orm with only one variable [7], i.e., the SNR. Conequently, the SNR etimator can be erive by olvin the polynomial equation. Simulation are one to tet the propoe alorithm, an accurate etimation have been oberve in a wie rane o velocitie an SNR. The ret o thi paper i oranie a ollow: Section preent the ytem moel uner conieration toether with the conventional ACFbae etimator o Doppler hit. The etimation bia, the linear ittin a well a the SNR etimator are preente in Section 3. Finally, numerical reult are preente an analye in Section 4, an concluion are ummarie in Section 5. Sinal Moel It i aume that a banwithlimite pilot inal i tranmitte over Rayleih ain channel, an the reolvable multipath ain channel are wieene tationary an mutually uncorrelate catterin (WSSUS procee. Ater ynchronouly matchin the pilot inal, it i eay to erive the expreion o channel etimate accorin to [] an the reerence therein: c ( n = c( n + ( n ( where c(n, c( n an (n repreent the actual channel, the channel etimate an AWGN (with variance at time inex n, repectively. Generally, the actual channel (c(n are moele a eromean complex Gauian ranom procee with variance.. ACFbae Doppler hit etimator Accorin to [7], the ACF o Rayleih channel ha the ollowin orm: R = J T ¹ ( ( ( p, R( = + (3 where T enote the pilot ymbol interval an J ( i the irt in Beel unction o ero orer. By nelectin the AWGN an uin erie expanion, there exit: J T» T (4 ( p [ ( p ] Ater collectin K ample, the oriinal ACFbae Doppler hit etimator can be preente a ollow: J ( p M T + lm = (5 p M T where, M enote the etimate o Doppler hit uin R( M, an R( M enote the etimate o channel ACF at correlation o la M.. Aaptive ACF metho The etimator o equation (4 i biae ue to the inluence o AWGN (inite SNR an the approximation error o R(. In orer to quantiy the bia, in [7] eine a ratio between the etimate o the Doppler hit uner the noiy cenario an that uner the noiyree cenario i eine a ollow: where l SNR= J( pmt = (6 p T = / enote the ymbol SNR. ( noiy an ( noiy ree enote the etimate o the Doppler hit with an without inluence rom AWGN, repectively. In equation (6, the numerator ( noiy an the enominator ( noiy ree are obtaine by calculatin A R( M / R( throuh equation (, where the ormer require > an the latter atiie =. Speciically, i h ( M =, which correpon to the ituation o no etimation error, then we have: EISSN: Volume 4, 5

3 h( M = + = + ( p MT (7 By olvin the above equation (7, we have: M = p T (8 Then, an aaptive ACF metho can be realie by an iterative proce illutrate a ollow where ( i an M(i enote the etimate o Doppler hit an the compute correlation la at the ith iteration, repectively. Due to it iterative characteritic, thi metho can be calle a either the aaptive ACF metho or the iterative ACF metho. 3 The SNR Etimator an the Reine Doppler Shit Etimator Compare with the oriinal ACF metho, the aaptive ACF metho in [7] alreay howe a reat perormance improvement. However, when the movinpee increae, the aaptive ACF metho prouce lare etimation biae ue to the approximation error, which wa caue by the erie expanion. Fiure how the imulation reult, which veriie the increae o the etimation bia with the increae o movinpee. S Fiure illutrate the accuracy o the iterative ACF etimator or the Doppler hit in comparion with the noniterative one. The reult veriy the improvement in etimation accuracy achieve by the aaptive (iterative proce. Neverthele, the improvement ecreae a the movinpee increae, which i caue by the erie approximation error when the movinpee i hih. However, it i apparent that the aaptive proce yiel almot the ame etimation curve or ierent SNR, which implie that a inle ittin proce can be applie to reine the Doppler hit etimation at ierent SNR. In aition, althouh the etimation curve reultin rom the iterative proce eem to be nonlinear to ome extent, the linear ittin technique can till be ue to prouce a imple etimator tructure an maintain mall ittin error. 3. The reine Doppler hit etimator Next, enote an a the th Doppler hit (unnown an it etimation in imulation. Here, = ; ;...;Q, an Q repreent the total number o Doppler hit, which i ten in Fi.. Given an etimation curve o a certain SNR, the ollowin linear expreion can be erive approximately: Q = Q (9 Fi.Perormance o the iterative ACF metho in comparion with the conventional one where i provie by the aaptive ACF metho. In equation (9, Q,, Q an are etermine in avance bae on the imulation reult, an thu are nown. Note that in act, equation (8 oe not require any SNR inormation becaue the propoe aaptive proce yiel imilar etimation at ierent SNR. Accorin to equation (8, the Doppler hit etimation can be reine a ollow In eneral, only one inle ittin ormula i require or all SNR, ince ierent SNR lea to almot the ame etimation curve a hown in Fi.. In thi tuy, the ittin ormula i et up accorin to the etimation curve at SNR 5 B. Moreover, in EISSN: Volume 4, 5

4 realworl application, an Q will be choen a the minimum poible value an the maximum poible value o the Doppler hit, an then their etimate will be obtaine accorin to the metho ecribe in Section.. Finally equation ( will be ue to reine the etimation at other actual Doppler hit. Note that in [7] the tability an converence o the aaptive ACF metho i prove. The propoe linear ittin technique in our tuy will not moiy thee oo propertie. 3. The SNR etimator A mentione beore in [7], it ha been proven that the aaptive ACF metho convere ater N iteration, reultin in the inal etimation ( N» at appropriate pee. Moreover, by equation (, thi relation can be extene to the cenario o hih movinpee. Speciically, we have: ( QPSK contellation et { ± ± j} atiyin: / N N å ( n = (3 n= Due to the limite pace, only the propoe iterative (aaptive ACF metho an a ew typical metho evelope in [3, 5, 6, 7] are meaure in term o their MSE an accuracy. The etaile imulation parameter are hown in Table. The total imulation uration lat or one thouan lot. The ITUR M.5 channel moel with ix inepenent path i utilie at the carrier requency o. GH. In aition, each lot conit o 56 bit with a bit rate o 3.84 Mbit/. In each lot, ive pilot ymbol, each o a lenth o thirty two bit, are timemultiplexe with our ata bloc. J ( p T + l = ( p T Throuh olvin the equation (, the SNR etimator can be iven by l p T = h( opt M ( = J ( ( + o 4 Numerical Reult an Analyi Each uer tranmit quarature phae hit eyin (QPSK moulate ymbol b ( m in bloc o lenth M. Each ymbol i prea by a ranom preain equence o lenth N an each chip i tranmitte over an iniviual ubcarrier. The number o ubcarrier i equal to the lenth o the preain equence. The element o the preain equence are ranomly choen rom the Fi. The reine Doppler hit etimation with a linear curve ittin Fiure illutrate the accuracy o the propoe Doppler hit etimator. The reult how that the propoe metho yiel excellent perormance an the bia i very mall even when SNR i B. Comparin Fiure with Fiure, we explicitly ee that the propoe linear ittin procein prouce trivial eviation between the ieal curve an the etimate curve, which mean that it i inenitive to the approximatin error in equation (3. Thereore, the propoe metho iniicantly improve the aaptive ACF metho [7] in a wie rane o mobile pee, which will be urther conirme by the ollowin MSE comparion. In aition, the maximum Doppler hit in our imulation i 586 H, which EISSN: Volume 4, 5

5 correpon to a pee o 3m/h. Alo irection o the tranmitter i towar to the receiver in our imulation. Fiure 3 compare the MSE o the propoe metho with ome typical etimator. Speciically, all reult are averae over the meaure o movinpee. In comparion, the iterative ACF metho maintain it MSE perormance irrepective o SNR value, an obtain at leat one orer o manitue ain when SNR rane rom B to B. Moreover, the propoe metho urther improve the MSE perormance an obtain at leat one orer o manitue ain compare with the iterative ACF metho. Thereore, the propoe metho i more uitable or practical mobile ytem than the other our metho. In aition, or the ae o clear preentation, we only how the comparion between our propoe metho an the other our metho. In act, our extenive imulation how that our iterative ACF metho alo outperorm many other etimator, uch a loarithmic envelope metho in [, 3], where their MSE at SNR 5 B are about.68 an.4, repectively. Fiure 4 emontrate the SNR etimation o the propoe etimator. Double coorinate are ue to illutrate both the accuracy an MSE rom Fi.4, we in that the SNR etimate are very accurate within a wie rane o velocitie an SNR. Speciically, the MSE curve how a U hape with it bottom at SNR 5 B. Thi pecial hape can be explaine or the ollowin two reaon. Firtly, the linear ittin o equation ( i erive at SNR 5 B but i applie to all SNR. Seconly, when the SNR i hih, the AWGN inluence become trivial, but the approximation error o R( i till iniicant. Fi.5 The ratio o etimation at ininite SNR (M= In Fi.5 when the SNR i ininite we can clearly in that the ratio luctuate trivially it mean le than.8%.hence we can conclue that the eect o the approximation error i neliible or the pee rane o mh to 3mh which i alo the uually concerne plane pee rane. Fi.3 The mean quare error (MSE perormance comparion o Doppler hit etimator Fi.4 The accuracy an the normalie MSE perormance or the propoe SNR etimator in ouble coorinate Fi.6 The ratio o etimation in ierent SNR(M= Fi.6 concern the cae o ininite SNR which we ee that the ratio ap are obervable or ierent EISSN: Volume 4, 5

6 SNR at low pee. Hence we can conclue that the eect o the aitive noie i the ominant actor or the etimation error o Doppler hit. Thi eect can be eectively reuce by the aaptive proce a hown in our paper. With the help o the aaptive proce an the linear ittin,the inluence o the approximation error i remove eectively an thereore accurate Doppler hit etimate are obtaine rearle o the actual approximation error.the orer o approximation we have chooen ha ome error in Doppler hit etimation but in the hiher peewill be more eeror o the ollowin erivation will reveal that the inluence o thee error can be reuce iniicantly or an appropriate choice o M.then thepropoe metho ha a oo perormance in wie pee rane. 5 Concluion A joint etimator o the Doppler hit an SNR ha been propoe. The etimator i erive accorin to the varyin bia between iterative procee o the aaptive ACF metho. The imulation reult how that our propoe metho achieve accurate etimation or the SNR an Doppler hit in a wie rane o velocitie an SNR. Reerence: [] T. Zemen, J. Wehiner, an R. Muller, Iterative etection an channel etimation or MCCDMA, in IEEE International Conerence on Communication, ICC, Anchorae (Alaa, USA, May 3. [] A. Sampath, J. Holtman, Etimation o maximum Doppler requency or hano eciion, Proc. o IEEE VTC 93, pp.85986, 993. [3] Z. Ma, Y. Yan, C. Zhao,X. You, An improve channel Etimation Alorithm Bae on Etimatin Level Croin Rate or CDMA Receiver, Chinee Journal o Electronic, vol., no., pp.3538, 3. [4] J. Wen, P. Li, Y. Wen, A new metho or unbiae timeelay etimation in noiy environment, International Journal o Aaptive Control an Sinal Procein, vol., no.7, pp.63634, 7. [5] C. Xiao, K. Mann, J. Olivier, Mobile pee etimation or TDMA bae hierarchical cellular ytem, IEEE Tran.Vech. Tech., vol.5, no.4, pp.9899,. [6] J. Hua, B. Shen, X. You, The phae probability itribution o eneral clare moel an it application in Doppler hit etimation, IEEE AWP. Letter, vol. 4, no. 4, pp , 5. [7] J. Hua, L. Men, G. Li, D. Wan, X. You, An Accurate Scheme or Channel Parameter Etimation in Mobile Propaation, IEICE Tran. Electro., vol.e9c, no., pp.6, 9. [8] N.C. Beaulieu, A.S. Tom, D. R. Paului, Comparion o our SNR etimator or QPSK moulation, IEEE Commun. Letter, vol.4, pp.4345,. [9] Y. Chen, N.C. Beaulieu, Etimation o Ricean K parameter an local averae SNR rom noiy correlate channel ample, IEEE Tran. Wirel. Communication, vol.6, no., pp.64648, 7. [] Z.J. Xu, K. Wan, J.Y. Hua, G.M. Zhon, Blin SNR etimation with empirical characteritic unction erivative in hihorer moulation ytem, Proc. IEEE ICCCAS 8, pp.445, 8. [] E. Karaterio, M. Sumanaena, B. Evan, Simple SNR etimator or mobile ain channel, IEEE Electronic Letter. vol.39, no., pp.4445, 3. [] X. Gao, B. Jian, X. You, Z. Pan, Y. Xue, E. Schul, Eicient channel etimation or MIMO inlecarrier bloc tranmiion with ual cyclic timelot tructure, IEEE Tranaction on Communication, vol.55, no., pp. 3, 7. [3] J. Hua, X. You, Doppler hit etimation metho in mobile communication ytem, J. Southeat Univ., vol., no.4, pp.454, 4. EISSN: Volume 4, 5