Heuristic Channel Estimation Based on Compressive Sensing in LTE Downlink Channel

Transcription

1 Communication and etwork, 013, 5, htt://dx.doi.org/10.436/cn b018 Publihed Online Setember 013 (htt:// Heuritic Channel Etimation Baed on Comreive Sening in LTE Downlink Channel Lin Wan 1, Min Wang 1,, Lifeng Su 1, Jun Wu 1 1 College of Electronic and Information Engineering, Tongji Univerity, Shanghai, China School of Mathematic and Comuter Science, Gannan ormal Univerity, Ganzhou, China @tongji.edu.cn, 011mwangc@tongji.edu.cn,ulifeng@tongji.edu.cn, wujun@tongji.edu.cn Received June, 013 ABSTRACT Pilot-aited channel etimation ha been invetigated to imrove the erformance of OFDM baed LTE ytem. LS and MMSE method do not erform excellently becaue they do not conider the inherent are feature of wirele channel. The are feature of channel imule reone atifie the requirement of uing comreive ening (CS) theory, which ha recently gained much attention in ignal roceing. Reult in the alication of uing comreive ening to etimate fading channel. And it achieve a much better erformance than that with traditional method. In thi aer, we rooe heuritic channel etimation baed on CS in LTE Downlink channel. According to the feature of recovery algorithm in CS, we deign a modified ilot lacement method. CS recovery algorithm for channel etimation don t conider the tatitic character of channel. So we rooed an otimization method which combine the CS and noie reduction. Firt we get initial channel tatitic obtained by LS. Let the channel tatitic a the heuritic information inut of CS recovery algorithm. Then we erform CS recovery algorithm to etimate channel. Simulation reult how thi aroach ignificantly reduce the comlexity of channel etimation and get a better mean quare error (MSE) erformance. Keyword: Channel Etimation; Comreed Sening; Sare Channel; LTE; oie Reduction 1. Introduction OFDM modulation i widely ued in LTE ytem which uffer from time and frequency fading channel. However, the erformance of wirele ytem relie heavily on the validity of OFDM channel etimation. Generally, we can achieve better erformance through two aroache, e.g., ilot deign and channel etimate method. Several ilot-aided channel etimation cheme have been dicued in [1-4], and meaured the erformance in term of bit error rate (BER) and ymbol error rate (SER). Many channel etimation method are rooed to imrove the erformance of wirele communication ytem. LS algorithm [1], a the imlet method, ha very low comlexity, but it i extremely enitive to AWG noie. The MMSE algorithm [] yield much better erformance than LS etimator. It high comlexity hinder the imlementation ractically becaue matrix inverion i needed each time [3]. Although the comlexity of MMSE i reduced by deriving ingular value decomoition technique, it highly deend on the detail channel tatitic [4]. Wirele channel in ractice are tyically are [5], * Thi work i financially uorted by SFC General Program under contract o with very few of channel imule reone i nonzero. Traditional channel etimation method mentioned above don t take the are feature of the channel into account, thi reult in much more detection error. Recently year, CS theory ha gained much attention in mathematic and ignal and communication roceing. CS theory declare that ignal can till be recovered exactly from amle ignal at a rate much le than yquit amling, if the ignal are are [6]. Conidering the are feature of imule reond in wirele fading channel, it i oible that CS can be alied on wirele channel etimation. Zhang et al [7] rooed an otimization of orthogonal matching uruit (OMP) algorithm, according to the channel characteritic, to increae the reciion of the algorithm and reduce the comlexity of the algorithm with the ame number of iteration. But the aroach till need much more comute while it cannot find the ueful value in the index et, more iteration mean more comlexity and calculating delay. ALL of the available method ued to channel etimation baed on CS are enitive to AWG noie [8], eecially at low ignal to noie ratio SR, a well a are recovery algorithm. Inired by thi, we rooed a novel otimization method for OMP, which i that jut need one iteration C

2 94 L. WA ET AL. with the channel characteritic abtracted from LS etimation. From the LS etimation, we can find the ueful value oition and an aroximate channel imule reond, which hel u to avoid iteration to find the oition and error location caued by noie at low SR. Thi aer i organized a follow: Section II review comreive ening theory. In addition, introduce the LTE downlink ytem model and the arely of the multi-ath blocking fading channel. Section III give modified ilot lacement trategy, and rooe heuritic channel etimation algorithm baed on CS. Section IV i the imulation and analyi of rooed channel etimation method. Section V i concluion.. Background In thi ection, we firt review comreive ening theory. Then, we reent the LTE framework model for multi-ath block-fading channel..1. Comreive Sening Comreive ening i a revitalized theory in ignal roceing for are and comreible ignal. Mathematically let ignal x R be a vector of 1. Aum- ing ignal x i k-are under the orthogonal bai. M Let y R be a et of linear meaurement of x by uing a meaurement matrix, which i not related to the are bai. y x A c (1) where i the ignal x rojected on the bai of. A i conidered a the oerator of CS to get obervation of. In order to be able to recover the original ignal from the obervation y, CS mut atify two eential condition. For accurate recontruction, the number of obervation M hould meet K cm log / M, where c i ufficiently mall, i the length of original ignal. A hould atify the retricted iometric roerty (RIP) [9], which i eential to CS recovery erformance. Signal recovery i the center of CS theory reearch, it can be conidered a otimization roblem. Under the arely of k, it can get from (1) by olving 0 - norm minimization roblem min x t.. y A 0 xr () Thi i combination and P hard roblem. Donoho et al [10] rooed that it can be relaced by an otimization 1 -norm roblem min x t.. y A 1 (3) xr In recent year, a collection of are recovery algorithm ha emerged with CS. Method for olving CS re- covery roblem can be roughly divided into two clae, including greedy algorithm and convex otimization algorithm. Orthogonal matching uruit (OMP) algorithm i commonly emloyed to recovery ignal. Tro et al [11] rooed ignal recovery from random meaurement by OMP. Reference [1, 13] rooed ubace uruit (SP) and comreive amling matching uruit (CoSaMP) to recontruct ignal, reectively... Sytem Model In thi aer, we only conider ingle-antenna cae in LTE downlink ytem, becaue it i eay extending from ingle-antenna cae to multi-antenna cae. The ytem model i hown in Figure 1. The comlex baeband rereentation of a multi-ath fading channel imule reone can be decribed by M g() t m( tmt ) (4) m1 where T i the amling interval, m i the delay of ath m, m i a comlex value that characterize the attenuation and initial hae of ath m. T G denoted a the time length of a cyclic extenion, and 0 mt TG. Let X x T k and Y y T k (k = 0,, -1) denote the frequency domain data at the tranmitter and the frequency domain data at the receiver, reectively. Let g g T n, n nn T and (n = 0,, -1), denote the time domain amled channel Imule reone and zero-mean, white, comlex Gauian noie, reectively. Define the DFT matrix a, W W F W W 00 0( 1) ( 1)0 ( 1)( 1) Figure 1. LTE downlink ytem model. C

3 L. WA ET AL. 95 W 1 e nk, j nk/ Furthermore, define F DFT ( g) Fg, the frequency domain channel imule reond. F i the frequency domain noie. T i the time domain noie. Under the aumtion that the interference are comletely eliminated, we can derive Y DFT ( IDFT( X) g) T) (5) XFg F (6) XH F (7) 3. Channel Etimation Baed on Comreive Sening In thi ection, we reent our channel etimation cheme bae on comreive ening. We firt give the modification of OFDM ilot lacement in tandard LTE ytem. Then, we give the derivation the rincile of channel etimation combined with CS, and rooe our otimization algorithm Pilot Placement LTE downlink ytem alie the comb-tye ilot lacement. Single-antenna ytem ilot lacement in one reource block i hown in Figure. The left figure deict the ilot lacement in tandard LTE ytem. We note that the ilot lacement of tandard i uniform ditribute in D lane, which comoed by frequency domain and ub carrier. The channel reone of non ilot ub-carrier are etimated by interolating neighboring ilot in ub channel. Suoe the block fading channel, the channel coefficient at the ame ubcarrier oition within on block are all the ame. So we can comletely etimate the channel coefficient only by one-dimenional interolation. In order to achieve better erformance of channel etimation by uing CS ignal recovery algorithm, we hould modify the oition of the ilot lacement in D lane. There i a imortant factor to conider in ilot lacement modification. That i the modification doe a little change to the LTE ytem. So we mut conidering the LTE ilot lacement and frame tructure. [14] Exre that CS-baed channel etimation cheme can achieve better erformance when ue random ilot lacement. In tandard LTE ilot lacement, every block ha to rovide four indexe to lace ilot in twelve lacement. So there i C4 1 combination. Through 1000 Monte carol imulation of random ilot lacement; we find that the modified ilot lacement, hown in the right figure of Figure, can achieve the bet erformance of channel etimation.. l 0 l 5 l 0 l 5 l 0 l 5 l 0 Figure. Pilot lacement. 3.. Heuritic Channel Etimation Baed on CS l 5 Traditional LS etimator minimize the arameter by where H H Hˆ arg min Y X Hˆ Y X Hˆ (8) LS mean the conjugate tranoe oeration, Y and X denote a received and tranmitted ilot value, reectively. LS etimator get initial etimation from ilot and interolate to all the data oition, we can get all the channel frequency reond. The ilot ignal vector can be exreed a Y X Fg F (9) where i an identity matrix with dimenion S S Becaue the ilot ha been known at the receiver, the imule reone of the channel at the ilot oint i decribed a ˆ Y H (10) X F S Fg (11) g F (1) where F i called ening matrix in the CS theory. Therefore, we can ue the olution of CS method for channel etimation. Once we recovery the channel imule reond from CS algorithm, we can get the CS etimation. Hˆ FFT ( g) (13) c If the channel imule reone i k-are, the recovery algorithm need k iteration at leat. So the CS-baed channel etimation algorithm till ha very high comlexity. Furthermore, the accuracy of etimation maybe much lower at low SR, reult in the decreae of erformance. C

4 96 L. WA ET AL. In thi ubection, we rooed a fat olution baed on the combination of OMP method and channel tatitic. The channel tatitic can be obtained from LS etimation. Firt get initial etimation from ilot and then interolate to all the data oition, we can get all the channel frequency reone. Evaluating the time domain etimation, we collect k of the mot imortant ta, where the imortance mean the valve i large than other. And let k equal the length of a cyclic extenion. We record the oition of the collected ta and ort them in decend by module value. Here we called the collected et a the delay rofile of channel, a ueful index that ued for OMP recovery. Here, the ueful index i denoted by Θ. Known the arely and the delay rofile of channel, it mean that we do not need iterate to find the oible oition. With the Θ, we can increae the reciion and reduce the comlexity of the algorithm to one. Figure 3 deict the comarion of the normalized MSE for tandard ilot lacement and otimized ilot lacement. In thi imulation, we erform LS and CS channel etimation algorithm for two ilot lacement trategy reectively, and SR range form -5 db to 30 db. It how that two ilot trategie have the ame erformance at low SR. But in LS etimation, comaring to tandard ilot lacement, the erformance of otimized ilot lacement i light wore at high SR. The reaon of thi henomenon i that the uniform ditribution average the noie at LS interolating, while the rand ditribution doe not have the ability when the noie i low enough at high SR. Figure 4 how the normalized MSE erformance among LS, MMSE, CS and CS-otimized channel etimation. At low SR range, the CS etimation aroximation effect i ignificantly better than LS, while much wore than MMSE. The reaon i the noie. For the otimized CS etimation, it erformance i much better than CS at low SR, and a well at high SR. The reaon i that the CS itelf can find the right oition a CS-OPT at high SR. However CS need more comlexity and iteration. Algorithm 1 OMP recovery Inut: CS obervation y, meaurement matrix Index I=Θ, reidual r=y, are rereentation Outut: 1: while toing criterion fale do :r = y Ω(:,I)[Ω(:,I)] y; 3:g(I) = [Ω(:,I)] y; 4: end while 5: return are rereentation g. mn R, g R. 4. Simulation and Reult We erformed comuter imulation to verify the erformance of the rooed method alied to the LTE downlink ytem. We imulated a LTE downlink ytem with 0 MHz bandwidth with = 048 ub-carrier. The channel model ue Vehicle model. Table 1 how the rofile of the channel arameter. Table II lit the imulation arameter of LTE ytem. Under the ame exerimental condition, we comare the erformance among LS, MMSE and rooed CS method by uing normalized MSE and bit error ratio (BER), reectively. The normalized MSE i defined a E ihi () Hi ˆ () MSE E i H() i (14) Figure 3. MSE Performance comarion between tandard ilot lacement and otimized ilot lacement. Figure 4. MSE Performance comarion among CS-OPT, CS, LS and MMSE channel etimation. C

5 L. WA ET AL. 97 Figure 5. BER erformance comarion among CS-OPT, CS, LS and MMSE channel etimation. Figure 5 decribe the BER erformance of LS, MMSE, CS and CS-otimized channel etimation. It i een that the BER erformance of CS i much better than LS. It ue the are of the channel and exactly recovery ome of channel imule reond at low SR, and well-done imule at high SR. The erformance of LS i the wort becaue it doe nothing about noie reduction and interolation, which may caue much more error. MMSE become the bet one excet Ideal along with the noie reduction by the channel autocorrelation. The otimized CS etimation. It i een that at low SR CS- OPT i much better than CS method; becaue of at high SR the CS itelf can find the right oition the ame a CS-OPT. 5. Concluion In thi aer, we tudy the channel etimation method baed on comreive ening theory. We firt reent modified ilot lacement trategy to uit CS channel etimation. We rooe an otimization recovery algorithm baed on OMP by uing the channel tatitic. Our imulation reult demontrate that the otimization of the CS-baed channel etimation algorithm ignificantly romote the erformance comared to the traditional etimation and the reduction of comlexity for CS recovery contribute to it imlementation. REFERECES [1] W. G. Jeon, K. H. Paik and Y. S. Cho, An Efficient Channel Etimation Technique for Ofdm Sytem with Tranmitter Diverity, In Peronal, Indoor and Mobile Radio Communication, 000. PIMRC 000, The 11th IEEE International Symoium on, Vol., [] J.-J. van de Beek, O. Edfor, M. Sandell, S. K. Wilon, and P. Ola Borjeon, On Channel Etimation in Ofdm Sytem, In Vehicular Technology Conference, 1995 IEEE 45th, Vol., [3] C. Mehlfuhrer, S. Caban and M. Ru, An Accurate and Low Comlex Channel Etimator for Ofdm Wimax, In Communication, Control and Signal Proceing, 008, ISCCSP 008, 3rd International Symoium on, [4] M.-H. Hieh and C.-H. Wei, Channel Etimation for Ofdm Sytem Baed on Comb-tye Pilot Arrangement in Frequency Selective Fading Channel, Conumer Electronic, IEEE Tranaction on, Vol. 44, o. 1, [5] A. M. Sayeed, Sare Multiath Wirele Channel: Modeling and imlication [6] E. J. Cande, J. Romberg and T. Tao, Robut Uncertainty Princile: Exact Signal Recontruction from Highly Incomlete Frequency Information, Information Theory, IEEE Tranaction on, Vol. 5, o., [7] S. Zhang, J. Kang, Y. C. Song and.. Wang, An Otimization for Channel Etimation Baed on Comreed Channel Eening, In Software Engineering, Artificial Intelligence, etworking and Parallel Ditributed Comuting (SPD), 01 13th ACIS International Conference on, [8] H. Zamiri-Jafarian, M. J. Omidi and S. Pauathy, Imroved Channel Etimation Uing oie Reduction for Ofdm Sytem. In Vehicular Technology Conference, 003.VTC 003-Sring, The 57th IEEE Semiannual, Vol., [9] E. J. Cande and T. Tao, Decoding by Linear Programming. Information Theory, IEEE Tranaction on, Vol. 51, o. 1, [10] D. L. Donoho, Comreed Sening. Information Theory, IEEE Tranaction on, Vol. 5, o. 4, [11] J. A. Tro and A. C. Gilbert, Signal Recovery from Random Meaurement via Orthogonal Matching Puruit, Information Theory, IEEE Tranaction on, Vol. 53, o. 1, [1] W. Dai and O. Milenkovic, Subace Puruit for Comreive Sening Signal Recontruction, Information Theory, IEEE Tranaction on, Vol. 55, o. 5, [13] D. eedell and J. A. Tro. Coam: Iterative Signal Recovery from Incomlete and Inaccurate Samle. Technical Reort, California Intitute of Technology, Paadena, 008. [14] C. H. Qi and L.. Wu, Otimized Pilot Placement for Sare Channel Etimation in Ofdm Sytem, Signal Proceing Letter, IEEE, Vol. 18, o. 1, 011, C