1 Introduction

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1 Published in IET Communications Received on 12th June 2009 Revised on 19th March 2010 ISSN Effect of baseband filter bandwidth in fractional sampling orthogonal frequency division multiplexing on indoor channel model with measured impulse responses T. Shinkai H. Nishimura M. Inamori Y. Sanada Department of Electronics and Electrical Engineering, Keio University, Hiyoshi, Kohoku, Yokohama, Kanagawa , Japan Abstract: In the IEEE a WLAN standard, orthogonal frequency division multiplexing (OFDM) modulation is employed. Diversity techniques are effective way to overcome multipath fading in the OFDM systems. A fractional sampling (FS) scheme is one of the diversity techniques with a single antenna. Through FS it is possible to separate multipath components and obtain diversity gain in OFDM. Though FS has been analysed numerically, the experiment of FS on actual indoor channels with real filter characteristics has not been carried out. In addition, though it has been suggested that in FS diversity a sharp filter limits the diversity gain, this limitation has not been confirmed especially with measurements. Therefore we investigate the effect of filter bandwidth in FS through simulation and an experiment. Numerical results through the simulation and the experiment indicate that the FS can achieve path diversity and improves the performance by about 2 db if the bandwidth of the baseband filter is larger than the minimal bandwidth. 1 Introduction IEEE a WLAN is one of the popular broadband communication standards and is employed all over the world. In the IEEE a/g WLAN standard, orthogonal frequency division multiplexing (OFDM) is used as a modulation scheme. OFDM has been prevailing technology such as terrestrial digital broadcasting, wireless broadband communications, or wireless local area networks [1, 2]. OFDM achieves high spectrum efficiency and is robust to a multipath channel with the use of subcarriers. Moreover, diversity techniques can improve the performance of the OFDM system on the multipath channel. One of the typical diversity techniques is antenna diversity. Multiple antenna elements must be located separately in order to reduce the correlation among the received signals [3]. However, it is difficult for small terminals to implement multiple antenna elements. Consequently, the fractional sampling (FS) scheme that obtains diversity gain with a single antenna has been proposed [4]. FS converts a single-input single-output (SISO) channel into a single-input multiple-output (SIMO) channel. It has been applied for blind channel estimation/equalisation [5 9]. Following the first proposal of FS diversity in [4], it has then been investigated as a path diversity scheme in terms of an appropriate sampling rate, adequate filter design, or combination with coding [10, 11]. However, the investigation of the FS on actual indoor channels has not been carried out. In addition, though it is suggested in [4] as a sharp filter limits the diversity gain through the FS, this limitation has not been confirmed especially on the actual indoor channels with real filters. The filter used in [4] is assumed to have the impulse response of a short sinc pulse that may not be widely used. Therefore we investigate the effect of filter bandwidth in 1934 IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

2 FS through simulation and an experiment. The computer simulation is conducted with indoor channel models with measured impulse responses and root raised cosine filters that are commonly employed. The simulation results and the experiment results have proven that the FS can achieve path diversity if the bandwidth of the baseband filter is wider than the minimal bandwidth. This paper is organised as follows. In Section 2, we describe a system model. Section 3 explains an experiment system. Section 4 presents numerical results. We conclude the paper in Section 5. 2 System model 2.1 OFDM with FS Suppose the information symbol on the kth subcarrier is s[k] (k ¼ 0,..., N 2 1), the OFDM symbol is given as u[n] = 1 N 1 ( s[k] exp j 2pnk ) N N k=0 where n(n ¼ 0,1,..., N 2 1) is the time index and N is the inverse discrete Fourier transform (IDFT) length. The transmitted signal in baseband form is given by x(t) = N 1 n=0 u[n]p tx(t nt s ), where p tx (t) is the impulse response of the transmission filter and T s is the symbol duration. This signal is up-converted and transmitted through a multipath channel with an impulse response, c(t). The received signal after the down-conversion is given as y(t) = N 1 n=0 (1) ( u[n]h(t nt s ) exp j 2pbt ) + O + v(t) (2) T s where h(t) is the impulse response of the composite channel and is given by h(t) := p tx (t) w c(t) w p rx (t), where w denotes convolution, p rx (t) is the impulse response of the receiving filter, O is the DC offset, b is the frequency offset normalised by the subcarrier separation, and v(t) is the noise. If y(t) is sampled at the rate of T s /G, where G is the oversampling rate, its polyphase components can be expressed as y g [n] = N 1 l=0 ( ) 2p(lN + g) u[l]h g [n l] exp j b + O + v NG g [n] where g = 0,..., G 1, y g [n], h g [n] and v g [n] are the polynomials of sampled y(t), h(t) and v(t), respectively, and are expressed as y g [n] := y(nt s + gt s /G) h g [n] := h(nt s + gt s /G) v g [n] := v(nt s + gt s /G) (3) After removing the guard interval and taking discrete Fourier transform (DFT), the received symbol on the kth subcarrier is given by z[k] = H[k]s[k] + w[k] (4) where z[k] = [z 0...z G 1 ] T, w[k] = [w 0...w G 1 ] T and H[k] = [H 0 H G 1 ] T are G 1 column vectors. The gth component of the received symbol is given as [z[k]] g := z g [k] = N 1 n=0 ŷg [n] exp ( j(2pkn/n )) and similarly for w g [k] and v g [k]. The channel response of the gth sample on the kth subcarrier is given as H g [k] = N 1 n=0 h g[n] exp ( j(2pkn/n )). 2.2 Noise-whitening and maximal-ratiocombining (MRC) The noise samples are uncorrelated when it is sampled at the baud rate, 1/T s. However, when the sampling rate is multiple of the baud rate, the noise samples have the correlation. Therefore it is necessary to whiten the noise samples. The ( g 1, g 2 )th element of a noise covariance matrix on the kth subcarrier, R w [k], can be given as follows [R w [k]] g1 g 2 = E[w g1 w g2] = 1 N N 1 N 1 n 1 =0 n 2 =0 p 2 ((n 2 n 1 + ( g 2 g 1 )/G)T s ) ( exp j 2pk(n ) 2 n 1 ) N where p 2 (t) := p rx (t) w p rx ( t) is the deterministic correlation of p rx (t). In order to perform noise-whitening, the both sides of (4) are multiplied by Rw 1/2 [k]. (5) R 1/2 w [k]z[k] = R 1/2 w [k](h[k]s[k] + w[k]) (6) z [k] = H [k]s[k] + w [k] (7) where z [k] = R 1/2 w [k]z[k], H [k] = Rw 1/2 [k]h[k], and w [k] = R 1/2 w [k]w[k]. Based on the channel response estimated by the long preamble of the OFDM packet defined in the standard [1]. Those samples are combined with an MRC algorithm to maximise the signal to noise ratio (SNR) ŝ[k] = H H [k]z [k] H H [k]h [k] w [k]h[k]) H (R 1/2 w [k]z[k]) w [k]h[k]) H (Rw 1/2 [k]h[k]) = (R 1/2 (R 1/2 where {.} H is the Hermitian operator. (8) IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

3 3 Experiment system 3.1 Measurement setup Fig. 1 shows the measurement environment. The wall is made of concrete while the door, the shelf, the desk and the locker are made of steel. Experiment conditions are shown in Table 1. Through the measurement, line-of-sight (LOS) and non-los (NLOS) conditions are evaluated. In order to realise the NLOS condition, the Rx antenna is placed on the ground behind the desk. For the LOS condition, the Rx antenna is placed on the desk, which is 1.0 m high from the ground. The Tx antenna is put on the shelf, which is 2.2 m high from the ground. The receiver is placed on nine different positions with 3 cm separation for each condition. Fig. 2 shows the experiment system. Table 2 shows the measurement equipments. The beacon signal of the IEEE a system is transmitted. The transmission interval of the beacon signal is set to be 10 ms. The received signal is Figure 2 Experiment system down-converted to the baseband with the down-converter. In the down-converter, the bandwidth of the baseband filter is set to 20/40 MHz. In the case of 20 MHz the gain of the LNA is set to +35 db in the LOS condition and +50 db in the NLOS condition. On the other hand, in the case of 40 MHz the gain is set to +40 db in the LOS condition and +50 db in the NLOS condition. The A/D boards digitise and save the I/Q outputs of the downconverter with the sampling rate of 250 MHz. The sampling period of the received signal is 1 s/measurement point. The sampling rate is converted to 240 MHz with the sample rate conversion scheme presented in [12] and then decimated to 20/40 MHz. 3.2 Demodulation process in the receiver DC offset cancellation: The DC offset of the received signal is estimated over every four beacon intervals Figure 1 Measurement room Table 1 Experiment conditions experimental environment number of measured positions In a room 5.2 m 6.7 m 3.4 m 9 points for LOS and NLOS Table 2 Measurement equipments wireless LAN BUFFALO WAPM-HP- AM54G54 receiving antenna I.O DATA WNO-AG/NDP IEEE a Frequency range: GHz non-directional antenna height: 10 cm modulation scheme 1st: BPSK 2nd: OFDM beacon interval 10 ms number of subcarriers 64 number of data subcarriers 52 total number of bit bit (4992 bit/1 point) fractional sampling 1, 2 down-converter Koden Electronics Co. A AD boards Signatec PDA1000 bandwidth of the baseband filter: 20/40 MHz Gain (20 MHz): +35 db in LOS and +50 db in NLOS Gain (40 MHz): +40 db in LOS and +50 db in NLOS sampling frequency: 250 MHz 1936 IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

4 Figure 3 IEEE a frame format with the following equation Ô = 1 4BNG 4BN 1 G 1 n=0 g=0 y g [n] (9) where B is the beacon interval normalised by the OFDM symbol duration. The DC offset is subtracted from the received samples as follows y g[n] = y g [n] Ô (10) Timing synchronisation: The short preamble is used for timing synchronisation. Fig. 3 shows the structure of the preamble signal in the IEEE a/g standards [1]. InFig. 3, t1 through t10 are the short preambles and T1 and T2 are the long preambles. Timing synchronisation is carried out by using the matched filter with the short preamble sequence as shown in Fig. 4. The peak output is detected with the threshold. The threshold is set to 0.5 of the maximum output Frequency offset estimation: The received signal with the frequency offset can be expressed as y g[n] = N 1 l=0 ( ) 2p(lN + g) u[l]h g [n l] exp j b + DO + v NG g [n] (11) where DO = O Ô is the residual DC offset. The frequency offset is calculated with the short preambles and the long preambles [13]. The frequency offset is estimated in the short preambles as follows b = 4 8 arg 2pG N 4 1 GT m=1 n=0 g=0 [ ] y g n + mn 4 [ y g n + mn 4 + N ] 4 (12) is estimated by the short preamble is given as ( ) y g [n] = y g[n]exp j 2pb NG n (13) The frequency offset is also estimated in the long preambles as follows b = 1 2pG arg N 1 GT n=192 g=0 y g [n]y g [n + N ] (14) where the long preamble starts from n ¼ 192. Therefore the received signal after removing the frequency offset is given as ( ) ŷ g [n] = y g [n]exp j 2pb NG n (15) Channel estimation: The channel response on each subcarrier is estimated with the first long preamble symbol. The phase and the amplitude of the received symbol is compensated on each subcarrier. The BER is then measured by demodulating the second long preamble symbol. 4 Numerical results 4.1 Measurement of indoor channel The computer simulation of this paper employs the channel model with measured impulse responses. The impulse responses are measured with a vector network analyser (VNA). Fig. 5 shows the measurement system with the where m is the index for the short preamble from t2 to t9. The received signal after removing the frequency offset that Figure 4 Timing detection Figure 5 Measurement system with VNA IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

5 Table 3 Measurement equipments Equipment VNA USB/GRIB Interface converter VNA software Tx antenna Rx antenna Version Agilent 8753ET Agilent 82357A Agilent technology Intuilink (version1.3) monopole antenna monopole antenna Figure 8 Normalised impulse response, LOS condition, G ¼ 2 Figure 6 Normalised impulse response, LOS condition, G ¼ 1 VNA. The equipments used for the measurement are shown in Table 3. The frequency range is set from 4.8 to 5.6 GHz with the resolution of 1 MHz. The impulse responses of the indoor channel with G ¼ 1 and G ¼ 2 in the LOS and the NLOS conditions are shown in Figs Figs. 6 and 8 show that there is a strong direct path in the case of the LOS condition. By increasing the sampling rate, the largest path in Fig. 6 is separated to the two dominant paths in Fig. 8. Figs. 7 and 9 show that multiple weak paths can be found in the case of the NLOS condition. The same as the LOS case, the number of resolvable paths increases as sampling rate grows from G ¼ 1toG ¼ 2. Figure 7 Normalised impulse response, NLOS condition, G ¼ 1 Figure 9 Normalised impulse response, NLOS condition, G ¼ IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

6 4.2 Simulation conditions Simulation conditions are presented in Table 4. The data is modulated with quadrature phase shift keying (QPSK) and multiplexed with OFDM. Following the IEEE a/g standards, the numbers of data subcarriers and pilot subcarriers are 48 and 4 while the DFT size is 64. The bandwidth of the subcarrier is khz. The oversampling rate, G, is 1 and 2, the number of packets per trial is , and the number of OFDM symbols per packet is 10. The impulse response over the threshold is employed in the channel model of the computer simulation. Uncorrelated multipath components are assumed in the channel model. The threshold is set to 0.2 of the maximum output. Square root raised cosine filters with the same roll-off factor (a ¼ 0 and 1) is used as the baseband filters in both the transmitter and receiver. 4.3 Bit error rate (BER) performance through simulation Figs. 10 and 11 show the BER performance against the E b /N 0 per sample with different channel conditions (LOS and NLOS) and roll-off factors (a ¼ 0 and a ¼ 1). When the roll-off factor of the baseband filter is a ¼ 0 and the bandwidth of the filter is 20 MHz, the BER curves with G ¼ 1 and G ¼ 2 are almost the same in Figs. 10 and 11. The reason of the same BER curves with G ¼ 1 and G ¼ 2 is that the sharp filter limits the diversity gain through FS although there are multipath components in the NLOS condition [4]. On the other hand, when the roll-off factor of the baseband filter is a ¼ 1 and the bandwidth of the filter is 20 MHz, the FS improves the BERs because of path diversity. This is because there are several paths on both the LOS and NLOS channel models. In addition, the FS scheme obtains more diversity Table 4 Simulation conditions modulation scheme 1st: QPSK 2nd: OFDM DFT size 64 number of subcarriers 64 number of data subcarriers 48 bandwidth of subcarriers khz roll-off factor of Tx/Rx filter a ¼ 0, 1 bandwidth of Tx/Rx filter 20 MHz over sampling rate G ¼ 1, 2 number of OFDM packets per trial number of OFDM symbols per 10 packet Figure 10 BER performance in the LOS condition, roll-off factors a ¼ 0 and a ¼ 1 Figure 11 BER performance in the NLOS condition, roll-off factors a ¼ 0 and a ¼ 1 gain in the NLOS condition because the number of paths in the NLOS condition is larger than that on the LOS condition. 4.4 BER performance through experiment The FS scheme is also evaluated through the experiment. Figs show the BER performance against the SNR per sample with different channel conditions and filter bandwidths. Figs. 12 and 13 show the BER performance in the LOS and NLOS conditions. The bandwidth of the baseband filter is 20 MHz. In Fig. 12, the BER with G ¼ 2 is about 2 db better than that with G ¼ 1. The reason is that the baseband filter in the LOS condition is not as sharp as the one in the NLOS condition. The frequency responses of the noise samples in the LOS and NLOS conditions are presented in Fig. 16. This difference is because of the characteristics of the down-converter. The IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

7 Figure 12 BER performance in the LOS condition (20 MHz) Figure 15 BER performance in the NLOS condition (40 MHz) Figure 13 BER performance in the NLOS condition (20 MHz) Figure 16 Frequency response of the noise samples down-converter shows different noise spectrum for the lowgain mode and high-gain mode of the LNA. Thus, if the received signal is sampled with the rate of 20 MHz, the alias component of the noise overlaps with the received signal. The oversampling eliminates the alias components of the noise, if it is sampled with the rate of 40 MHz (G ¼ 2). The MRC then improves the SNR by about 3 db. Figure 14 BER performance in the LOS condition (40 MHz) On the other hand, in Fig. 13, the bandwidth of the baseband filter in the NLOS condition is narrower, the amount of the alias component of the noise is smaller. No alias component of the noise is observed when G ¼ 1. The MRC then does not change the performance. In addition, as suggested in [4], the sharp filter limits the diversity gain through FS though there are multipath components. Therefore the BER performance with G ¼ 1 and G ¼ 2 are almost the same. These tendencies are corresponding with the numerical results through the simulation with the 1940 IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010

8 7 References [1] IEEE Std a, 1999 [2] Transmission system for digital terrestrial television broadcasting, ARIB STD-B31 Version 1.6, November 2005 [3] OUYANG X., GHOSH M., MEEHAN J.P.: Optimal antenna diversity combining for IEEE a System, leee Trans. Consum. Electron., 2002, 48, (3), pp [4] TEPEDELENLIOĜLU C., CHALLAGULLA R.: Low-complexity multipath diversity through fractional sampling in OFDM, IEEE Trans. Signal Process., 2004, 52, (11), pp Figure 17 Amplitude distribution in the LOS condition roll-off factor a ¼ 0inFigs. 11. Figs. 14 and 15 show the BER performance with the baseband filter of 40 MHz. In Fig. 14, no diversity gain is obtained when G ¼ 2. This result dose not correspond to the simulation result with the roll-off factor a ¼ 1 in Fig. 10. The reason is that the distribution of the received signal amplitude has relatively large probability density at around the normalised amplitude of 0.4 as shown in Fig. 17. For the case of the NLOS condition, the SNR difference between the BER curves with G ¼ 1 and G ¼ 2 enlarges from 3 to 5 db. This is because multiple paths exist as shown in Fig. 9. In addition, excessive bandwidth of the baseband filter allows the FS scheme to achieve path diversity. This tendency follows the simulation results. 5 Conclusions In this paper, we investigate the effect of the filter bandwidth in the FS scheme on the actual indoor channels with the real filter characteristics. In the simulation, the FS scheme with the roll-off factor a ¼ 1 improves by about 2 4 db in the NLOS condition. Similarly in the experiment, the FS scheme with the baseband filter of 40 MHz improves by about 2 db. In the NLOS condition with wider bandwidth of the baseband filter than the minimal bandwidth, the FS scheme has achieved path diversity and improved the performance. The experiment results have also proven that the multipath components on the NLOS channel provides diversity gain with FS. 6 Acknowledgments This research was partially supported by the Grant-in-Aid for Young Scientists (B), No and the Global Center of Excellence for High-Level Global Cooperation for Leading-Edge Platform on Access Spaces from the Ministry of Education, Culture, Sport, Science, and Technology in Japan. [5] TUGNAIT J.K.: Blind equalization and estimation of FIR communications channels using fractional sampling, IEEE Trans. Commun., 1996, 44, (3), pp [6] KANNO I., SUZUKI H., FUKAWA K.: Blind equalization with fractional sampling metric combining for avoiding channel estimate ambiguity in mobile radio. Proc. 17th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, September 2006 [7] GITLIN R.D., WEINSTEIN S.B.: Fractionally-spaced equalization: an improved digital transversal equalizer, Bell Syst. Tech. J., 1981, 60, pp [8] TONG L., XU G., KAILATH T.: Blind identification and equalization based on second-order statistics: a time domain approach, IEEE Trans. Inf. Theory, 1994, 40, (2), pp [9] ROY S., LI C.: A subspace blind channel estimation method for OFDM systems without cyclic prefix, IEEE Trans. Wirel. Commun., 2002, 1, (4), pp [10] NISHIMURA H., INAMORI M., SANADA Y.: Sampling rate selection for fractional sampling in OFDM, IEICE Trans. Commun., 2008, E91-B, (9), pp [11] INAMORI M., KAWAI T., KOBAYASHI T., NISHIMURA H., SANADA Y.: Effect of pulse shaping filters on a fractional sampling OFDM system with subcarrier-based maximal ratio combining, IEICE Trans. Commun., 2009, E92-B, (5), pp [12] BOSTAMAM A.B., SANADA Y., MINAMI H.: Modified direct insertion/cancellation method based sample rate conversion for software defined radio, IEICE Trans. Commun., 2008, E91-B, (8), pp [13] INAMORI M., BOSTAMAM A.B., SANADA Y., MINAMI H.: Frequency offset estimation scheme in the presence of timevarying DC offset for OFDM direct conversion receivers, IEICE Trans. Commun., 2007, E90-B, (10), pp IET Commun., 2010, Vol. 4, Iss. 16, pp & The Institution of Engineering and Technology 2010