Weight Tracking Method for OFDM Adaptive Array in Time Variant Fading Channel

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1 Weight Tracking Method for OFDM Adaptive Array in Time Variant Fading Channel Tomohiro Hiramoto, Atsushi Mizuki, Masaki Shibahara, Takeo Fujii and Iwao Sasase Dept. of Information & Computer Science, Keio University Hiyoshi, Kohoku, Yokohama, Kanagawa JAPAN Tel: ext.43235, Fax: Dept. of Electrical Engineering Faculty of Engineering, Tokyo University of Agriculture and Technology , Nakacho, Koganei, Tokyo JAPAN Abstract - In Orthogonal Frequency Division Multiplexing (OFDM) system, in order to reduce the influence of Co-Channel Interference (CCI), Minimum Mean Square Error-Adaptive Array Antenna (MMSE-AAA) is attractive. To get the space diversity gain, the distance between adjacent elements should be set to be more than several wavelengths. However, it is difficult to derive the optimal weights with a few training symbols because fading status is independent in each element. As a result, Bit Error Rate (BER) performance is deteriorated. In this paper, we propose a novel weight tracking method to achieve space diversity gain and fast convergence with a few pilot symbols. In the proposed method, before updating the weights, channel estimation is applied to track the multipath fading of the desired signals. By computer simulation, we show that the proposed system can improve BER performance compared to the conventional system without channel estimation, even if the Doppler frequency is high. Keywords: OFDM, Adaptive Array Antenna, Antenna Separation, MMSE, SINR, CCI 1. INTRODUTION Orthogonal frequency division multiplexing (OFDM) has attracted much attention to achieve the high speed data rate in the forth generation wireless communication. OFDM is the modulation scheme in which the data is transmitted in parallel by using many subcarriers. In OFDM, since each subcarrier is put into orthogonal and the frequency spacing of each subcarrier is minimum, the channel is regarded as flat fading. Since the shape of the frequency spectral is similar to the rectangle, OFDM achieves high spectral efficiency. When OFDM is used in wireless cellular system, the same frequency should be used with small frequency reuse distance to achieve high spectral efficiency. In this case, Co-Channel interference (CCI) occurs. As a result, the Bit Error Rate (BER) performance degrades. To remove the influence of CCI, adaptive array antenna (AAA) is attractive [1] [3]. In particular, minimum mean square error-aaa (MMSE- AAA) is effective because it is not necessary to estimate the direction of arrival of the desired and undesired signals. In general, the distance between adjacent elements in MMSE-AAA is set to have half the wavelength of the carrier frequency. However, it is difficult to get the enough space diversity gain [4]. This is because the angular spread of incident waves is small and the correlation between elements becomes high at the base station. To get the space diversity gain, the distance between adjacent elements should be set to be more than several wavelengths. When the distance between adjacent elements is more than several wavelengths, it is necessary not only to track the different multipath fading in each element, but also to suppress the undesired signals by weight control because the multipath fading is independent in each element. In this situation, when a few pilot symbols are used, it is difficult to track the multipath fading by only updating the weights. As a result, Signal to Interference plus Noise power Ratio (SINR) in AAA is deteriorated compared to the case that the optimal weights are used. Therefore, when the distance between adjacent elements has several wavelengths, many pilot symbols are required to derive the optimal weights. However, the use of many pilot symbols reduces the efficiency of data transmission. Moreover, OFDM has the longer symbol duration compared to that of single carrier system. Therefore, since the fading in one frame is fluctuated, the deterioration of the tracking performance

2 2. OFDM ADAPTIVE ARRAY Fig. 1 Structure of the receiver with OFDM adaptive array. of the fading becomes serious. In this paper, we propose a novel weight tracking method to achieve the space diversity gain and fast convergence with a few pilot symbols. In the proposed method, before updating the weights, we estimate the channel of the desired signals to track the multipath fading. Moreover, we use the weights decided in the previous frame as the initial weights in the present frame, and update these weights by using pilot symbols in the present frame. The features of our proposed system are as follows. First, we can improve the BER performance. This is because we can compensate the fluctuation of the phases and amplitudes, in which the desired signals are sustained in each element, by channel estimation before updating the weights. Second, we can achieve faster convergence of the weights with a few pilot symbols. This is because channel estimation is applied before updating the weights. By computer simulation, we evaluate the BER performance of the following schemes: (i) the case that the channel is estimated before updating the weights (proposed system), (ii) the case that the channel is not estimated and the weights are updated using the weights decided in the previous frame as the initial weights, and (iii) the case that the weights are independently decided in each frame. As a result, we show that (i) can improve the BER performance compared to (ii) and (iii) with fewer pilot symbols, especially when the Doppler frequency is high. In OFDM system, a serial-parallel converter separates the date stream into many output streams. These streams are modulated into subcarriers by passing through Inverse Fast Fourier Transform (IFFT). At the receiver, the subcarrier signals are obtained by using FFT and demodulated. The detected data streams are converted into serial stream. In this paper, we apply AAA to the receiver side of the OFDM system. Figure 1 shows the structure of the receiver with OFDM adaptive array. In Fig. 1, λ represents the wavelengths of the carrier frequency, m(m = 1, 2,,M) is the element number, k(k =1, 2,,K) is the subcarrier number and n is the positive constant number, respectively. After OFDM signals are received in each element, these signals are inputed into FFT. The output signals from the different elements are weighted in each subcarrier and combined. The signal y km, which represents the weighted signal of the kth subcarrier and the mth element, is given by y km = x km ωkm, (1) where x km represents the signals after FFT and ω km represents the weights of the kth subcarrier and the mth element, respectively. Then, the signal y k, which represents the signal of the kth subcarrier after weighted and combined among elements, is given by y k = y km = x km ωkm, (2) where ( ) represents the complex conjugate. In the conventional system, a lot of algorithms to update the weight are proposed. In this paper, we apply for Recursive Least Squares (RLS) algorithm. In RLS algorithm, the reference signal r k is generated in advance. Then, the weights are updated iteratively so that the root mean square error e k is minimum. e k is given by e k = r k y k. (3) The weight vector ω k is given by ω k = R 1 xx k r xr k, (4) where R xx k and r xr k are given by R xx k = E[x kx T k ] (5) r xr k = E[x k r k] (6) x k =[x k1 x k2 x km ], (7)

3 signals are different in each element. Therefore, in the proposed system, we estimate the channel condition in each element and each subcarrier before updating the weights, as shown in Fig. 2. In the CE of Fig. 2, the channel is estimated by averaging the pilot symbols at the head of each frame. Then, we perform the channel compensation for the uth symbol of the lth frame by linear interpolation between the estimated channel of the lth and (l + 1)th frame, where u(u =1, 2,...,U)is the symbol number in one frame, l(l =1, 2,...,L) is the frame number, respectively. Then, the estimated channel of the mth element, the kth subcarrier and the uth symbol of the lth frame h (l) ukm is given by h (l) ukm = h(l) km + u U (h(l+1) km h(l) km ), (8) Fig. 2 Structure of the proposed receiver with OFDM adaptive array. where ( ) T represents the transpose operation and E[ ] represents ensemble expectation respectively. In MMSE-AAA, to get the diversity gain, the distance between adjacent elements should be set to be more than several wavelengths so that the correlation between elements can become low. When the distance between adjacent elements is more than several wavelengths, the phases and amplitudes fluctuation of the desired signals are different in each element. Therefore, it is required not only to track the different multipath fading in each element, but also to suppress the undesired signals by weight control. Many pilot symbols are required to derive the optimal weights. However, the use of many pilot symbols reduces the efficiency of data transmission. Moreover, it also may be difficult to track the fading because time-selective fading occurs in mobile communication, even if many pilot symbols are used. In particular, since the OFDM system has a longer symbol duration, the tracking performance of the fading is deteriorated. 3. PROPOSED SYSTEM MODEL 3.1 Channel estimation Figure 2 shows the structure of the proposed receiver with OFDM adaptive array. In the proposed system, we set the distance between adjacent elements of a linear array expanding to nλ (n >1/2) in order to get the space diversity gain. In the proposed system, since the distance between the adjacent element is large, the fading is independent in each element even though the angular spread of the incident waves is small. Consequently, the phases and the amplitudes of the received where h (l) km represents the estimated channel obtained by using pilot symbols at the head of the lth frame. In the proposed system, we can compensate the fluctuation of the phases and amplitudes of the desired signals by channel estimation before updating the weights. Therefore, we have only to reduce the CCI in MMSE. Consequently, the proposed system can improve the BER performance with a few pilot symbols compared to MMSE-AAA without channel estimation. 3.2 Updating the weight After the channel estimation, the weights are updated, as shown in Fig. 2. The procedure of updating the weights in the proposed system is as follows. First, we decide the weights in each element and each subcarreir by using the pilot symbols in the first frame. In the second and higher frames, we use the weights decided in the lth frame as the initial weights in the (l + 1)th frame, and update these weights by using pilot symbols in the (l + 1)th frame. As a result, we can remove the undesired signals with fewer pilot symbols, and increase the percentage of the data symbols in each frame. Moreover, in this paper, we perform the weight compensation for the uth symbol of the lth frame by linear interpolation between the updated weights of the lth and the (l +1)th frame as well as the channel compensation. The reason why we perform the weight compensation by linear interpolation is as follows. In the lth frame, the value of the channel compensation comes close to the estimated channel of the (l + 1)th frame in proportion as latter part of the lth frame, because we perform the channel compensation by linear interpolation. Therefore, it is expected that the accuracy of the compensation of the weight is improved by linear interpolation. In addition,

4 Table 1 Simulation parameters Modulation QPSK Number of elements M = 4 Distance between 10λ adjacent elements (n = 10) Received signals desired :1 undesired :1 Distribution of Angular normal distribution Angular spread 12 degrees Direction of Arrival desired : 30 degrees undesired : -40 degrees Number of subcarriers 512 Number of FFT points 512 Symbol duration 6.4µsec Guard interval duration 20 % of a OFDM symbol Fading model 8 path Rayleigh fading Channel estimation linear interpolation MMSE algorithm RLS Forgetting factor 0.60 Number of symbols (i), (ii) to update the weights 1st frame : 64 in each frame 2nd frame and higher frames : 4 (iii) 64 Length of data symbols 60 in each frame Noise AWGN since we use the weights decided in the lth frame as the initial weights in the (l + 1)th frame and update these weights, it is not necessary to insert many pilot symbols in each frame. As a result, the data transmission efficiency is improved. The weight of the mth element, the kth subcarrier and the uth symbol of the lth frame ω ukm is given by ω (l) ukm = ω(l) km + u U (ω(l+1) km ω(l) km ). (9) The signal y ukm after multiplying the weights is given by y ukm = x ukm h ukm ω ukm, (10) where, x ukm is the received signal of the mth element, the kth subcarrier and the uth symbol. Therefore, array output signal y uk is given by y uk = y ukm = x ukm h ukmωukm. (11) 4. SIMULATION RESULTS We evaluate the BER performance of the proposed system by computer simulation. For comparison, we show the performance of the following schemes. Fig. 3 Frame configuration used in (i) and (ii) Fig. 4 Frame configuration used in (iii) (i) Both channel estimation and weight update with linear interpolation are done (Proposed system) (ii) Non channel estimation is done and weight update is performed using the weights decided in the previous frame as the initial weights (iii) Independent weight decision is done in each frame Table 1 shows the simulation parameters. The form of AAA is the linear array. The desired and undesired signals are received at the same time and are equal in the average power. Figure 3 shows the frame configuration used in (i) and (ii). In order to derive the optimal weight, the first frame is composed of pilot symbols for channel estimation and for updating the weight. The second and higher frames are composed of pilot symbols and data symbols. Figure 4 shows the frame configuration used in (iii). In Fig. 4, all frames are composed of pilot symbols for updating the weights and data symbols. Figure 5 shows the average BER performance versus Eb/N0 in each element with Doppler frequency = 100 Hz. In Fig. 5, compared to (i) and (ii), (i) improves the BER performance except the case that Eb/N0 is high. This is because in (i), we can compensate the fluctuation of the phases and amplitudes of the received desired signals, by channel estimation before updating the weight when the Eb/N0 is small. However, the BER performance in (ii) is better compared to (i) when the Eb/N0 is large. Compared to (i) and (iii) with 64 pilot symbols, (i) improves the BER performance with a few pilot symbols, especially when the Eb/N0 is large. This is because in (iii), the convergence of the weight is unstable since the forgetting factor is small. On the other hand, because

5 (iii) : pilot symbol = 4 in each frame (iii) : pilot symbol = 4 in each frame Average BER 10 2 (iii) : pilot symbol = 64 in each frame Average BER 10 1 (ii) : without channel estimation 10 4 (i) : Proposed (ii) : without channel estimation 10 2 (i) : Proposed (iii) : pilot symbol = 64 in each frame Eb/N0 [db] Fig. 5 Average BER performance versus Eb/N0 with Doppler frequency = 100 Hz. in (i), the fluctuation of the phases and amplitudes of the desired signals is compensated by channel estimation, the interference component is reduced by updating the weight. Consequently, (i) improves the BER performance with small forgetting factor. Figure 6 shows the average BER performance versus Eb/N0 in each element with Doppler frequency = 400 Hz. In Fig. 6, (i) dramatically improves the BER performance compared to (ii) and (iii). This is because in (i), we can compensate the fluctuation of the phases and the amplitudes of the desired signals by channel estimation before updating the weight. When Doppler frequency is 400 Hz, it is difficult to track the fading by only updating the weight with a few pilot symbols. Additionally, in (i), the percentage of the pilot symbols can reduce less than 20% compared to that of (iii) with 64 pilot symbols. In fact, in (i), we can improve the BER performance with a few pilot symbols by channel estimation in advance. 5. CONCLUSION In this paper, we have proposed a novel weight tracking method to achieve the space diversity gain and fast convergence with fewer pilot symbols. In the proposed method, before updating the weights, we estimate the channel of the desired signals to track the multipath fading. By computer simulation, we evaluate the BER performance of the following schemes: (i) the case that the channel is estimated before updating the weight (proposed system), (ii) the case that the channel is not estimated and the weights are updated using the weights decided in the previous frame as the initial weights, and Eb/N0 [db] Fig. 6 Average BER performance versus Eb/N0 with Doppler frequency = 400 Hz. (iii) the case that the weights are independently decided in each frame. As a result, we showe that (i) can improve the BER performance compared to (ii) and (iii) with fewer pilot symbols, especially when the Doppler frequency is high. REFERENCES [1] Y. Li, and N. R. Sollenberger, Adaptive Antenna Arrays for OFDM Systems With Cochannel Interference, IEEE Trans. Commun., Vol. 47, No. 2, pp , Feb [2] S. Kapoor, D. J. Marchok, and Yih-Fang Huang, Adaptive Interference Suppression in Multiuser Wireless OFDM Systems Using Antenna Arrays, IEEE Trans. Signal Processing, Vol. 47, No. 12, pp , Dec [3] Kai-Kit Wong, R. S. -K. Cheng, K. B Letaief and R. D Murch, Adaptive Antenna at the Mobile and Base Stations in an OFDM/TDMA System, IEEE Trans. Commun, Vol. 49, No. 1 pp , Jan [4] H. Yoshinaga, M. Taroumaru, Y. Akaiwa, Performance of Adaptive Array Antenna at PHS Basestation IEICE Trans. Communications, Vol. J84-B, No. 3, pp , March