Channel Estimation Modeling

Transcription

1 S Postgraduate Course i Radiocommuicatios Fall 2000 Chael Estimatio Modelig Markku Pukkila Nokia Research Ceter markku.pukkila@okia.com HUT

2 Cotets I. INTRODUCTION...3 II. BACKGROUND FOR CHANNEL ESTIMATION...4 III. LEAST-SQUARES (LS) CHANNEL ESTIMATION...5 A.CHANNEL ESTIMATOR FOR SINGLE SIGNAL...5 B.JOINT CHANNEL ESTIMATOR FOR 2 SIGNALS [5-8]...6 C.SIMULATION OF JOINT CHANNEL ESTIMATION...8 IV. ITERATIVE CHANNEL ESTIMATION [10,11]...10 A.FIRST ITERATION ROUND (CONVENTIONAL)...10 B.FURTHER ITERATIONS...11 C.SIMULATION OF ITERATIVE SYSTEM...12 V. CONCLUSIONS...13 VI. REFERENCES...14 VII. HOMEWORK

3 I. Itroductio The radio chaels i mobile radio systems are usually multipath fadig chaels, which are causig itersymbol iterferece (ISI) i the received sigal. To remove ISI from the sigal, may kid of equalizers ca be used. Detectio algorithms based o trellis search (like MLSE or MAP) offer a good receiver performace, but still ofte ot too much computatio. Therefore, these algorithms are curretly quite popular. However, these detectors require kowledge o the chael impulse respose (CIR), which ca be provided by a separate chael estimator. Usually the chael estimatio is based o the kow sequece of bits, which is uique for a certai trasmitter ad which is repeated i every trasmissio burst. Thus, the chael estimator is able to estimate CIR for each burst separately by exploitig the kow trasmitted bits ad the correspodig received samples. I this report we give first some geeral backgroud iformatio o chael estimatio. The we itroduce Least-squares (LS) chael estimatio techiques. Normal LS chael estimatio for sigle sigal is just from ay textbook, but the chapter of joit chael estimatio for 2 co-chaels simultaeously is based o several our ow publicatios. Some commets o the simulatio of joit chael estimatio system are give, too. The we preset iterative chael estimatio method that is also based o our ow publicatios. The idea is to use the chael decoded symbols as a ew log traiig sequece i the chael estimator ad thereby improve the quality of estimates. Simulatio layout for this iteratio is also show. Fially, coclusios are draw. 3

4 II. Backgroud for chael estimatio Fig.1 shows a geeric simulatio layout for a TDMA based mobile system, which exploits chael estimatio ad sigal detectio operatios i equalisatio. The digital source is usually protected by chael codig ad iterleaved agaist fadig pheomeo, after which the biary sigal is modulated ad trasmitted over multipath fadig chael. Additive oise is added ad the sum sigal is received. Due to the multipath chael there is some itersymbol iterferece (ISI) i the received sigal. Therefore a sigal detector (like MLSE or MAP) eeds to kow chael impulse respose (CIR) characteristics to esure successful equalisatio (removal of ISI). Note that equalizatio without separate chael estimatio (e.g., with liear, decisio-feedback, blid equalizers [2]) is also possible, but ot discussed i this report. After detectio the sigal is deiterleaved ad chael decoded to extract the origial message. Sigal source Chael ecoder Iterleaver Modulator Multipath chael oise Chael decoder Deiterleaver Detector Receiver filter Chael estimator Figure 1. Block diagram for a system utilisig chael estimator ad detectio. I this report we are maily iterested i the chael estimatio part. Usually CIR is estimated based o the kow traiig sequece, which is trasmitted i every trasmissio burst as Fig.2 presets for the curret GSM system. The receiver ca utilise the kow traiig bits ad the correspodig received samples for estimatig CIR typically for each burst separately. There are a few differet approaches of chael estimatio, like Least-squares (LS) or Liear Miimum Mea Squared Error (LMMSE) methods [3,4]. tail data traiig data tail Figure 2. GSM burst structure; chael estimator utilises the kow traiig bits. 4

5 III. Least-squares (LS) chael estimatio A. Chael estimator for sigle sigal Cosider first a commuicatio system, which is oly corrupted by oise as depicted i Fig.3 below. Digital sigal a is trasmitted over a fadig multipath chael h L, after which the sigal has memory of L symbols. Thermal oise is geerated at the receiver ad it is modelled by additive white Gaussia oise, which is sampled at the symbol rate. The demodulatio problem here is to detect the trasmitted bits a from the received sigal y. Besides the received sigal the detector eeds also the chael estimates ĥ, which are provided by a specific chael estimator device. NOISE SIGNAL SOURCE a MULTIPATH CHANNEL h L RECEIVER FILTER y MLSE DETECTOR â y ĥ CHANNEL ESTIMATOR Figure 3. Block diagram of a oise-corrupted system. The received sigal y ca be expressed as follows y = Mh + (1) where the complex chael impulse respose h of the wated sigal is expressed as [ h h L ] T h = (2) 0 1 h L ad deotes the oise samples. Withi each trasmissio burst the trasmitter seds a uique traiig sequece, which is divided ito a referece legth of P ad guard period of L bits, ad deoted by [ m ] T m = L (3) m0 1 m P + L 1 5

6 havig bipolar elemets m { 1, + 1} i. Fially to achieve Eq. (1) the circulat traiig sequece matrix M is formed as ml L m1 m0 ml+ 1 L m2 m1 M = M M M ml+ P 1 L mp mp 1. (4) The LS chael estimates are foud by miimisig the followig squared error quatity 2 hˆ = arg mi y Mh. (5) h Assumig white Gaussia oise the solutio is give by [3] H H ( M M) M y 1 hˆ LS =. (6) where () H ad ( ) 1 deote the Hermitia ad iverse matrices, respectively. The give solutio (6) is also the best liear ubiased estimate (BLUE) for the chael coefficiets [3]. The give solutio is further simplified to hˆ = 1 P M H y (7) provided that the periodic autocorrelatio fuctio (ACF) of the traiig sequece is ideal with the small delays from 1 to L, because the correlatio matrix M H M becomes diagoal. This holds for GSM traiig sequeces, wheever referece legth 16 is chose. The estimates give by the last equatio (7) are simply scaled correlatios betwee the received sigal ad traiig sequece. B. Joit chael estimator for 2 sigals [5-8] Let us cosider ow a commuicatio system i the presece of co-chael iterferece that is show i Fig.4. Two sychroised co-chael sigals have idepedet complex chael impulse h h 0,, h1,, K, hl, resposes [ ] T L, =, =1,2 ad where L is the legth of the chael memory. The sum of the co-chael sigals ad oise is sampled i the receiver. The joit demodulatio problem is to detect the trasmitted bit streams a 1 ad a 2 of the two users from the received sigal y. To assist that joit detectio operatio the joit chael estimator provides chael estimates h ˆ ad hˆ

7 NOISE SOURCE 1 a 1 CHANNEL 1 h L,1 SOURCE 2 a 2 CHANNEL 2 h L,2 RECEIVER FILTER y JOINT MLSE DETECTOR â 1, â 2 y h 1, h 2 JOINT CHANNEL ESTIMATOR Figure 4. Block diagram of co-chael sigal system. The complex chael impulse resposes of the two sychroous co-chael sigals are expressed with a vector h ~ as follows ~ h L,1 h = (8) h L,2 cotaiig the chael taps of the idividual sigals deoted by h L, h h = M h 0, 1, L,, = 1, 2. (9) Hece, h ~ has totally 2 ( L + 1) elemets. Both the trasmitters sed their uique traiig sequeces with a referece legth of P ad guard period of L bits. The sequeces are deoted by m0, m1, m =, = 1, 2. (10) M mp+ L 1, The circulat traiig sequece matrices are deoted by ml, L m1, m0, ml+ 1, L m2, m1, M =, = 1,2. (11) M M M ml+ P 1, L mp, mp 1, ad they are gathered ito oe large matrix ~ M =. (12) [ M M ] 1 2 7

8 With these otatios the received sigal y is agai give by ~ ~ y = Mh +. (13) The LS chael estimates ca be foud simultaeously for the both users by miimisig the squared error quatity, which produces i the presece of AWGN the followig solutio ~ ~ 2 hˆ ~ H ~ 1 ~ H = arg mi y Mh = ( M M) M y. (14) h A approximatio for the sigal-to-oise ratio (SNR) degradatio caused by oisy chael estimatio is derived i [9]. If the chael estimatio errors are ucorrelated ad the traiig sequeces are properly desiged (the correlatio matrix M ~ H M ~ is close to diagoal), SNR is degraded approximately by the followig factor 10 ~ ~ ( 1+ tr{ ( M ) }) H 1 d / db = 10 log M. (15) ce Hece, it is very importat to desig those two traiig sequeces i the joit chael estimatio so that their cross-correlatio is as low as possible to reduce oise ehacemet. For istace, the pairwise properties of the curret GSM traiig sequeces are varyig from excellet to very bad [5]. C. Simulatio of joit chael estimatio Simulatio layouts for joit chael estimatio ad sigle chael estimatio are show i Fig.5 ad 6, respectively. I both cases there is similar co-chael iterferece preset, but oly joit chael estimator takes it ito accout. I the latter case, the iterferece ca be modelled by ay radom biary sigal, which is just modulated ad trasmitted over a multipath chael. But for joit chael estimatio it is required to sed a proper traiig sequece also for the iterferig sigal, hece the burst formattig is very importat for the iterferer also. Shortly, joit chael estimatio requires more accurate modelig for the iterferer, because the receiver exploits some kow iformatio o the iterferece as well. Aother apparet differece betwee those two simulatio cases is the receiver structure. The joit chael estimator provides two sets of chael estimates, whereas the covetioal LS estimator gives oly the estimates for the sigal of iterest. 8

9 Sigal source 1 Chael ecoder Iterleaver Burst formatter 1 Modulator Multipath chael 1 Sigal source 2 Chael ecoder Iterleaver Burst formatter 2 Modulator Multipath chael 2 oise Chael decoder Deiterleaver Joit detector Receiver filter Joit chael estimator Figure 5. Simulatio layout for 2 co-chael sigals ad joit chael estimatio. Sigal source 1 Chael ecoder Iterleaver Burst formatter 1 Modulator Multipath chael 1 Sigal source 2 Modulator Multipath chael 2 oise Chael decoder Deiterleaver Detector Receiver filter Chael estimator Figure 6. Simulatio layout for sigle sigal with iterferece ad LS chael estimatio. 9

10 IV. Iterative chael estimatio [10,11] chael estimator iterleaver symbol decisios updated chael estimate r sigal equaliser deiterleaver chael decoder û Figure 7. Block diagram for iterative chael estimator. This chapter presets a decisio-directed adaptive chael estimatio method, which dimiishes the degradatio due to the chael estimatio ad thereby improves the receiver performace. The idea i short is to feed back the decoded symbols to the chael estimator ad by that meas update the earlier chael estimate assumig that the whole burst is ow kow by the receiver (see Fig.7). A. First iteratio roud (covetioal) Let us assume block fadig chael (costat durig a burst), so the received block is the give as rc r = Ah + w = r rc 1 m 2 A1 ad where A = M, (16) A 2 where h is the chael impulse respose to be estimated. Received sample vectors r c1 ad r c2 are correspodig to coded data blocks c 1 ad c 2, whereas r m correspods to the kow traiig sequece (midamble). Respectively, A 1 ad A 2 cotai trasmitted data bits ad M cotais traiig bits. Covetioal chael estimatio is based o the traiig bits usig the received midamble samples r = Mh + w m The LS chael estimate i the presece of AWGN is give by H H ( M M) M rm h ˆ 1 LS (17) =. (18) After this we ca solve for istace by MLSE detector the coded data c as follows 10

11 c ( r h,c ˆ ) cˆ = arg max p. (19) I order to improve decisio reliability further, the chael decodig operatio is performed. Hece, the iformatio bits u are foud by u ( cˆ u) uˆ = arg max p. (20) B. Further iteratios As the coded data is eeded i the feedback to the chael estimator, re-ecodig performed ad the a exteded traiig sequece matrix ( c = Ξuˆ is A = [A 1 M A 2 ] T (21) is formed usig these coded data bits c ( ad the kow traiig bits i the middle. Now the chael estimator kows the whole burst ad ca re-estimate CIR. If oe-shot LS estimatio were performed usig the whole burst, the ew estimator would be H H ( A A) A r exted 1 hˆ LS =, (22) where matrix A is defied like i Eq. (21). The matrix iversio requires a lot of computatio, which ca be avoided by usig a simple updatig rule, like Least Mea Square (LMS) adaptatio as follows [4] ˆ + hˆ ( A hˆ r) = hˆ H 1 k µ A k k, (23) k+ k where h k 1 is the ew estimate, A k is the data matrix cotaiig the kow symbols (data+traiig), r is the received sample vector ad µ is the step size of the iterative algorithm (typically small value). Also some other adaptatio rules like Recursive Least Squares (RLS) [4] could be cosidered. That could improve the speed of covergece, but o the other had it is computatioally more complex tha LMS. 11

12 C. Simulatio of iterative system Sigal source Chael ecoder Iterleaver Modulator Multipath chael oise BER3 Module 3 Module 2 Module 1 Receiver filter BER2 BER1 data re-ecodig iterleaver chael estimator chael estimates samples sigal equaliser deiterleaver chael decoder ifo bits Figure 8. Simulatio layout for a pipelied structure ad oe iteratio module. It is beeficial to simulate a iterative system i a pipelied structure as depicted i Fig.8. There are several cosecutively placed receiver modules, each of which is describig oe iteratio roud. Hece, the receiver is able to start processig the ext radio block although the previous block is still uder further iteratios. It is also easy to evaluate the receiver performace (BER, BLER etc.) after each module i the simulator, which are correspodig to differet iteratios. LMS adaptatio rule, which is used i this iterative chael estimatio scheme, is quite sesitive for the step size parameter µ. Therefore oe has to be careful, whe selectig this parameter value, as a wrog selectio may rui a log simulatio due to possible divergece problems. It is better to be sure that the selected parameter value is suitable for the whole SNR rage of iterest ad all possible chael profiles. 12

13 V. Coclusios This report presets some approaches, how to model chael estimatio i simulatios. First we show a geeral simulatio layout, which idicates that MLSE or MAP type of detectio algorithms require a separate chael estimator to provide CIR estimate. It is also show that the estimatio is usually based o the kow traiig bits ad correspodig received samples. LS chael estimatio is thoroughly described. First we preset the usual LS chael estimatio for a sigle sigal i the presece of oise. The we elarge the estimatio for 2 cochael sigals simultaeously, which is eeded by a specific joit detectio algorithm. This joit chael estimatio requires a careful desig of traiig sequeces, sice the cross-correlatio properties should also be good for the sequeces. Whe this joit chael estimatio is simulated, oe has to ote that the iterferig sigal eeds a proper modelig as well, because it is exploited i the receiver. Normally, iterferece ca be just modulated radom biary sigal without ay burst formattig. Iterative chael estimatio method is the preseted. The first iteratio is covetioal; e.g., LS chael estimatio based o traiig sequece ca be used. The received sigal is the equalised ad chael decoded. The decoded decisios are the iterleaved back to the chael estimator, which begis the ext iteratio. The chael estimator ca ow use the whole burst (both data ad traiig bits) as kow ad re-estimate CIR. We propose LMS adaptatio rule here to avoid heavy computatios. Iterative systems are ofte useful to simulate by usig cosecutive modules, which are describig differet iteratios. 13

14 VI. Refereces [1] M. C. Jeruchim, P. Balaba, ad K. S. Shamuga, "Simulatio of Commuicatio Systems", Pleum Press, 1992, 731 p. [2] J. G. Proakis, "Digital Commuicatios", 3 rd editio, McGraw-Hill, 1995, 929 p. [3] S. M. Kay, "Fudametals of Statistical Sigal Processig: Estimatio Theory", Pretice-Hall, 1998, 595 p. [4] S. Hayki, "Adaptive Filter Theory", Pretice-Hall, 3 rd Ed., 1996, 989 p. [5] M. Pukkila, "Chael Estimatio of Multiple Co-Chael Sigals i GSM", Master s Thesis, HUT, [6] P. A. Rata, A. Hottie ad Z-C. Hokasalo, "Co-chael Iterferece Cacellig Receiver for TDMA Mobile Systems", Proc. of IEEE It. Cof. o Commu. (ICC), 1995, pp [7] P. A. Rata ad M. Pukkila, "Recet Results of Co-Chael Iterferece Suppressio by Joit Detectio i GSM", 6 th It. Cof. o Advaces i Commuicatios ad Cotrol (COMCON 6), Ju 1997, pp [8] M. Pukkila ad P. A. Rata, "Chael Estimator for Multiple Co-chael Demodulatio i TDMA Mobile Systems", 2 d Europea Mobile Commu. Cof. (EPMCC 97), Bo, [9] B. Steier ad P. Jug, "Optimum ad suboptimum chael estimatio for the uplik CDMA mobile radio systems with joit detectio", Europea Tras. o Telecommuicatios, vol. 5, o. 1, Ja-Feb 1994, pp [10] N. Nefedov ad M. Pukkila, "Iterative Chael Estimatio for GPRS", It. Symp. o Persoal, Idoor ad Mobile Radio Commuicatios (PIMRC), pp , Lodo, Sep, [11] N. Nefedov ad M. Pukkila, "Turbo Equalizatio ad Iterative (Turbo) Estimatio Techiques for Packet Data Trasmissio", 2 d It. Symp. o Turbo Codes, Brest, Frace, 4-7 Sep,

15 VII. Homework Show that for GSM traiig sequece ormal LS chael estimatio ca be simplified to scaled correlatio betwee the kow traiig sequece bits ad received samples. Use the followig variables/parameters: sequece {-1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1} referece legth P = 16 chael memory L = 5 15