RESEARCH Open Access Adaptive ow-rank channe estimation for mutiband OFDM utra-wideband communications Chia-Chang Hu * and Shih-Chang Lee Abstract In this paper, an adaptive channe estimation scheme based on the reduced-rank (RR) ing (WF) technique is proposed for muti-band (MB) orthogona frequency division mutipexing (OFDM) utra-wideband (UWB) communication systems in mutipath fading channes. This RR-WF-based agorithm empoys an adaptive fuzzy-inference-controed (FIC) fiter rank. Additionay, a comparative investigation into various channe estimation schemes is presented as we for MB-OFDM UWB communication systems. As a consequence, the FIC RR-WF channe estimation agorithm is capabe of producing the bit-error-rate (BER) performance simiar to that of the fu-rank WF channe estimator and superior than those of other interpoation-based channe estimation schemes. Keywords: channe estimation, MB-OFDM, utra-wideband (UWB), 1. Introduction Utra-wideband (UWB) wireess systems have generated considerabe interest as an indoor short-distance highdata-rate transmission in wireess communications over the past few years. A number of promising advantages, such as ow power consumption, ow cost, ow compexity, noise-ike signa, resistant to dense mutipath and jamming, and exceent time-domain resoution, have made UWB systems perfecty suitabe for persona computing (PC), consumer eectronics (CE), mobie appications, and home entertainment networks. Appications of UWB radio techniques to short-range wireess communications, such as sensor networks and wireess persona area networks (WPANs), are currenty being expored [1]. Two competing UWB technoogies for physica ayer (PHY) of the WPANs are investigated by the IEEE 80.15.3a standards task group (TG3a) []. One is the direct-sequence (DS) UWB ink scheme and the other is the muti-band (MB) orthogona frequency division mutipexing (OFDM) UWB system. The MB-OFDM UWB communication systems [3] have recenty drawn extensive attention due to potentia for providing high data rate under a ow transmission power. The MB-OFDM deveoped by the WiMedia Aiance [4] is the first UWB radio transmission technoogy * Correspondence: ieecch@ccu.edu.tw Department of Communications Engineering, Nationa Chung Cheng University 168 University Road, Min-Hsiung, Chia-Yi 61, Taiwan to obtain internationa standardization. This promising wireess-connectivity technique increases successfuy both the traffic capacity and the frequency diversity. In MB-OFDM UWB wireess systems, by utiizing severa types of time-frequency codes (TFCs) in the preambe part,mutipeusersareaowedtousethesamefrequency-band group simutaneousy to provide frequency diversity as we as channeization and mutipe-access capabiity among different piconets. That is the primary reason why the preambe symbos gain a high probabiity of being corrupted by mutipe-access interference (MAI). To enhance the system performance, piotassisted channe estimation schemes are commony empoyed for the MB-OFDM UWB systems. In particuar, the performance of channe estimation in a piotaided MB-OFDM UWB system has been investigated based on the east-squares (LS) agorithm [5], the maximum ikeihood estimator (MLE) [6], and the minimum mean-square error (MMSE) estimator [5,7]. The channe estimation with the use of the MLE obviates the necessity of the information of either the channe statistics or the operating signa-to-noise ratio (SNR). However, it is aready known that the computationa costs for these estimators are very expensive and thus ead to a imited usage in practice. This requirement is, in genera, prohibitive for ow-power and cost-effective wireess UWB devices. 011 Hu and Lee; icensee Springer. This is an Open Access artice distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/icenses/by/.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the origina work is propery cited.
Page of 1 In this paper, an adaptive ow-rank channe estimation scheme based on the ing (WF) technique is proposed for MB-OFDM UWB communication systems. This reduced-rank (RR) WF-based agorithm empoys an adaptive -to-1 fuzzy-inference controed (FIC) fiter rank. It can be shown that the fuzzy-inference system (FIS) [8] offers an effective and robust means to monitor instantaneous fuctuations of a dense mutipath channe and thus is abe to assist the RR-WF-based channe estimator in seecting an appropriate time-varying fiter rank p. As a resut, the proposed RR-WF-based channe estimation possesses the potentia to accompish substantia saving on computationa compexity without affecting system bit-error-rate (BER) performance. To emphasize the importance of the use of an adaptive RR- WF scheme, both the MSE and the BER performances are evauated and compared with the piecewise inear [9], the -order [10], the cubic-spine [10], the LS, and the furank WF channe estimation [5] agorithms. Simuation resuts have shown that the proposed FIC RR-WF scheme reduces successfuy computationa compexity without sacrificing the BER performance under different UWB channe conditions. The remainder of this paper is organized as foows. In Section, a brief introduction of the MB-OFDM UWB system architecture and channe mode is presented. The reduced-rank channe estimation scheme is deveoped in Section 3. Principes of the -to- 1 fuzzy-inference-determined fiter-rank seection mechanism are introduced in Section 4. Section 5 anayzes the computationa compexity of the -to-1 FIC fiter-rank seection scheme. Simuation resuts are compared and anayzed in Section 6. Finay, some concuding remarks are drawn in Section 7.. MB-OFDM UWB SYSTEM MODEL In an MB-OFDM UWB system, the spectrum from 3.1 GHz to 10.6 GHz is divided into 14 sub-bands with a bandwidth of 58 MHz each, and the data are transmitted across these sub-bands using a specific TFC [3]. The system operates in one sub-band and then switches to another sub-band after a short time. In each subband, the OFDM moduation scheme is used to transmit data symbos. The transmitted symbos are time-intereaved across the sub-bands to utiize the spectra diversity in order to improve the transmission reiabiity. Additionay, it is important to note that depending on the seected TFC, the MB-OFDM system is equipped with the frequency-hopping (FH) contro mechanism. ThefeatureoftheFHpatterncontroedbytheTFCs enabes mutipe simutaneousy operating piconets (SOPs) at the same band group. However, this is of itte impact on the channe estimation since it is assumed that each sub-band is estimated independenty. The fundamenta transmitter and receiver structure of an MB-OFDM system is iustrated in Figure 1. At the transmitter of an MB-OFDM system, the bits from information sources are first mapped to quadrature phase-shift keying (QPSK) symbos. To expoit time-frequency diversity and combat mutipath fading, the coded bits are intereaved according to some preferred time-frequency patterns, and the resuting bit sequence is mapped into consteation symbos and then converted into the th OFDM bock of N symbos X (, 0), X (, 1),..., X (, N - 1) by the seria-to-parae converter. The N symbos are the frequency components to be transmitted using the N subcarriers of the OFDM moduator and are converted to OFDM symbos x(, 0),x(, 1),..., x(, N - 1) by the unitary inverse fast Fourier transform (IFFT), i.e. x(, n) = IFFT{X(, k)} = 1 N 1 X(, k)e jπkn N N, n =0,1,..., N 1. (1) k=0 A cycic prefix (CP) of ength P (P N) is added to the IFFT output to eiminate the intersymbo interference caused by the mutipath propagation. The resuting N + P symbos are converted into a continuous-time baseband signa x(t) for transmission. The UWB channe mode proposed for the IEEE 80.15.3a standard is considered [11]. The mutipath UWB channe impuse response can be expressed as h(t) =χ J j=1 D α d,j δ(t T j τ d,j ), () d=1 where c represents the ognorma shadowing factor of propagation channes, δ(t) is the Dirac deta function, T j denotes the deay of the jth custer s first path, a d,j is the mutipath gain coefficient and τ d,j is the deay of the dth mutipath component (ray) reative to the jth custer arriva time T j, J is the custer number, and D is the mutipath number in a custer. Based on the Saeh- Vaenzuea (S-V) mode [11-13] and the measurements of actua channe environments, four types of indoor mutipathchannes,nameycm1,cm,cm3,and CM4, are defined by the WiMedia Aiance with different vaues for parameters [4]. In particuar, the IEEE 80.15 standard mode assumes that the channe stays either competey static or changes competey from one data burst to the next. In other words, the time variations (coherence time) of the channe are not considered since most of appications are targeted for high-data-rate communications in sowy fading indoor environments, such as pedestrian speeds or sower [4,13]. With a choice of the CP ength greater than the maximum deay spread of the UWB channe [4], OFDM aows for
4 # 5 Hu and Lee EURASIP Journa on Advances in Signa Processing 011, 011:64 Page 3 of 1 Input Bits x() t cos( π ft) c x(, N P) xn (, P+ 1) xn (, 1) x(,0) xn (, 1) x(,0) x(,1) xn (, ) xn (, 1) X(,0) X(,1) XN (, ) X(, N 1) y(t)! ( ' 3 # $ $ % & (a) y (,0) y (,1) y (, N ) Y (,0) Y (,1) YN (, ) cos( π ft) c yn (, 1) YN (, 1) Output Bits Figure 1 Bock diagrams of (a) the transmitter and (b) the receiver of an MB-OFDM system. (b) 6! % &! each UWB sub-band to be divided into a set of N orthogona narrowband channes. In such conditions, the intersymbo interference (ISI) can be effectivey suppressed, and thus, sufficient mutipath energy is captured to make the impact of the intercarrier interference (ICI) minimized. Therefore, perfect frequency synchronization is assumed, and the ICI is negigibe in what foows. Furthermore, it is important to notice that in thepresenceoficiduetothehighdeayanddopper spread, dedicated ICI mitigation agorithms [14-17] are required to suppress the ICI over fast time-varying fading channes. The UWB channe in the discrete time domain is modeed as a N h -tap finite-impuse-response (FIR) fiter whose impuse response of the th OFDM bock on a sub-band is denoted by h() =[h(,0), h(,1),..., h(, N h 1)], (3) where ( ) denotes the transposition operation. The corresponding channe frequency responses H() =[H(,0), H(,1),..., H(, N 1)]. (4) are given by H() =F Nh h(), where is the first N h coumns of the N-point DFT matrix. For channe estimation, a tota of N p piot signas are uniformy inserted into the transmitted OFDM symbos at known ocations {i n :1 n N p }. Let X p () =diag { X(, i 1 ), X(, i ),..., X(, i Np ) }, (5) denote the N p N p matrix containing the FFT output of the th OFDM bock at the piot subcarriers. At the demoduator, after removing the cycic prefix, the unitary FFT is performed on the remaining N symbos to obtain Y() = X()H() + W(), (6) where X() = diag {X (, 0), X (, 1),..., X (, N - 1)} in (6) stands for the transmitted data symbo, Y() =[Y (, 0), Y (, 1),..., Y (, N -1)] represents the received data symbo, H() as in (4) indicates the channe frequency response, and W() =[W (, 0),W (, 1),..., W (, N -1)] denotes the additive noise component, of the th OFDM bock. 3. Reduced-rank channe estimation The (WF) estimator [5] empoys the second-order statistics of the channe conditions to minimize the MSE. The WF yieds much better performance
Page 4 of 1 than the LS-based estimator, especiay under the ow SNR scenarios. A major drawback of the WF estimator is its high computationa compexity, especiay if matrix inversion operation is required each time as the data in the transmitted vector are atered. The WF estimation of H() [5] can be obtained as Ĥ WF () =R H()H() {R H()H() + σ w[ X () X H () ] 1 } 1ĤLS (), (7) Ĥ RR WF () =U p U H Ĥ LS (), (13) Where Δ p is a diagona matrix containing the vaues δ k = λ k + λ k β, k =0,1,..., p 1, SNR 0, k = p, p +1,..., N 1. where ( ) H means the conjugate transpose operation, σw is the variance of the AWGN, R H() H() denotes the auto-covariance matrix of the channe, given by R H() H () E {H() H H ()}, and the LS estimator of H() [5]is [ ] Ĥ LS () =X 1 ()Y() = Y(,0) X(,0), Y(,1) X(,1),..., Y(,N 1). X(,N 1) The computation of the WF-estimated channe transfer function requires the matrix inversion operation. A simpified WF estimation is obtained by averaging over the transmitted data to avoid the inverse matrix operation [18], and then Eq.(7) can be simpified as ( Ĥ WF () =R H()H() R H()H() + β ) 1ĤLS(), SNR I (8) where SNR = E{ X(, k) } σw, (9) { β = E{ X(, k) 1 } }E. (10) X(, k) Here, b is a constant of the consteation used for the signa mapper, I is an identity matrix, and indicates the absoute vaue. To reduce the computationa compexity, a ow-rank approximation by using singuar vaue decomposition (SVD) [18] is adopted. This scheme reduces the rank of R H()H() up to a threshod eve p. The SVD of R H()H() is performed as foows: R H()H() = UU H, (11) where U is the decomposed unitary matrix from R H() H() containing the singuar vectors and Λ is a diagona matrix containing the singuar vaues 0 1... N-1 on its diagona. Then, substituting (11) into (8) derives Eq.(1) given by ( Ĥ WF () =U + β ) 1 SNR I U H Ĥ LS(). (1) Subsequenty, the rank-reduction technique appied for the WF estimation is given as foows: 4. Fuzzy-inference fiter-rank seection The-to-1fuzzyinferencesystem(FIS)[8],basedon the principe of fuzzy ogic [19], uses the squared error (e ()) and the squared error variation (Δe ()) as the input variabes at OFDM bock to assign the number of the fiter rank p( + 1). That is, p( +1) =FIS(e (), e ()), (15) where e () = 1 N 1 H(, k) Ĥ(, k), (16) N and k=0 e () = e () e ( 1). (17) In essence, the basic configuration of the FIS comprises four essentia procedures, namey (i) fuzzy sets for parameters, (ii) fuzzy contro rues, (iii) fuzzy operators, and (iv) defuzzification processes, which map a twoinput vector, (e (), Δe ()),intoasinge-outputparameter p for the adaptive time-varying fiter-rank seection, as iustrated in Figure. Note that the input variabes of a fuzzy ogic system can be appropriatey determined to incude other types of parameters, such as duration of training, input power, and other usefu variabes [8,0,1], which depend primariy on the appications in reaity. Owing to the fexibiity and richness of the FIS, it is abe to produce many different mappings. The function of each procedure in the FIS is introduced briefy as foows: 1) Fuzzy sets for parameters The input variabes of the FIS are transformed to the respective degrees to which they beong to each of the appropriate fuzzy sets, via membership functions (MBFs).Inwhatfoows,the(e, Δe )-FIS system with the (4, 4)-partitioned regions to the fuzzy I/O domains [8] is empoyed, due to its exceent performance and moderate compexity. The output of the fuzzification process demonstrates a fuzzy degree of membership between 0 and 1.
Page 5 of 1 H, k X Y RR-WF Channe Estimation Hk ˆ (, ) 1 N N 1 k 0 () p () Defuzzification Interface Fuzzy Rue Based Inference Engine Fuzzification Interface e e e ( 1) Deay Fuzzy Inference System (FIS) (a) 1 e 1 e 1 p me ( ) m ( e ) mp ( ) 0 CM1 S = 0.0001 M = 0.001 L = 0.005 VL = 0.01 CM S = 0.0001 M = 0.0005 L = 0.001 VL = 0.01 e CM3 S = 0.0005 M = 0.001 L = 0.01 VL = 0.05 0 CM4 S = 0.001 M = 0.005 L = 0.01 VL = 0.1 CM1 S = 0.00001 M = 0.0001 L = 0.001 VL = 0.01 (b) CM S = 0.00001 M = 0.0005 L = 0.005 VL = 0.01 e 0 CM3 S = 0.00005 M = 0.001 L = 0.005 VL = 0.01 CM4 S = 0.0001 M = 0.001 L = 0.005 VL = 0.01 p S M 4 L 6 VL 8 e p S M L e S M M L S M L L M M L L VL L L (c) Figure The fuzzy-inference-based variabe fiter-rank seection agorithm is iustrated by means of (a) bock diagram, (b) three membership functions, and (c) predicate box, of the -to-1 fuzzy inference system. L VL ) Fuzzy contro rues This procedure is focused on constructing a set of fuzzy IF-THEN rues. Here, we caim that the convergence is just at the beginning in case of a VL e and a VL Δe, and thus a VL vaue for p is used to speed up its convergence rate. On the other hand, the fiter is assumed to operate in the steady-state status when e and Δe show S, andthena S p is adopted to ower its steady-state MSE. In particuar, we may decare that a huge estimation error has occurred when e is S and
Page 6 of 1 Δe indicates VL and the L vaue of parameter p is assigned to system in order to stabiize system performance. 3) Fuzzy operators The fuzzified input variabes are combined using the fuzzy OR operator, which seects the maximum vaue of the two, to obtain a singe vaue. Subsequenty, this is foowed by the impication process, which defines the reshaping task of the consequent (THEN-part) of the fuzzy rue based on the antecedent (IF-part). A min (minimum) operation is generay empoyed to truncate the output fuzzy set for each rue. Since decisions are based on the testing of a of the rues in an FIS, the rues need to be combined in some manner in order to make a decision. Aggregation is the process by which the fuzzy sets that represent the outputs of each rue are combined into a singe fuzzy set. The input of the aggregation process is the ist of truncated output functions returned by the impication process for each rue. The output of the aggregation process is one fuzzy set for each output variabe. 4) Defuzzification processes The defuzzification process converts fuzzy contro decision into non-fuzzy, contro signas. These contro signas are appied to adjust the variabe of p in order to improve convergence/tracking capabiity of the receiver. The crisp, physica contro command is computed by the centroid-defuzzification method. The centroiddefuzzification output p is cacuated by [] ϒ p (i) () m (i) (p (i) ()) i=1 p( +1)=, (18) ϒ m (i) (p (i) ()) i=1 where the scaar ϒ denotes the number of sections used for approximating the area under the aggregated MBFs, p (i) () is the vaue at the ocation used in approximating the area under the aggregated MBF, and m (i) (p (i) ()) Î [0, 1] indicates the MBF vaue at ocation p (i) (). The cacuation of p( + 1) in (18) returns the center of the area under the aggregated MBFs. It shoud be further emphasized that the determination of ϒ is a trade-off between the system performance and the computationa compexity of the FIS system. In order to aeviate the computationa oad in the centroid-defuzzification cacuation of (18), fewer points ϒ are preferred. 5. Computationa compexity anaysis The cacuation of the inverse of ( R H()H() + product of R H()H() ( R H()H() + ) β SNR I and the ) 1 β SNR I of the simpified WF estimator Ĥ WF () in (8) costs N 3 + N compex mutipications if R H()H() and SNR are assumed to be known beforehand or are set to fixed nomina vaues [3]. In what foows, the LS estimate of Ĥ LS () = X 1 ()Y() adopted in a three WF-based estimators requires N mutipications The computationa requirement of the ) 1 product of R H()H() (R H()H() + β SNR I and ĤLS () is N mutipications. Therefore, the computationa compexity of the simpified WF estimation in (8) expressed in terms of the number of compex mutipications is approximatey given by N 3 +N + N for each OFDM bock. For the RR-WF estimator, the rank-p approximation of the WF estimator in (13) can be re-expressed as a sum of rank-1 matrices as foows: ( p ) Ĥ RR WF () = δ k u k u H k Ĥ LS (), (19) k=1 where u k denotes the kth coumn vector in the matrix U. It shoud be noted that the vectors u k for k = 1,,..., p, can be tracked by means of the PASTd agorithm proposed in [4,5] with a substantiay reduced compexity of Np for each OFDM bock. The inear combination of p vectors of ength N in (19) requires Np mutipications. Thus, the RR-WF estimation of Ĥ RR WF () accompishes the tota number of 3Np + N compex mutipications, which is much ess than that of the WF estimator. Remarkaby, the compexity cost of the simpified WF estimator can be further reduced from N 3 +N + N to 3N + N if the PASTd agorithm is appied to simpify Equation (1). Even though the compexity of the simpified WF estimator is st i much higher than that of the rank-p RR-WF estimator due to p N. The FIC RR-WF estimation with the time-varying fiter rank p() incurs a sighter computationa compexity of Np() in the tracking procedure of vectors u k, k =1,,..., p(), than the RR-WF scheme with the predetermined rank p, owing to the fact of p() <p. However, the additiona computationa oad introduced by the (-to- 1)-FIS, in terms of mutipications, is ϒ + N + at each OFDM bock, in which the preparation of e () requires N + 1 mutipications and the centroid-defuzzification output process costs ϒ + 1 mutipications. Furthermore, some specia instructions (with a tota of 4 ookups + 16 compares + 16ϒ MAX operations) are required to perform the FIS, which come primariy from the fuzzification of two input variabes (8 ookups), fuzzy OR operations (16 compares), fuzzy minimum impication (16 ookups), and aggregation of the output (16ϒ MAX operations). Fortunatey, these operations can be done
Page 7 of 1 very efficienty in the atest range of DSPs, which provide singe cyce mutipy and add, tabe ookups and comparison instructions [6,7]. Thus, the FIC RR-WF estimation has the computationa requirement of 3Np() + N + ϒ + compex mutipications for the th OFDM bock. Consequenty, the saving of the FIC RR- WF scheme in compexity over the RR-WF estimator can be achieved when the extra burden incurred by the (-to-1)-fis is ower than the advantage of 3N (p - p()) provided by the FIC-based rank reduction, i.e. ϒ + N + <3N (p - p()). In addition, it shoud be further emphasized the fact that the RR-WF estimation with the use of a time-varying FIC rank possesses exceent channe dynamic tracking and adaptation capabiity over both the fu-rank WF estimator and the RR-WF scheme with a fixed fiter rank. 6. Numerica resuts The channe estimation of MB-OFDM UWB systems can be performed by either adopting preambe training sequence or inserting piot signas into each OFDM symbo. Here, we use a few piots that are inserted into each OFDM symbo to estimate the channe frequency response (CFR) [5] in the interpoation-based channe estimators. In the piecewise inear interpoation agorithm, the estimation of the frequency-domain channe response ocated in between the piots is performed by the inear interpoation, and the estimated piot channe Ĥ p (, i n ) is updated by the LS estimation [9], given by Ĥ p (, i n )=λĥ p ( 1, i n )+(1 λ) Y p(, i n ) X p (, i n ), (0) where is a forgetting factor (0 < <1).Theparameters of computer simuations are mainy based on the Tabe1whichsummarizesthekeyparametersofthe MB-OFDM UWB communication system. This MB- OFDM UWB system uses an OFDM moduation scheme that utiizes 18 subcarriers per band, 1 of which are used to transmit the information. Of the 1 tota subcarriers used, there are 100 used as data carriers, 1 used as piot carriers, and 10 used as guard carriers. In our simuations, UWB channe modes CM1, CM, CM3, and CM4 are adopted. The channe mode CM1 describes a ine-of-sight (LOS) scenario when the distance between the transmitter and the receiver is ess than 4 m, whereas the CM, CM3, and CM4 channe modes represent the non-ine-of-sight (NLOS) mutipath channe environments with various deay dispersions [11]. Additionay, the (e, Δe )-FIS system with the (4, 4)-partitioned regions to the fuzzy I/O domains is empoyed, due to its exceent performance and moderate compexity. Moreover, the MSE and the BER are used as the measures of their error performance reated Tabe 1 The parameters for MB-OFDM UWB systems in PHY Parameter Vaue Moduation QPSK Bandwidth 58 MHz σw 1 ϒ 4 0.5(CM1,CM,CM3), 0.3(CM4) N h 5(CM1,CM,CM3), 15(CM4) N p 1 FFT Size (N) 18 Cycic Prefix (P) 3 Piot Spacing (L = i n+1 - i n, n Î [1, N p ]) 8 N SD : Number of data carriers 100 N SP : Number of piot carriers 1 N SG : Number of guard carriers 10 N ST : Number of tota subcarriers used 1(= N SD +N SP +N SG ) Δ F : Subcarrier frequency spacing 4.15 MHz(= 58 MHz/18) T FFT : IFFT/FFT period 4.4ns(= 1/Δ F ) T CP : Cycic prefix duration 60.61ns(= 3/58 MHz) T GI : Guard interva duration 9.47ns(= 5/58 MHz) T SYM : Symbo interva 31.5ns(= T CP +T FFT +T GI ) to the impementation of the agorithms. The MSE is defined as the mean-squared error difference between the transfer function of transmission channe H(, k) and its estimate Ĥ(, k)[10,8], as shown beow { H(, ε E k) Ĥ(, k) }, k = 0, 1,..., N 1. (1) Remarkaby, the main difference between the MB- OFDM UWB system and the common OFDM system is that the MB-OFDM UWB system uses a time-frequency kerne to specify the center frequency in the frequencyband group for the transmission of each OFDM symbo. When the specific sub-band signa transmission is identified by means of the TFCs, the transmitted symbos have no difference with the common OFDM systems. Hence, the proposed MB-OFDM UWB scheme can aso be appied to perform signa detection in the OFDM systems. In Figure 3, the MSE and the BER performance comparisons between the rank-reduction scheme based on the FIC RR-WF, the RR-WF, the piecewise inear, the -order, the cubicspine, the LS, and the fu-rank WF schemes are evauated in terms of SNR (db) in CM1. The proposed FIC RR-WF agorithm performs the fuzzy controed fiter-rank seection over both rank seection ranges [,8] and [,11]. In both figures, it is observed that the performance of the cubicspine interpoation is better than those of the piecewise inear and the -order and is simiar to
Page 8 of 1 Mean Square Error Mean Square Error FIC RR WF [,8] FIC RR WF [,11] FIC RR WF [,8] FIC RR WF [,11] (a) (a) FIC RR WF [,8] FIC RR WF [,11] FIC RR WF [,8] FIC RR WF [,11] (b) Figure 3 Performance comparisons of (a) the MSE and (b) the BER, between the FIC RR-WF, the RR-WF, the piecewise inear, the -order, the cubic-spine, the LS, and the WF in CM1. (b) Figure 4 Performance comparisons of (a) the MSE and (b) the BER, between the FIC RR-WF, the RR-WF, the piecewise inear, the -order, the cubic-spine, the LS, and the WF in CM. that of the LS. This is reasonabe because the higherorder interpoation scheme makes the given data points more smoothy. In addition, to evauate how far the proposed FIC RR-WF scheme is from the optima performance, we generaize the optima estimator derived in [18],denotedastheWienerfiter.Hence,theperformance of the WF coud serve as the performance reference. As seen in Figure 3, the performance of the RR- WF agorithm with the use of p =8andtheproposed FIC RR-WF scheme is cose to that of the fu-rank WF
Page 9 of 1 Mean Square Error Mean Square Error FIC RR WF [,8] FIC RR WF [,11] FIC RR WF [,8] FIC RR WF [,11] (a) (a) FIC RR WF [,8] FIC RR WF [,11] FIC RR WF [,8] FIC RR WF [,11] (b) Figure 5 Performance comparisons of (a) the MSE and (b) the BER, between the FIC RR-WF, the RR-WF, the piecewise inear, the -order, the cubic-spine, the LS, and the WF in CM3. (b) Figure 6 Performance comparisons of (a) the MSE and (b) the BER, between the FIC RR-WF, the RR-WF, the piecewise inear, the -order, the cubic-spine, the LS, and the WF in CM4. estimator and is much better than those of other existing channe estimation schemes. However, the fu-rank WF estimator is readiy known to have more expensive computationa cost than the RR-WF and the FIC RR- WF channe estimators. Fortunatey, the RR-WF estimation with the use of a time-varying FIC rank is capabe of producing the BER performance simiar to that of the fu-rank WF channe estimator whie accompishing a substantia saving in compexity. In addition, resuts in the figure demonstrate that the FIC RR-WF
Page 10 of 1 with a arger rank seection range [,11] provides better performance than that of the FIC RR-WF with the seection range [,8], especiay at the high SNR region. In Figures 4 and 5, the MSE and the BER performance comparisons between different channe estimation schemes are presented in terms of SNR for UWB channes CM and CM3, respectivey. Resuts in Figures 4 and 5 demonstrate that simiar MSE and BER performances to the CM1 in Figure 3 are achieved. Additionay, due to the stronger deay dispersion nature of both channes CM and CM3, the MSE and the BER performances degrade sighty as compared with that of the channe CM1. The MSE and the BER performances of those different channe estimation schemes with the use of the channe mode CM4 are presented in Figure 6 in terms of SNR. It is observed from both figures that the MSE and the BER performances of a channe estimation schemes degrade dramaticay as the channe mode CM1 is switched to the CM4. This is because the time deay spread under the channe mode CM4 is much more severe than that of the channe mode CM1; therefore, the frequency seectivity between subcarriers 10 4 RR WF (p=4) RR WF (p=6) FIC RR WF 10 4 RR WF (p=4) RR WF (p=6) FIC RR WF 10 4 RR WF (p=4) RR WF (p=6) FIC RR WF 10 4 RR WF (p=4) RR WF (p=6) FIC RR WF Figure 7 The BER performance comparisons between the RR-WF, the fu-rank WF, and the FIC RR-WF in (upper-eft) CM1, (upper-right) CM, (ower-eft) CM3, and (ower-right) CM4.
Page 11 of 1 of the CM4 is more serious than that of the CM1. However, it is seen from Figure 6 that the MSE and the BER performances of the RR-WF scheme with p 8areabe to produce an identica BER performance eve to the fu-rank WF and superior than those of other interpoation-based channe estimation schemes. In Figure 7, the BER performance is compared between the RR-WF, the fu-rank WF, and the FIC RR-WF agorithms in terms of SNR for channe modes CM1, CM, CM3, and CM4, respectivey. Resuts in Figure 7 demonstrate that the BER performance of a three WF-based schemes degrades as the UWB channe deay spreads are more severe. The proposed FIC RR-WF agorithm, which performs the fuzzy-ogic fiter-rank seection over the range of [,8], is abe to take advantages of both sma and arge ranks in convergence and steady-state characteristics. The mean numbers of seected ranks achieved by the FIC RR-WF agorithm in 50 OFDM-frame cacuations are, respectivey, 5.19, 5.8, 5.41, and 5.66 for CM1, CM, CM3, and CM4. The resuts in a figures show that the FIC RR-WF agorithm is abe to accompish a simiar performance as the fu-rank WF approach at a ow rank (i.e. p 8). In other words, the FIC RR-WF agorithm is capabe of achieving a substantia saving in compexity whie maintaining a near fu-rank WF performance. 7. Concusion In this paper, an adaptive FIC RR-WF channe estimation agorithm is proposed for the MB-OFDM UWB communication systems. This RR-WF-based agorithm empoys an adaptive FIC fiter rank in response to the time-invariant mutipath fading channes. As a consequence, the FIC RR-WF channe estimation agorithm is capabe of producing not ony the BER performance simiar to that of the fu-rank WF channe estimator but aso a substantia saving in compexity. Therefore, the proposed FIC RR-WF channe estimator is more feasibe for appications in the MB-OFDM UWB wireess systems. Endnotes Four trianguar MBFs with centroids of the very arge (VL), arge (L), medium (M), and sma (S), respectivey, are seected to cover the entire universe of discourse for variabes e, Δe, and p. Acknowedgements This work was supported by Taiwan Nationa Science Counci under Grant NSC 97-1-E-194-03. Competing interests The authors decare that they have no competing interests. Received: 3 November 010 Accepted: 18 September 011 Pubished: 18 September 011 References 1. H-J Park, M-J Kim, Y-J So, Y-H You, H-K Song, UWB communication system for home entertainment network. IEEE Trans Consum Eectron. 49(), 30 311 (003). doi:10.1109/tce.003.109518. Z Liang, S Zhu, S Wang, Space-time spreading based DS-UWB ink scheme for wireess home entertainment networks. IEEE Trans Consum Eec. 5(3), 857 863 (006). doi:10.1109/tce.006.1706481 3. A Batra, et a, MutiBand OFDM Physica Layer Proposa for IEEE80.15.3a. MutiBand OFDM Aiance SIG (004) 4. A Batra, J Baakrishnan, GR Aieo, JR Foerster, A Dabak, Design of a mutiband OFDM system for reaistic UWB channe environments. IEEE Trans Microw Theory Tech. 5(9), 13 138 (004). doi:10.1109/ TMTT.004.834184 5. JJ van de Beek, O Edfors, M Sande, SK Wison, PO Börjesson, On channe estimation in OFDM systems, in Proceedings of IEEE 45th Veh. Techno. Conf., Chicago, Iinois, USA., 815 819 (1995) 6. M Morei, U Mengai, A comparison of piot aided channe estimation methods for OFDM systems. IEEE Trans Signa Process. 49(1), 3065 3073 (001). doi:10.1109/78.969514 7. R Negi, J Cioffi, Piot tone seection for channe estimation in a mobie OFDM system. IEEE Trans Consum Eectron. 44(3), 11 118 (1998). doi:10.1109/30.71344 8. H-Y Lin, C-C Hu, Y-F Chen, J-H Wen, An adaptive robust LMS empoying fuzzy step size and partia update. IEEE Signa Process Lett. 1(8), 545 548 (005) 9. P-Y Tsai, T-D Chiueh, Frequency-domain interpoation-based channe estimation in piot-aided OFDM systems, in Proceedings of IEEE 59th Veh. Techno. Conf., Mian, Itay. 1, 40 44 (004) 10. SG Kang, YM Ha, EK Joo, A comparative investigation on channe estimation agorithms for OFDM in mobie communications. IEEE Trans Broadcast. 49(), 14 149 (003). doi:10.1109/tbc.003.81063 11. JR Foerster, et a, Channe Modeing Sub-Committee Report Fina. IEEE Piscataway, NJ, P80.15-0/490r1-SG3a, Fina Report (November 003) 1. A Saeh, R Vaenzuea, A statistica mode for indoor mutipath propagation. IEEE J Seect Areas Commun. 5(), 18 137 (1987) 13. AF Moisch, JR Foerster, M Pendergrass, Channe modes for utrawideband persona area networks. IEEE Wireess Commun. 10(6), 14 1 (003). doi:10.1109/mwc.003.165848 14. Y Mostofi, DC Cox, ICI mitigation for piot-aided OFDM mobie systems. IEEE Trans Wireess Commun. 4(), 765 774 (005) 15. H-C Wu, Anaysis and characterization of intercarrier and interbock interferences for wireess mobie OFDM systems. IEEE Trans Broadcast. 5(), 03 10 (006). doi:10.1109/tbc.006.87989 16. H-C Wu, Y Wu, Distributive piot arrangement based on modified m- sequences for OFDM intercarrier interference estimation. IEEE Trans Wireess Commun. 6(5), 1605 1609 (007) 17. X Huang, H-C Wu, Robust and efficient intercarrier interference mitigation for OFDM systems in time-varying fading channes. IEEE Trans Veh Techno. 56(5), 517 58 (007) 18. O Edfors, M Sande, JJ van de Beek, SK Wison, PO Börjesson, OFDM channe estimation by singuar vaue decomposition. IEEE Trans Commun. 46(7), 931 939 (1998). doi:10.1109/6.70131 19. LA Zadeh, Fuzzy sets. Inf Contr. 8, 338 353 (1965). doi:10.1016/s0019-9958 (65)9041-X 0. W-S Gan, Designing a fuzzy step size LMS agorithm. IEEE Proc-Vis Image Signa Process. 144(5), 61 66 (1997). doi:10.1049/ip-vis:19971417 1. L-X Wang, JM Mende, Fuzzy adaptive fiters, with appication to noninear channe equaization. IEEE Trans Fuzzy Syst. 1(5), 161 170 (1993). V Kecman, Learning and Soft Computing: Support Vector Machines, Neura Networks, and Fuzzy Logic Modes (MIT Press, Cambridge, MA, 001) 3. M Noh, Y Lee, H Park, Low compexity LMMSE channe estimation for OFDM. IEE Proc- Commun. 153(5), 645 650 (006). doi:10.1049/ipcom:005006 4. B Yang, Projection approximation subspace tracking. IEEE Trans Signa Process. 43(1), 95 107 (1995). doi:10.1109/78.36590 5. B Yang, An extension of the PASTd agorithm to both rank and subspace tracking. IEEE Signa Process Lett. (9), 179 18 (1995). doi:10.1109/ 97.410547
Page 1 of 1 6. MJ Patyra, JL Grantner, K Koster, Digita fuzzy ogic controer: design and impementation. IEEE Trans Fuzzy Syst. 4(4), 439 459 (1996). doi:10.1109/ 91.544304 7. A Costa, A De Goria, P Faraboschi, A Pagni, G Rizzotto, Hardware soutions for fuzzy contro. Proc IEEE. 83(3), 4 434 (1995). doi:10.1109/5.364488 8. B Yang, KB Letaief, RS Cheng, Z Cao, Channe estimation for OFDM transmission in mutipath fading channes based on parametric channe modeing. IEEE Trans Commun. 49(3), 467 479 (001). doi:10.1109/ 6.911454 doi:10.1186/1687-6180-011-64 Cite this artice as: Hu and Lee: Adaptive ow-rank channe estimation for muti-band OFDM utra-wideband communications. EURASIP Journa on Advances in Signa Processing 011 011:64. Submit your manuscript to a journa and benefit from: 7 Convenient onine submission 7 Rigorous peer review 7 Immediate pubication on acceptance 7 Open access: artices freey avaiabe onine 7 High visibiity within the fied 7 Retaining the copyright to your artice Submit your next manuscript at 7 springeropen.com