PAPER Channel Estimation Scheme for a RAKE Receiver with Fractional Sampling in IEEE802.11b WLAN System

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1 946 IEICE TRANS COMMUN, VOLE92 B, NO3 MARCH 2009 PAPER Channel Estimation Scheme for a RAKE Receiver with Fractional Sampling in IEEE80211b WLAN System Yu IMAOKA a),hiroshiobata b),yoheisuzuki c), Student Members, and Yukitoshi SANADA, d), Member SUMMARY The IEEE80211b WLAN standard employs directsequence/spread-spectrum (DS/SS) modulation With a fractional sampling RAKE receiver, it is possible to achieve diversity and reduce the BER in DS/SS communication In order to realize the diversity through fractional sampling, the impulse response of the channel must be estimated In this paper, a channel estimation scheme for a RAKE receiver with fractional sampling in IEEE80211b WLAN system is investigated through a computer simulation and an experiment In order to estimate the impulse response of the channel, a pseudo-inverse matrix with a threshold is employed Numerical results indicate that the channel can be estimated with an optimum threshold in both the simulation and the experiment key words: IEEE80211b, channel estimation, fractional sampling, DS/SS, pseudo-inverse matrix 1 Introduction IEEE80211b WLAN is one of the popular broadband communication standards and is employed all over the world In the IEEE80211b WLAN standard, direct-sequence spreadspectrum (DS/SS) is used as the modulation scheme In DS/SS systems, a RAKE receiver is employed to improve the signal-to-noise ratio (SNR) in a multipath environment and achieves path diversity The effect of tap spacing on the performance of the DS/SS RAKE receiver has been analyzed [1] [5] If the tap spacing is narrower than the chip duration, the performance can be improved In order to decide the tap position of the RAKE receiver, accurate channel estimation is required while it is not taken into consideration in [1] [5] In those literatures, it is assumed that the channel response is known to a receiver There are many papers regarding channel estimation for CDMA systems [6] [8] However, most of them are not applicable to a RAKE receiver with fractional sampling In this paper, a channel estimation scheme for the RAKE receiver with fractional sampling in IEEE80211b WLAN system is investigated In the conventional scheme, the impulse response of a multipath channel is estimated with a pseudo-inverse of an auto-correlation matrix of a received signal waveform [9] However, this scheme is not ro- Manuscript received December 25, 2007 Manuscript revised October 6, 2008 The authors are with the Dept of Electronics and Electrical Engineering, Keio University, Yokohama-shi, Japan The author is with Sony Computer Science Laboratories, Inc, Tokyo, Japan a) yu imaoka@sndeleckeioacjp b) hiroshi@sndeleckeioacjp c) suzuki@sndeleckeioacjp d) sanada@eleckeioacjp DOI: /transcomE92B946 bust to thermal noise Therefore, the pseudo-inverse matrix with a threshold is proposed [3] The threshold is introduced to suppress the influence of the noise The proposed scheme is evaluated through computer simulation and measurement in this paper This paper is organized as follows In Sect 2, the conventional and proposed schemes are explained Section 3 shows numerical results through computer simulation Section 4 shows the measurement results Section 5 gives our conclusions 2 Channel Estimation Schemes 21 Estimation with an Inverse Matrix Here, the chip shape is assumed to be rectangular At the beginning of the packet, N S y synchronization symbols are transmitted The synchronization symbol, s(t), is represented as, s(t) = d s (t)c(t) (1) where d s (t) is the transmitted symbol and c(t) is the spreading sequence, and d s (t) = c(t) = N S y 1 n=0 m= d(n)p(t nt s ), (2) c b (m mod M)q(t mt c ) (3) where p(t) is the signal waveform, and q(t)isthechipwaveform c b (m) isthemth spreading sequence, d(n) isthenth symbol for synchronization, T s is the symbol duration, T c is the chip duration, and M is the length of the spreading sequence Therefore, MT c = T s The influence of the multipath can be modeled by a transversal filter as shown in Fig 1 {h 0, h 1,, h L 1 } are the impulse responses of the channel and L is the number of paths The received signal is given as r(t) = h l s(t lt d ) + n(t) (4) l=0 where h l is the response of the lth path, n(t) isthethermal noise, and T d is the interval of the samples For fractional sampling, N times oversampling is assumed, and NT d = T c If the received signal is sampled with the interval of T d,the Copyright c 2009 The Institute of Electronics, Information and Communication Engineers

2 IMAOKA et al: CHANNEL ESTIMATION SCHEME FOR A RAKE RECEIVER 947 Fig 1 Transversal filter kth sample of the received signal, r s (k), is expressed as r s (k) = h l s((k l)t d ) + n s (k) l=0 = s T h + n s (k) (5) where n s (k)isthekth noise sample h and s are given as h = [h 0, h 1,, h L 1 ] T, (6) s(k) = [s(kt d ), s((k 1)T d ),, s((k (L 1))T d )] T (7) The received signal is input into a matched filter The output of the matched filter is x(k) = c s (m)r s (m k) (8) The auto-correlation function of the spreading sequence is given as u s (k) = c s (m)c s (m k) (9) where c s (m)isthemth coefficient of the matched filter M s = MN represents the number of the samples for one spreading sequence c s (m) is given by sampling c(t) with the interval of T d An example of auto-correlation of the waveform is shown in Fig 2 From Eq (5), the output of the matched filter is derived as x(k) = = = c s (m)r s (m k) { L 1 c s (m) { Ms 1 l=0 + l=0 Assuming that d s (t) = 1 in Eq (1), } h l s((m k l)t d ) + n s (m k) } c s (m)s((m k l)t d ) h l (10) c s (m)n s (m k) (11) Fig 2 Auto-correlation of the spreading sequence s((m k l)t d ) = c s (m k l) (12) Therefore, { Ms 1 } x(k) = c s (m)c s (m k l) h l where n c (k) = l=0 + c s (m)n s (m k) = u s (k l)h l + l=0 = u T s (k)h + n c (k) c s (m)n s (m k) c s (m)n s (m k) (13) The outputs of the matched filter are averaged over N S y symbols to reduce the influence of the noise x(k) = N S y 1 n=0 x(k + nm S ) (14) As shown in Fig 2, the output of the matched filter is determined by the auto-correlation function, u s (k), of the spreading sequence, c s (k), and the impulse response, h l Suppose u s (k) is the matrix whose elements are given by the autocorrelation function, u s (k) u s (k) = [u s (k), u s (k 1),, u s (k (L 1))] T (15) The auto-correlation matrix of the spreading sequence is U s = [u s (0), u s (1) u s (L 1)] T u s (0) u s ( (L 1)) u s (1) u s ( (L 2)) = (16) u s (L 1) u s (0)

3 948 IEICE TRANS COMMUN, VOLE92 B, NO3 MARCH 2009 Here, the noise is neglected for simplicity The output of the matched filter is x(0) x(1) Hence, where x(l 1) u s (0) u s ( (L 1)) u s (1) u s ( (L 2)) = u s (L 1) u s (0) h 0 h 1 h L 1 (17) X = U s h, (18) X = [x(0), x(1),, x(l 1)] T (19) Therefore, the impulse response, h, can be estimated with the output of the matched filter, X, and the inverse matrix of the auto-correlation matrix, U s, as follows h = U 1 s X (20) 22 Pseudo-Inverse with a Threshold If the baseband filter is used for pulse shaping, the chip waveform is no longer the rectangular shape and the waveform of the spreading sequence becomes smooth The impulse response of the channel is estimated by using this filtered spreading sequence The impulse response of the channel is estimated as h = U 1 s X (21), is used, the response of the channels, h, cannot be estimated In order to improve the accuracy, the channel estimation with a pseudo-inverse matrix, U s +, instead of the inverse matrix, U, is employed [9] Singular value decomposition is applied to U s, from Eqs (16) (19) where X is the output of the matched filter and U s is the auto-correlation matrix of the filtered spreading sequence However, h cannot be estimated precisely with the filtered spreading sequence due to the waveform of the spreading sequence When the differences between the samples in c s (k) are small, the columns of U s are not independent and the rank of the matrix reduces Hence, the inverse matrix of U s cannot be derived precisely Therefore, if the matrix, U 1 s where q is the rank of U s Singular value decomposition is then applied to the pseudo-inverse matrix, U s +, U s+ = W + Σ + V +T (24) and the singular values of U s + are [1/σ 1,, 1/σ q ] Hence, ( ) 1 Σ = diag,,,, 0,, 0 (25) σ 1 σ 2 σ q From Eqs (23) and (25), when the singular value, σ q, in U s is small, small difference in σ q makes large fluctuation to its reciprocal 1/σ q Hence, the pseudo-inverse matrix, U s +, cannot be derived precisely In the proposed scheme, a threshold is set for deriving the pseudo-inverse matrix If the singular value is smaller than the threshold, the singular value is set to 0 3 Numerical Results with Computer Simulation 31 Channel Model The computer simulation is conducted to investigate the relation between the threshold of the singular value and the mean square errors (MSE) of the estimated impulse response In this paper, an exponential channel model is assumed [10] As shown in Fig 3, the path delay profile for this model has the form: P[τ] = 1/τ d exp( τ/τ d ), (26) where the parameter τ d completely characterizes the path delay profile For the exponential model, the maximum excess delay is given as A τ d τ m = 10 log 10 (e), where A is the amplitude of the smallest noticeable amplitude given in db relative to the amplitude of the 0th delay (line-of-sight) path In this paper, τ m and A are set based on the JTC model [11], [12] Table 1 shows τ d and A for the U s = WΣV T (22) where W and V are the matrices that have orthogonal columns and the singular values of U s are [σ 1,,σ q ] Hence, Σ=diag(σ 1,σ 2,,σ q, 0,, 0) (23) Fig 3 Path delay profile for an exponential channel model

4 IMAOKA et al: CHANNEL ESTIMATION SCHEME FOR A RAKE RECEIVER 949 Table 1 Indoor residential JTC channel model Channel A Channel B τ d [ns] A [db] Table 2 Simulation conditions Number of Trials times Modulation Scheme BPSK Preamble Length 128 bits Sampling Speed T c /4 Spreading Sequence Barker code Sequence Length 11 Fig 5 Waveform of the spreading sequence Fig 4 Measurement environment of the spreading sequence indoor residential channel model 32 Simulation Conditions The simulation conditions are shown in Table 2 BPSK is employed as the modulation scheme Barker code with the length of 11 is used for spreading The received signal is sampledineveryt c /4 E b /N 0 is set from 0 db to 20 db The MSE is calculated with 128 preamble bits The spreading sequence is obtained through the measurement of the signal from the actual WLAN terminal (corega KK, CG- WLCB54GTU2) Figure 4 shows the measurement environment Both a transmitting antenna and a receiving antenna are covered with radiowave absorbers to detect only the direct path The received signal is downconverted to the baseband signal in the down converter and then digitized by the oscilloscope The sampling frequency in the oscilloscope is 8 [GHz] The samples are decimated to be the sampling speed of 44 [MHz] The signal waveform of the spreading sequence is shown in Fig 5 33 Numerical Results through Simulation Figures 6 and 7 show numerical results of the proposed scheme They show the relation between the threshold of the singular value and the MSE From Figs 6, 7, it can be found that when the threshold is smaller, the MSE increases Fig 6 Threshold vs MSE, Indoor residential JTC channel model A, Threshold= This is because if the threshold is smaller, small singular values are included in Eq (23) In Fig 6, as the number of the paths are small, the fluctuation on those singular values deteriorates the estimation accuracy In Fig 7, as the number of the paths are large, the small singular values represent the weak paths Therefore, smaller threshold leads to the trade off between the errors on the estimation of the path strength and on the number of the paths When the threshold is larger than the certain value, the MSE also increases This is because as the threshold becomes larger, the number of singular values decreases in Eq (23) and the pseudo-inverse in Eq (25) becomes inaccurate Moreover, the discrete values of the MSE can be observed in both Figs 6 and 7, especially when the threshold is around 10 This is because the singular values in Eq (25) smaller than the threshold is set to 0 as mentioned in Sect 22 and the MSE also changes discretely

5 950 IEICE TRANS COMMUN, VOLE92 B, NO3 MARCH 2009 Fig 7 Threshold vs MSE, Indoor residential JTC channel model B, Threshold= Numerical Results through Experiment 41 Experiment Setup 411 Reference Impulse Response Measurement with a Vector Network Analyzer The measurement is conducted to investigate the impulse response of the channel in a room whose size is 52[m] 67[m] 34 [m] The measurement environment and the floor plan of the measurement room is shown in Figs 8(a) and (b) The wall is made of concrete and the door, the shelf, the desk, and the locker are made of steal The impulse response of the channel is measured in both line-of-sight (LOS) and non-los (NLOS) situations In order to realize the NLOS condition, the Rx antenna is placed at the outside of the room Tx antenna is put on the shelf which is 22 [m] high from the ground Rx antenna is put on the ground in both situations Figure 9 shows the experiment system with a vector network analyzer (VNA) and the equipments used for the measurement are shown in Table 3 Table 4 shows the measurement conditions of the VNA The impulse response of the channel is obtained with the measured S 21 parameters The chip rate of the spreading sequence of the IEEE80211b receiver is 11 [Mcps] When the RAKE receiver with fractional sampling is employed, the sampling frequency is 44 [MHz] Therefore, the resolution of the delay is 0189 [ns] which is equal to the inverse of 44 [MHz] 412 Impulse Response Estimation with an IEEE80211b WLAN Card Figure 10 shows the experiment setup with a WLAN card Table 5 shows the measurement equipments and their specifications The WLAN card is set as an access point and Fig 9 Fig 8 Measurement room Experiment system with a VNA beacon signal is used as a transmitted signal which is continuously generated The beacon interval is set to be 1 [ms] [13] [15] The transmitted signal is received at the receiving antenna and downconverted to the baseband signal The baseband signal is digitized by the A/D boards at the rate

6 IMAOKA et al: CHANNEL ESTIMATION SCHEME FOR A RAKE RECEIVER 951 Table 3 Measurement equipments Equipment Version Vector Network Analyzer (VNA) Agilent 8753ET USB/GPIB Interface Converter Agilent 82357A VNA Software Agilent technology Intuilink (version 13) Tx Antenna Monopole antenna Rx Antenna Collinear array antenna Table 4 Measurement conditions Frequency range from 22 [GHz] to 264 [GHz] Measurement points 801 Sweep time 03[s] Measurement step 055 [MHz] Fig 11 Normalized impulse response (LOS) Fig 10 Experiment system with a WLAN card Equipment WLAN card Table 5 Receiving antenna Down converter A/D boards Measurement equipments Manufacturer Version Spec corega KK CG-WLCB54GTU2 IEEE80211b, IEEE80211g I-O DATA DEVICE, INC WNO-AG/NDP For WLAN in 52,24 [GHz] Monopole antenna Koden Electronics Co, Ltd A Center frequency:2437 [GHz] Bandwidth:40 [MHz] NF:15 [db] (Loading four boards ( MAX2829 ) made in Maxim Integrated Products, Inc) MISH International Co, Ltd PDA1000 Maximum sampling rate:1 [GHz] 8bit 1CH of 1 [GHz] Those samples are then moved into the personal computer The detection period of the received signal is 1/4 [s] The samples are decimated to achieve the sampling speed of 44 [MHz] Finally, the impulse response of the channel is estimated by the proposed scheme Fig Measurement Results Normalized impulse response (NLOS) 421 Measurement with the VNA The impulse responses in the LOS situation and the NLOS situation are shown in Figs 11 and 12 Figure 11 shows that the direct path is strong in the case of the LOS condition, and Fig 12 shows that multiple weak paths can be found in the case of the NLOS condition The path is considered to exist if the normalized impulse response is larger than 01 These responses are used as the reference in order to calculate the MSE performances of the proposed scheme Here, a window is employed to derive the MSE correctly because the number of multipath is unknown

7 952 IEICE TRANS COMMUN, VOLE92 B, NO3 MARCH 2009 Fig 13 Threshold vs MSE (LOS), Threshold=02 60 Fig 14 Threshold vs MSE (NLOS), Threshold=02 60 to the receiver In this measurement, the window size for MSE calculation is set 3 [T c /4] in Fig 11 and 5 [T c /4] in Fig 12 This is because the major paths exist within the delay of 3 [T c /4] in case of LOS and 5 [T c /4] in case of NLOS The window is not employed in the simulation because the number of multipath is fixed 422 Estimation with the IEEE80211b WLAN Card The measurement with the IEEE80211b WLAN card is compared with that of the VNA The relation between the threshold of the singular value and the MSE are shown in Figs 13 and 14 Both impulse responses with VNA and WLAN card are normalized before deriving the MSE Numerical results through simulation based on the impulse response of the channel measured through the experiment are shown as well as the measurement results Figure 13 shows that the minimum MSE is gained when the threshold is in the range of about 06 to10inthe case of the LOS condition On the other hand, in the case of the NLOS condition, the minimum MSE can be found when the threshold is in the range of about 06 to30asshownin Fig 14 Next, the minimum value of the MSE in the case of the LOS condition is compared with that of the NLOS condition especially in the case of measurement Figures 13 and 14 show that the minimum MSE for the LOS situation is about 0013 and for the NLOS situation is about 0158 Therefore, the accuracy of channel estimation in the case of the LOS condition is better than that in the case of the NLOS condition This is because strong paths can be observed in the LOS situation while multiple weaker paths can be observed in the NLOS situation Moreover, the MSEs with the conventional scheme are also calculated, which are about 0087 for the LOS situation and about 0382 for the NLOS situation These results indicate that the proposed scheme with the appropriate threshold is more accurate than the conventional scheme 5 Conclusions In this paper, a channel estimation scheme for the IEEE80211b WLAN system is investigated through the computer simulation and the measurement In the conventional scheme, the impulse response of the multipath channel is estimated with a pseudo-inverse matrix However, this sheme is not robust to noise Therefore, the pseudo-inverse matrix with the threshold has been proposed According to the numerical results through the computer simulation and the experiment, it has been shown that the channel can be estimated with the optimum threshold References [1] KJ Kim, SY Kwon, EK Hong, and KC Whang, Effect of tap spacing on the performance of direct-sequence spread-spectrum RAKE receiver, IEEE Trans Commun, vol48, no6, pp , June 2000 [2] T Baykas and A Yongacoglu, Effects of tap spacings to discretetime RAKE receivers in exponentially decaying delay profiles, Proc 2nd IEEE Information and Communication Technologies Conf, vol2, pp , April 2006 [3] Y Suzuki, AM Bostaman, M Inamori, and Y Sanada, Directsequence/spread-spectrum communication system with sampling rate selection diversity, IEICE Trans Commun, vole91-b, no1, pp , Jan 2008 [4] GE Bottomley, T Ottosson, and Y-PE Wang, A generalized RAKE receiver for interference suppression, IEEE J Sel Areas Commun, vol18, no8, pp , Aug 2000 [5] C Cozzo, GE Bottomley, and AS Khayrallah, Rake receiver finger placement for realistic channels, Proc 5th IEEE Wireless Communications and Networking Conf, vol1, pp , March 2004 [6] G Yue, X Zhou, and X Wang, Performance copmarisons of channel estimation techniques in multipath fading CDMA, IEEE Trans Wireless Commun, vol3, no3, pp , May 2004 [7] XG Doukopoulos and GV Moustakides, Adaptive power techniques for blind channel estimation in CDMA systems, IEEE Trans Signal Process, vol53, no3, pp , March 2005 [8] A Burnic, A Vieβmann, T Scholand, C Spiegel, AH Alinejad, A Seebens, GH Bruck, and P Jung, Synchronization and channel estimation in wireless CDMA systems, Proc 9th IEEE International Symposium on Spread Spectrum Techniques and Applica-

8 IMAOKA et al: CHANNEL ESTIMATION SCHEME FOR A RAKE RECEIVER 953 tions, pp , Aug 2006 [9] Z Quan, S Han, C Ahn, and W Kwon, Pseudo-inverse based estimation algorithms for singular region, Proc 5th IEEE Asian Control Conf, vol2, pp , July 2004 [10] N Chayat, Tentative criteria for comparison of modulation methods, IEEE P /96, Sept 1997 [11] Joint Technical Committee of Committee T1 R1p14 and TIA R4633/TR 4544 on Wireless Access, Draft Final Report on RF Channel Characterization, Paper nojtc(air)/ r4, Jan 1994 [12] MG Laflin, Draft final technical report on RF channel characterization and system deployment modeling, Joint Technical Committee, JTC(AIR)/ R4, 1994 [13] IEEE Std 80211b-1999 [14] IEEE Std [15] IEEE Std 80211g-2003 (Amendment to IEEE Std 80211, 1999 Edn (Reaff 2003) as amended by IEEE Stds 80211a-1999, 80211b- 1999, 80211b-1999/Cor , and 80211d-2001) Yukitoshi Sanada was born in Tokyo in 1969 He received his BE degree in electrical engineering from Keio University, Yokohama Japan, his MASc degree in electrical engineering from the University of Victoria, BC, Canada, and his PhD degree in electrical engineering from Keio University, Yokohama Japan, in 1992, 1995, and 1997, respectively In 1997 he joined the Faculty of Engineering, Tokyo Institute of Technology as a Research Associate In 2000 he jointed Advanced Telecommunication Laboratory, Sony Computer Science Laboratories, Inc, as an associate researcher In 2001 he jointed Faculty of Science and Engineering, Keio University, where he is now an associate professor He received the Young Engineer Award from IEICE Japan in 1997 His current research interest is in software defined radio and ultra wideband systems Yu Imaoka was born in Tokyo, Japan in 1983 He received his BE degree in electronics engineering from Keio University, Japan in 2007 Since April 2007, he has been a graduate student in School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University His research interests are mainly concentrated on software defined radio Hiroshi Obata was born in Kobe, Japan in 1982 He received his BE degree in electronics engineering from Keio University, Japan in 2007 Since April 2007, he has been a graduate student in Graduate School of Information Science and Technology, The University of Tokyo Yohei Suzuki was born in Tokyo, Japan in 1983 He received his BE degree in electronics engineering from Keio University, Japan in 2006 Since April 2006, he has been a graduate student in School of Integrated Design Engineering, Graduate School of Science and Technology, Keio University His research interests are mainly concentrated on software defined radio