AN FFICINT ITRATIV DFT-BASD CHANNL STIMATION FOR MIMO-OFDM SYSTMS ON MULTIPATH CHANNLS Jan Hafang Graduate Unversty of the Chnese Academy of Scences Insttute of Semconductors, CAS Beng, Chna hf@sem.ac.cn Sh Yn SmartChp Integraton Inc. Suzhou, Chna ysh@sem.ac.cn Abstract n ths paper, an effcent teratve dscrete Fourer transform (DFT) -based channel estmator wth good performance for multple-nput and multple-output orthogonal frequency dvson multplexng (MIMO-OFDM) systems such as I 80.n whch retan some sub-carrers as null sub-carrers (or vrtual carrers) s proposed. In order to elmnate the mean-square error (MS) floor effect exsted n conventonal DFT-based channel estmators, we proposed a low-complexty method to detect the sgnfcant channel mpulse response (CIR) taps, whch nether need any statstcal channel nformaton nor a predetermned threshold value. Analyss and smulaton results show that the proposed method has much better performance than conventonal DFTbased channel estmators and wthout MS floor effect. Keywords-Channel estmaton; MIMO-OFDM; DFT-based; I P80.n D.0 I. INTRODUCTION Orthogonal Frequency Dvson Multplexng (OFDM) has been appled wdely n wreless communcaton systems such as I 80.a and the uropean equvalent HIPRLAN/ due to ts hgh data rate transmsson capablty wth hgh bandwdth effcency and ts robustness to mult-path delay. But wth the development of the nformaton technology, the demand of faster and more relable wreless communcaton systems s gradually ncreased. Multple-nput multple-output (MIMO) systems whch employ multple antennas at both transmtter and recever can mprove the data rate wth hgher bandwdth effcency and better performance by usng spatal multplexng(sm) and space-tme block codng (STBC) schemes. These benefts have made the combnaton of MIMO- OFDM an attractve technque for future hgh data rate systems, such as DAB, DVB, WLAN, and WMAN []. The latest 80.n techncal proposal based on MIMO-OFDM can acheve a maxmum data rate of 600 Mbps [0]. Channel estmaton s a challengng problem n wreless systems due to mult-path propagaton, moblty, and local scatterngs, and so on. In ths paper, we focus on plot-aded channel estmaton technques whch are commonly used n MIMO-WLAN system. Generally speakng, the realzaton of plot-aded channel estmaton s based on ether least squares (LS) approach or lnear mnmum mean square error (LMMS) approaches. The LS estmaton s the smplest channel estmaton based on parallel Gaussan channel model n frequency doman, whch does not use any nformaton about channels, but the performance s not qute acceptable. The LMMS estmaton can acheve better performance by usng channel statstcs such as channel covarance matrx n frequency doman and average sgnal-to-nose rato (SNR), but ths method requres very large amount of computaton, such as matrx nversng. Though there are many attempts to reduce the complexty of the LMMS [][3], these modfed LMMS methods stll requre exact channel covarance matrces. Furthermore, they have qute hgh-computatonal complexty for practcal mplementaton. The dscrete Fourer transform (DFT) -based channel estmator gve us an alternatve, low-complexty choce [4]. In contrast to the frequency doman estmaton, the transform doman estmaton method uses the tme doman propertes of channels. In [5], dfferent channel estmaton technques are analyzed and dscussed, from whch we can see that f the length of the channel mpulse response (CIR) or the number of sgnfcant channel taps are estmated correctly, the DFT-based estmaton can acheve performance very close to the deal CIR. Most of the publshed work on DFT-based channel estmaton assumes the nformaton about the CIR length s known at the recever, however, ths assumpton generally does not hold n practce. The CIR length can be smply assumed to be the length of the cyclc prefx (CP), but ths assumpton wll result n overall performance degradaton [6]. Alternatvely, for more accurate results, some method of obtanng the channel length must be used. Some algorthms are also developed to estmate the number of sgnfcant channel taps [7] [8], however these
algorthms wll ncrease the complexty of the channel estmaton method obvously. In ths paper, we propose a modfed teratve DFT-based channel estmaton algorthm whch can smply obtan the sgnfcant taps and cope wth the mean-square error (MS) floor so as to ncrease the estmaton accuracy n MIMO- OFDM systems. The novelty n our proposed method les n how the sgnfcant channel taps are determned. On the other hand, n practcal system such as I80.a, only 5 out of the total 64 sub-carrers are used, and the other sub-carrers wll be retaned as null sub-carrers (vrtual carrers), whch wll make the conventonal DFT-based estmator not work well[9]. The I80.n system has also the same problem. Our proposed method can nterpolate the frequency response of null sub-carrers by explotng the frequency correlaton of lmted tme excess delay channels to mprove the performance of the DFT-based estmator. Ths paper s organzed as follows. Secton II descrbes the MIMO-OFDM system model used. In secton Ⅲ, the effcent teratve DFT-based channel estmaton method s dscussed n detal. Secton Ⅳ shows the smulaton results and performance of the novel channel estmaton method. Fnally the conclusons are drawn n secton V. II. SYSTM MODL FOR MIMO-OFDM We consder a MIMO-OFDM system wth N tx transmt and N rx receve antennas. The nformaton bts are mapped nto data symbols dependng on the modulaton type and then are demultplexed for dfferent transmtter antennas. And we consder the channel between each transmtter recever lnk s a frequency selectve, Raylegh fadng channel, modeled as a mult-taps channel wth the same statstcs. The typcal channel at tme t s expressed as L- ht (, τ ) = α () tδ( τ - τ ) () l= 0 l l Where L s the number of taps, α l s the lth complex path gan, and τ l s the correspondng path delay. The path gans are Wde-Sense statonary (WSS) complex Gaussan processes. The ndvdual paths can be correlated, and the channel can be sparse. At tme t, the channel frequency response (CFR) of the CIR s gven by, + π fτ H (, t f) h(, t τ ) e d = τ () Compared to sngle antenna I80.a system, more tranng sequences are needed to estmate the MIMO channel, whch s due to the hgher number of channel parameters n the MIMO systems. To ths end, each antenna transmts at least N r OFDM tranng symbols T t,n (t, n =,, N r, ), and these tranng symbols are orthogonal across antennas. The result of the channel estmaton process s a N t N r matrx for each of the 64 tones. The transmt dversty scheme can be acheved by space-tme block code and spatal multplexng. III. PROPOSD CHANNL STIMATION MTHOD If we take the LS estmate H LS as the ntal FD channel estmate. The nth estmated sample of CIR can be expressed wth the LS estmaton, and then we have hls[ n] = IFFTN { H LS[ k]} = hn [ ] + wn [ ] Where h[n] s the deal CIR and w[n] s the nose. For practcal mult-path wreless channels, there are not so many channel paths wth sgnfcant energy compared to the FFT sze N. It s mentoned that n general the CIR length s much smaller than the length of CP, that s, L < N CP. Hence, among N samples (taps) of the CIR estmate, many samples (taps) wll have lttle or no energy at all except nose perturbaton. So we can thnk that all nformaton of channels s contaned n the frst L samples that are the sgnfcant taps whch values relatvely have more energy or magntude than the nose, and other samples are only nose, whch can be gven by hn [ ] + wn [ ],0 n L hdft [ n] w[ n], otherwse (4) Snce the nose s assumed to be AWGN n frequency doman, t s AWGN n transform doman as well. If the sgnfcant values of the transform doman sgnal are retaned, and the non-sgnfcant ones are treated as zero, then the nose term wll be elmnated sgnfcantly. The tradtonal DFT-based channel estmaton explots ths property of OFDM systems whch have the symbol perod much longer than the duraton of the CIR to reduce the nose power that exsts n only outsde of the CIR part. Hence takng the frst L samples only and gnorng nose-only samples, we can obtan a better performance. xpressng these processes n equatons, we obtan DFT h [ ] h [ n],0 n L wndowed n = 0, otherwse (5) Ths nose reducton scheme for OFDM transmssons s also regarded as to wndow the channel estmate n tme-doman (TD) so as to preserve the energy of the sgnfcant channel taps whle reducng the energy of others. The wndowed TD channel estmaton s then brought back to the FD and nverted to form the nose-reduced ntal taps. The nformaton about the CIR length s mportant n achevng hgher performance n DFT-based transform doman approaches. A CIR length taken to be smaller than the actual CIR length wll elmnate the (3)
sgnfcant taps, whle a channel taken to be longer wll result n less nose suppresson. However, the frst case s more crtcal than the second one, and hence n the practcal DFTbased estmaton, the length of CP s usually taken as the CIR length. On the other hand, ths smple method, however, wll generally not work well f the orgnal FD channel estmate can not be determned for all frequences, as s n the case of the I80.a, whch has only 5 out of the total 64 FD ponts defned n a symbol. To smply assgn arbtrary values to the channel estmate at these frequences(e.g. make them 0 ) means to create a sgnfcant TD channel estmate energy spread, whch makes t mpossble to wndow out the TD nose energy wthout dstortng the orgnal channel mpulse response. In [9], an effcent algorthm for sngle antenna I 80.a systems shows how the frequency response of null sub-carrers can be nterpolated by explotng the frequency correlaton of lmted tme excess delay channels. The algorthm s brefly descrbed as follows:. Obtan ntal channel estmate (typcally performed usng the smple LS method).. Convert channel estmate to the tme doman (TD) and wndow sgnfcant taps. 3. Convert ths TD sgnal back to the frequency doman. 4. Replace the values of the known sub-carrers wth the ntal estmate n step (gnore ths step for the last teraton). 5. Repeat steps -4. For ths operaton, some sort of threshold s needed to dfferentate between the sgnfcant values of the sgnal and nose terms. Now we propose a new method to determne the sgnfcant taps, and extend ths teratve estmaton algorthm to MIMO systems. Consder a MIMO-OFDM system wth M transmt, N receve antennas, and K sub-carrers used. Let C m,k be a plot symbol transmtted from antenna m for sub-carrer k. The receved sgnal at receve antenna n can be modeled as: M r = H C + W nk, nmk,, mk, nk, = Where H n,m,k s the frequency response of sub-carrer k between transmt antenna m and receve antenna n, and W n,k represents addtve whte Gaussan nose wth zero mean and varance σ n/ per-dmenson. Hence, the receved symbol at each receve antenna s a lnear combnaton of transmtted symbols that are modfed by channel gans and nose. Obvously, the key dfference between the MIMO and sngle antenna case s the superposton of transmtted symbols at the recever. The key to our method s how to determne the sgnfcant CIR taps. nergy detecton can be used to detect sgnal n addtve Gaussan nose []. Some methods have been proposed to detect energy of CIR n tme doman based on the LS algorthm s result h ls and search the sgnfcant taps of (6) channel []. In these methods, a constant value of threshold s needed to dfferentate between the sgnfcant taps and the others, but t s not practcal n real OFDM system because we must preset dfferent threshold values for dfferent envronment. For example, n [], the taps are searched from N to, where N s the FFT length, and for each h ls ( N), the decson s gven by K = h = 5 N + ls N = + /5 h ls A constant threshold value λ s preset, and when K λ, we ll get the sgnfcant taps: h s ls ( s ). Fg. the CIR nformaton n tme-doman We propose a new Low-Complexty method to dstngush the sgnfcant taps and the others. In the teratve DFT-based estmator, we replace the values of the known sub-carrers of H wndowed wth the ntal LS estmate s values, and covert t nto tme-doman h ls, as llustrated n Fg, and we can use h ls to get the sgnfcant taps. We calculate the max nose power max from the ntal LS estmate and take t as the threshold nstead a constant value, here ( ls ) max = MAX h,( CP < N ) In the th teratve step of our algorthm, s calculated by = h = /3 Here, we take the average value of three taps to get a more accurate result. When max, we get the sgnfcant taps. The proposed algorthm s summarzed as follows: (7) (8) (9)
Step : calculate the ntal FD channel estmate H LS n the usual LS manner. Covert H LS to Tme doman h LS ; hl S = IFFT ( H LS ) Step : max = Max( hls ),( CP < N ) ; Step 3: = CP; Step 4: for the frst teratve, h = h LS, otherwse: h = IFFT{ H wndowed} = h /3 = Step 5: f ( > max ), go to Step 7 ; h wndowed h[ n], 0 n [ n] 0, otherwse Hwndowed = FFT{ hwndowed} HLS[ k], k V H wndowed[ k] Hwndowed[ k], k V Where V ndcate the null sub-carres ; Step 6: = -, go to Step 4; Step 7: the number of sgnfcant taps =, the proposed estmate: Table. Fg.3 shows the CFR nformaton between the antenna pars gotten by dfferent estmate method, and compared wth the perfect channel status nformaton (CSI), when SNR = 5 db. TABL I. Channel parameters RMS delay Channel length, L (taps) 0ns 5 30ns 8 50ns Fg. The I P80.n frame format H = H wndowed ; IV. SIMULATION RSULTS In ths secton, we nvestgate the performance of the proposed channel estmaton algorthm on mult-path channels. The MS and bt-error-rate (BR) performances are examned. A transmt - receve antenna (x) MIMO-OFDM system wth symbols modulated by 6QAM s smulated. We construct the preamble and data feld accordng to the I P80.n D.00 [0]. In ths paper, we only consder the mxed mode, but ths channel estmaton method s also adapted to the HT Greenfeld mode. The system bandwdth s 0MHz, whch s dvded nto 64 tones wth a total symbol perod of 4ηs. An OFDM symbol thus conssts of 80 samples, 6 of whch are ncluded n the CP. The constructed..d. Raylegh fadng channel has L paths determned by root mean squares (RMS) channel delay, and the ampltude of the each path vares ndependently wth an exponental power delay profle []. Unt delay of channel s assumed to be the same as OFDM sample perod. Thus, there s no power loss caused by nonsample spaced. We assume the channel are statc over one OFDM frame, where the HT long tranng feld s OFDM symbol long and data are composed of 00 OFDM symbols as Fg.. A new channel s generated at each smulaton, and the system performance s averaged over CIR realzatons. We smulate the system wth three dfferent channels shown n Fg. 3 the CFR nformaton between the antenna pars (Tx =, Rx = ), SNR = 5 db A 4 transmt - 4 receve antenna (4x4) MIMO-OFDM system wth symbols modulated by 6QAM s also smulated. Fg.4, 5 respectvely confrms the (x) and (4x4) MS performance of the conventonal DFT-based estmaton and shows the performance mprovement of the proposed DFTbased channel estmaton n three common ndoor..d. Raylegh fadng cases: RMS delay = 0, 30, 50 ns. Fnally, the BR performance of the proposed method s examned and compared wth the LS estmate and conventonal DFT-based method. As shown n Fg.6, when we apply the proposed algorthm, the requred SNR s ~db lower than the conventonal DFT-based estmaton wth 50ns RMS delay.
V. CONCLUSIONS Fg.4 MS of x system wth 0, 30, 50ns RMS delay, (taps = 5, 8, respectvely). An effcent teratve DFT-based channel estmaton algorthm for MIMO-OFDM systems s proposed n ths paper. The proposed method can smply detect the sgnfcant channel mpulse response taps, whch don t need any channel statstcal nformaton. The novel method calculates the max nose power max from the ntal LS estmaton result and takes t as the threshold nstead of a constant value preset, so t s adaptve n practcal system. Moreover, the proposed method can nterpolate the frequency response of null subcarrers to mprove the MS performance of channel estmator by explotng the frequency correlaton of lmted tme excess delay channels. We evaluated the performance of the proposed algorthm by computer smulaton wth x and 4x4 MIMO- OFDM system n 5,8,-tap..d. Raylegh fadng channels respectvely. The proposed algorthm can also work well n other types of fadng channels such as Rcan fadng channel. Furthermore, ths technque can be easly extended to systems wth other number of antennas. Smulaton results show that the proposed scheme s very robust aganst varatons of the propagaton envronment and acheves a satsfyng tradeoff between performance and complexty. RFRNCS Fg.5 MS of 4x4 system wth 0, 30, 50ns RMS delay, (taps = 5, 8, respectvely). Fg. 6 BR performance wth 50ns RMS delay (taps = ) [] Mehmet Kemal Ozdemr, Huseyn Arslan. Channel stmaton For Wreless OFDM system, I Communcatons Surveys & Tutorals,Vol9,No., pp.8-48. [] I. Tolochko, M. Faulkner. Real Tme Lmmse Channel stmaton for Wreless OFDM Systems wth Transmtter Dversty Proc. I Vehc. Tech. Conf. Vol. 3, Vancouver, Canada, Sept. 00, pp. 555 559. [3] M. K. Özdemr, H. Arslan,. Arvas. Towards Real Tme Adaptve Low Rank Lmmse Channel stmaton of MIMO OFDM Systems, I Trans. Wreless Commun.,vol.5,no.0,Oct. 006, pp. 675 678. [4] Zhao, Y., and Huang, A., A novel channel estmaton method for OFDM moble communcaton systems based on plot sgnals and transform-doman processng, I Vehcular Technology Conf., 998, vol.46, pp.93-939. [5] O. dfors, M. Sandell, J. J. van de Beek, S. K. Wlson, and P. O. Boresson, Analyss of DFT-based channel estmaton for OFDM, Wreless Personal Commun., vol., no., Jan. 000, pp. 55 70. [6] Peter Hammarberg, Ove dfors, A comparson of DFT and SVD based channel estmaton n MIMO OFDM systems, The 7th Annual I Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons(PIMRC 06), 006. [7] Y. L, L. J. Cmn, and N. R. Sollenberger, Robust channel estmaton for OFDM systems wth rapd dspersve fadng channels, I Trans.Commun., vol. 46, July 998, pp. 90 95. [8] Songpng Wu, Bar-Ness Y, OFDM channel estmaton n the presence of frequency offset and phase nose [J], Proceedngs of I, 003, 5(), pp. 3366-3370. [9] M.Belotserkovsky, An equalzer ntalzaton algorthm for OFDM recevers, Dgest of Techncal Papers Internatonal Conference on Consumer lectroncs, 00, pages 37 373, 00. [0] I P80.n/D.00, February 007. [] Wrtrsal.K,Yong-Ho Km, A new method to measure parameters of frequency selectve rado channel usng power measurements, I Trans. Commun., vol. 49, Oct. 00, pp.788 800. [] Y. Kang, k. Km and H. Park, ffcent DFT-based channel estmaton for OFDM systems on multpath channels, I IT Commun, 007,, (), pp. 97-0.