Low Complexity LMMSE Channel Estimation on GPP

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1 0 7th Iteratoal ICT Coferece o Commucatos ad etworkg Cha (CIACOM) Low Complexty LMME Chael Estmato o GPP We h, Tao Peg, Rogrog Qa Key Lab. Of Uversal Wreless Commucato, Mstry of Educato, BUPT Bejg 00876, Cha shwe_bupt@63.com Abstract Ths paper proposes a mproved lear mmum mea square error (LMME) algorthm of adaptve order determato by takg advatage of the structure characterstcs of tme doma least square (L) chael estmato based o geeral-purpose processor (GPP), whch provdes the approxmate estmato approach of max-tme delay ad ose power. I addto, ths algorthm acheves a practcal chael estmato formula whch greatly reduces the complexty of the algorthm by decomposg the autocorrelato matrx to some sub-matrxes o the foudato of correlato badwdth. The comparsos are made betwee the smulato performace of mproved LMME algorthm wth those of other estmato methods for further aalyss. Fally, a hardware mplemetato scheme of the proposed algorthm o GPP s gve. Keywords-GPP; LMME; adaptve order determato; chael parameter; algorthm complexty I. ITRODUCTIO I wreless telecommucato systems, due to the fluece of the tme-varyg of wreless fadg chael ad mult-path trasmsso, the chael estmato module must be fshed before the recever so that the recever ca make some compesato to the receved sgal formato. Therefore, chael estmato s oe of the key techologes of wreless trasmsso. LTE uplk recever system adopts block plot patter. The correspodg chael estmato approaches [] maly clude L ad MME. L takes o accout for Gaussa whte ose ad the terrupto amog carrers. o ts performace s worse tha MME but ows smpler algorthm. MME makes up the dsadvatages of L ad has a greatly mproved performace. owever, the algorthm of MME eed to kow the autocorrelato formato ad has a hgh complexty, eve though t has bee smplfed by sgular value decomposto (VD) algorthm. I respose o above problems, ad usg the obvous characterstcs of the sgle structo multple data (IMD) Ths work s sposored by atoal cece ad Techology Major Projects uder grat 0ZX ad 0ZX , oka, ad part by the atoal Key Basc Research Program of Cha (973 Program) uder grat o.0cb36005, the Jot Fuds of FC- Guagdog uder Grat U Ra Dua, Kul Che Dvso of Wreless Techology Cha Moble Research Isttute Bejg, Cha extesos parallel structo computg order, Cache mechasm ad hgh speed fast fourer trasform (FFT) lbrary o GPP, ths paper proposes a adaptve LMME chael estmato mproved algorthm based o the state of the chael. Ths algorthm ca choose chael mpulse respose (CIR) effectve order ad the average sgal to ose rato (R) of chael. The the tme doma results of chael estmato are processed to reduce the ose power ad rest ter-carrer terferece (ICI) power. Fally, the autocorrelato matrx s smplfed by o-overlappg techology. Eve though the performace s damaged a bt, the complexty of LMME chael estmato s reduced at a large extet. The R s 5dB hgher tha L chael estmato the performace. II. YTEM MODEL Fgure llustrates LTE physcal uplk shared chael (PUC) Chael Base Bad Trasmsso []. The emtter trasforms the frequecy doma data {X[k]} to the tme doma data {x[]} through IFFT module. To elmate the terrupto amog symbols, the cyclc prefx s troduced ad ts legth s geerally larger tha the max tme delay of chael. Fgure. LTE Uplk PUC Chael Base Bad Trasmsso model. Mult-path chael mpulse respose ca be modeled as followg[3]: r π h( ) a exp j f T ( ), 0 δ λ τ D () //$ IEEE

2 where r s the total umber of propagato paths. a s the complex mpulse respose of the umber th path. f D s the th path Doppler frequecy shft, λ s delay spread dex, τ s the th path delay ormalzed by the sample tme. Cosderg the fluece by ICI, the receved frequecy doma sgal from C-FCDMA sgal processed by FFT s: Yk [ ] Xk [ ] k + Wk + I k 0, k () where W k s the Addtve Whte Gaussa ose o frequecy doma. I k that s ICI because of Doppler frequecy. It s decded by the modulato value of emttg sgal X k o other sub-carrers. III. LOW COMPLEXITY LMME CAEL ETIMATIO DEIG A. LMME chael estmato As the value of the plot sgal s kow, we ca get the chael frequecy respose the plot subcarrers by the L algorthm as follows: Yk [ ] Wk + I k k k + 0, k (3) ls Xk [ ] X[ k] Obvously, the chael based o L does t eed ay chael statstcs, ad the calculato s very smple. But the sgals o each subcarrer are dsturbed by ose ad other subcarrers ad the ME of the output sgal s large. The MME chael estmato have a good hbtory effect o the ICI ad the Gaussa ose, that s based o the L chael estmato[3-5]: where mmse mmse k W ls k W R R + σ ( XX ) k (4) s the results of MME chael estmato, R s the autocorrelato matrx of chael mpulse respose, σ represets the ose varace. I geeral, by replacg the term ( ) E{ XX }, the XX (4) wth ts expectato ( ) LMME chael estmator ca be represeted as follow: ( / ) lmmse k R R β R I k + l s (5) where { Xk } k β E E{/ X }, s a costat depedg o the type of modulato. For the QPK, β, for the 6QAM, 7 / 9 β, { k } R E x / σ s the average R. Ad the referece [4] shows that the chael autocorrelato matrx s: { }, R E [ r ] m L( + πj ( m )/ τ rms e r m, L τ rms τ ( e )( + j π( m ) / ) rms τrms I summary, LMME algorthm eeds to kow the pror probablty of the chael ad ose, whch eeds to calculate the autocorrelato ad verso matrx, thus the complexty wll be much hgher tha L algorthm. The followg wll use the characterstcs of GPP platform ad LMME algorthm to put forward the mproved algorthm for the hghly complex calculato descrbed above. B. Based o adaptve order of chael model parameter estmato From (6) we ca see that the autocorrelato values deped o L whch s the largest legth of mult-path delay. If we use the fxed L the chael whch has a great chages the multpath delay, t wll make the correlato fucto msmatch, the cause some loss of system estmato performace. Meawhle the sgal eergy s relatvely cocetrated the cyclc prefx (CP) legth the tme doma. Based o these two aspects above, ths paper presets a adaptve order determato estmato algorthm. Frst, we rapdly trasform the result of L estmato frequecy doma to tme doma by IFFT lbrary of GPP platform, ad the get the followg formula: ˆ ( ) π h k exp j k, 0 L ls k 0 (7) We defe the effectve order of CIR as, accordg to the ĥ the characterstcs of CIR, all of the ( ) L are terferece ad ose. Therefore, we ca set the sgal to 0 these places, that s: hˆ L ( ) h ( ), 0 ˆL 0, o far, the choce of becomes partcularly mportat. Takg the complexty of the code mplemeted o the GPP to accout, we determe the throgh the relato betwee the useful sgal eergy ad total eergy: (6) (8) 857

3 R h h L L ˆ ( ) / ˆ ( ) (9) I [6], whe R0.9~0.95, s determe, the the average power of ose o the s also determed as followed: ĥ L ˆ ( ) ˆ L ( ) σ h h L Oce get ( ) σ, we ca fd β / R (0), ad trasform to frequecy doma by FFT lbrary. Fally we ca get the relato fucto match the actual chael order whe to (6). I the practcal applcato, the 0 L part wll be dvded to several tervals depedg o the legth of the subcarrers, Δ s steppg to fd the effectve order of the CIR. o the creased complexty ths process are: tmes FFT, tmes complex multplcato, ++ tmes real addto ad / Δ + tmes real dvso. C. Based o o-overlappg blocks of LMME chael estmato algorthm I [4], LMME chael estmator uses ose weghtg ad chael correlato property. ghly correlated elemets of chael autocorrelato matrx have a great effect o the performace of estmator, whle the effect by lowly correlated elemets s small. o these chael coeffcets of correlato matrx ca be gored. Coherece badwdth s defed as a rage frequecy where correlato fucto values greater tha 50%, o you ca use the cocept of coherece badwdth to reduce the complexty of the LMME algorthm[4]. We subdvde the chael vector usg the defto of coherece badwdth. ( ) h [ h T, h T,, h T M,] () Therefore, the chael auto-correlato matrx ca be parttoed to sub-matrces of the sze of coherece badwdth as show Fgure. ote that the o-overlap chael estmator s equvalet to the cocept of parttog to the subsystem proposed. Fgure. Decomposto of chael autocorrelato matrx by ooverlap techque Usg (5), subvector Ĥ ca be expressed as: lmmse,m ˆ β R R I, m M lmmse, m mm + mm ls,m R () where m m R s a auto-correlato matrx of sze k k, m s a sub-matrx dex. Thus, the LMME chael estmato vector usg the o-overlap techque s: ˆ ˆ T ˆ T ˆ T,,, lmmse _ ooverl ap l mmse, l mmse, l mmse,m (3) Below to aalyze the computatoal complexty of the algorthm. Through the chael autocorrelato matrx decomposto, the computatoal complexty of matrx multplcato ad addto have bee sgfcatly reduced, as show Table. TABLE I. TE COMPUTATIOAL COMPLEXITY OF MATRIX MULTIPLICATIO AD ADDITIO LMME o-overlap Real_multplcato K MK Real_addto MK K IV. IMULATIO REULT AD AALYI Ths paper bulds the LTE uplk PUC chael smulato for the varous performace test by usg the MATLAB. I the LTE protocol [7], t defes three kds of mult-path fadg model for dfferet scearos, that s: the EPA chael, the EVA chael, the ETU chael. ow we select A4-6 cofgurato uder the codtos of the EPA 5 z(6qam, 50RB, 3/4 Codg rate) ad A3- cofgurato uder the codtos of the ETU 70z(QPK, RB, /3 Codg rate) as the test case. We have carred out the correspodg test for the L algorthm, the LMME algorthm ad the mproved LMME algorthm. I the smulato curve, the horzotal axs s the R ad the vertcal axs s the ThroughPut. Fgure 3. Algorthms performace comparso the EPA 5z chael 858

that the performace of L chael estmato s the worst, ad the dfferece betwee the three

I the ormal crcumstace, there s a gap of betwee L ad LMME, ad the mproved LMME algorthm

Ths performace deterorato s maly due to the smplfed chael model parameters ad estmated

Despte ths, the mproved low complexty LMME compared to the L chael estmato algorthm stll has

5dB compared to the requremets of the protocol.

lbrary ad all the developmets of GPP platform that make t very well data coverso, calculato

GPP use the IMD exteso techology, whch ca hadle a umber of cotuous data cocurretly, so that

four data IMD parallel computg schematc "OP" the fgure represets a arthmetc or logcal

s the value source regster, after OP computg at the same tme, ther results depost the target

The above example computg complete by oly oe IMD structo, t hadle four data cocurretly.

Whe the CPU wat to read a data, frst fd t from the cache, f foud, read mmedately ad set to

to the CPU for processg, ad trasferred the data blocks cotag the data to the cache.

CPU up to about 90%). Ths saves CPU tme to read the memory drectly.

4 model Fgure 4. Algorthms performace comparso the ETU 70 z chael model From Fgure 3 ad Fgure 4, t ca be draw that the performace of L chael estmato s the worst, ad the dfferece betwee the three algorthms was ot very obvous uder the codto of hgh R. I the ormal crcumstace, there s a gap of betwee L ad LMME, ad the mproved LMME algorthm proposed ths paper has gap of db compared wth the LMME. Ths performace deterorato s maly due to the smplfed chael model parameters ad estmated accurate result. Despte ths, the mproved low complexty LMME compared to the L chael estmato algorthm stll has a elevato of about 3~4dB ga, whch s a mprovemet of 4.5dB compared to the requremets of the protocol. o the mproved LMME algorthm for the GPP platform has hgh relablty. V. GPP PLATFORM IMPLEMETATIO A. GPP platform I recet years, parallel E structos, effcet cache mechasm as well as the FFT lbrary ad all the developmets of GPP platform that make t very well data coverso, calculato ad accessg the feld of dgtal sgal processg. GPP use the IMD exteso techology, whch ca hadle a umber of cotuous data cocurretly, so that processg speed s doubled ad redoubled. A typcal schematc dagram show Fgure 5: Fgure 5. four data IMD parallel computg schematc "OP" the fgure represets a arthmetc or logcal operator, such as "plus", "mus", "multply", "ad", "or" etc; X s the value source regster, Y s the value source regster, after OP computg at the same tme, ther results depost the target regster. The above example computg complete by oly oe IMD structo, t hadle four data cocurretly. GPP has a effcet cache mechasm. Whe the CPU wat to read a data, frst fd t from the cache, f foud, read mmedately ad set to the CPU for processg; f ot foud, usg a relatvely slow speed to read from the memory ad set to the CPU for processg, ad trasferred the data blocks cotag the data to the cache. The readg mechasm makes the ht rate of the CPU to read from the cache very hgh (most of the CPU up to about 90%). Ths saves CPU tme to read the memory drectly. I addto, supported by the uderlyg hardware, the FFT lbrary [8] o GPP ca acheve the coverso betwee tme ad frequecy doma rapdly. GPP platform lay the most mportat foudato the mplemetato of the mproved algorthm above. B. The flow dagram of algorthm o GPP Fgure 6 s the whole mplemetato process of the mproved LMME algorthm o GPP platform. We trasformed the results of L chael estmato to the tme doma by usg the hgh-speed FFT lbrary. The value s determed to the eergy search ad detecto, the R ca obtaed drectly. Ad through the method whch chael autocorrelato matrx s broke dow to a umber of ooverlappg sub-matrx, we ca complete the calculato of the autocorrelato fucto. Fally the datas after bee added to the threshold are put to the frequecy doma. 859

5 Fgure 6. The flow dagram of mproved LMME algorthm o GPP C. Optmzato o GPP I the process of eergy search ad detecto, order to reduce the sestvty of the algorthm to ose, ad make use of E structo to optmze computg. We dvde the sgals that are less tha search value a certa rage to groups, there are 4 cotuous sgals every group, the we accumulate the eergy by step of a group sgal, ad ths result would be regarded as the estmated value of sgal eergy. As s show fgure 7, we ca use 3 hadd structos to compresso 6 3-bt-log data to 4 3-bt-log data, ad tradtoal method structos s eeded [9]. I ths way, we successfully mprove the le load, but also mprove the effcecy of program after calculato Fgure 7. Optmal desg by usg the commad of hadd Adaptve order determato algorthm ca make the match the correlato fucto of the chael maxmally match to the actual chael. But practcal applcato process, whe the result of chael estmato chaged, the MME equalzato coeffcet matrx W (4) also eed to be reupdate, ad there s a matrx verso the calculato of the coeffcet W, ths computato o GPP platform s tolerable. Therefore, we stll use the offle method of calculato. By smplfed estmate of the chael model parameters, r, (6) oly deped o the dstace betwee m ad, so we ca save R matrx a table whch has calculated by the MATLAB. The the maxmum possble R ad multpath delay s dvded to several tervals, each terval correspods to a W coeffcet whch has bee computed. We select the correspodg terval of W as the LMME coeffcet matrx whe we get the results of R ad chael order estmato. I addto, order to further reduce the computatoal complexty, adaptve order determato estmato process ca complete a estmato after a certa tme, whch ca also meet the actual stuato that the chael type chages slowly the commucato system. VI. COCLUIO I ths paper, for chael estmato uplk PUC o GPP platform, we propose a low complexty LMME modfed algorthm. Frstly, for the tectoc characterstcs of L chael estmato tme doma results, ad combed wth the wreless chael mpulse respose of fte legth tme doma, we take eergy detecto of tme-doma results L chael estmato, search CIR effectve order umber ad calculate the chael average R, add a threshold L chael estmato tme doma results through the use of the estmated value. Ad the we dvded the chael autocorrelato matrx to a umber of o-overlappg sub-matrx, ths way the complexty of LMME estmato ca be smplfed at a large extet. Fally, the smulato accordg to the requremets of the agreemet shows that through ths algorthm we ca easly get the effectve order wreless chael estmato results. By usg the results to estmate the average R of the chael, the chael model parameters ca be smplfed. Whe compared wth the L chael estmato algorthm, the crease calculated amout s smaller, but the performace o cotrary has bee greatly mproved. mulato results show that: the complexty of the mproved algorthm s better tha LMME, the performace of the mproved algorthm s better tha the L algorthm. The algorthm has a good practcal value the realzato of the geeral processor platform. REFERECE [] em Coler, Mustafa Erge, Auj Pur, ad Ahmad Baha, Chael Estmato Techques Based o Plot Arragemet OFDM ystems, IEEE Trasactos o Broadcastg vol.48, o.3, pp.3-9, eptember 00. [] 3GPP T 36., V Evolved Uversal Terrestral Rado Access (E-UTRA)(Release 0), December 009. [3] J.J.Va de Beek, O.Edfors, M.adell,.K.Wlso, P.O.Borjesso, O chael Estmato OFDM ystems, IEEE 45 th Vehcular Techology Coferece, Chcago, vol., pp.85-89, July 995. [4] M.oh, Y.Lee, ad.park, Low Complexty LMME Chael Estmato for OFDM ystem, IEE Proceedgs. vol.53, o.5, pp , October 006. [5] Xu Y-tao, Wag Cheg-gu, A MME chael Estmator Based o Adaptve Order Determato OFDM ystems, Joural of Electrocs & Iformato Techology, vol.9, o., pp.7-0, Jauary 007. [6] L Guo-sog, Zhou Zheg-ou, A Algorthm to Reduce ME of L Chael Estmato Moble OFDM ystem, Joural of Electrocs & Iformato Techology, vol.7, o.9, pp , eptember 005. [7] 3GPP T 36.04,V0..0. Evolved Uversal Terrestral Rado Access (E-UTRA) (Release 0), December 009. [8] Itel, Itel Itegrated Performace Prmtves Referece Maual, vol., pp , ovember 009. [9] Itel, FIR Flter Algorthm Implemetato Usg Itel E Istructos, March

Module 6. Channel Coding. Version 2 ECE IIT, Kharagpur

Module 6. Channel Coding. Version 2 ECE IIT, Kharagpur Module 6 Chael Codg Lesso 36 Coded Modulato Schemes After readg ths lesso, you wll lear about Trells Code Modulato; Set parttog TCM; Decodg TCM; The modulated waveform a covetoal ucoded carrer modulato