A Novel Transmit Scheme for OFDM Systems with Virtual Subcarriers

Transcription

1 Ü ÒÐ Õ OFDM Í Æ ² 1, Đ («Æ Å ) Ê Ý Ó Ñ ÀÐÖ OFDM Î ±Çµ³ µ³ ÓÁÔ ÅÞ» ÃÔ ÁÔÄß Á ʺ Î Ó IFFT ¼ ÂÉ Û ¼ Ì Ã ¹µ³ ʺ Ó Î OFDM ±Çµ³ Ï ±Çµ³ Ñ Ë¾ È Ø Ñ Ú ½ Ù Á ¼ Äß Á ÀÐÖ A Novel Transmit Scheme for OFDM Systems with Virtual Subcarriers Chen Xiang, Zhou Shidong, Yao Yan (Department of Electronic Engineering, Tsinghua Univ., Beijing , P.R.China) Abstract: In this paper, a novel transmit scheme for OFDM systems with virtual subcarriers is proposed. Based on the doublerepetition structure and pulse shaping filter, the proposed scheme with comb-type pilot can provide additional feasibility to reduce the channel estimation error at the band edges with conventional IFFT-based estimator. Also this transmit scheme can provide additional diversity compared to the conventional OFDM scheme. All these efficacies are confirmed by simulations. Key words: OFDM, channel estimation, comb-type pilot, virtual subcarriers 0 Introduction In recent years, orthogonal frequency division multiplexing (OFDM) has been considered one of the major techniques for next-generation wireless communications because of its various advantages in suppressing the severe effect of frequency-selective fading. However, the OFDM systems with high spectrum efficiency, which employ high-order modulation (e.g., 16QAM) generally require accurate estimation and tracing of fading channels. The channel estimation in OFDM systems is usually performed through exploiting pilot subcarriers. Among all pilot based schemes, comb-type pilots [1][] have been the focus in order to reduce the training overhead, while some proper interpolation methods are needed. In the existing interpolation techniques, the Minimum Mean-Square Error (MMSE) interpolation [1] uses all pilots in both frequency and possibly time directions and accordingly such interpolation technique tends to have very high computational complexity and needs some prior statistics on channels. In contrast, the linear or polynomial interpolation [3] method has low computational complexity but brings an obvious performance degradation in certain worse fading channels. The IFFT-based estimator [] has fairly low computational complexity by IFFT operating on the pilot subcarriers. However, this estimator needs equidistantly distributed pilot subcarriers in all subcarriers to achieve the best performance [4]. This condition is not usually tenable for most standards of physical layers using OFDM with virtual subcarriers and thus the IFFT-based estimator will suffer from higher errors at the band edges than the MMSE estimator. Some other schemes have been proposed to overcome the performance degradation caused by virtual subcarriers for the IFFT-based channel estimator in OFDM systems [5][6]. In [5], the frequency domain data windowing is considered to 1 Supported by the High Technology Research and Development Program of China (No. 006AA01Z74). To whom correspondence should be addressed. chenxiang98@mails.tsinghua.edu.cn 1

2 minimize the channel estimation mean square error (MSE), while the optimal generalized window depends on exhaustive search for different signal-to-noise ratios (SNRs). Another method in [6] is based on the use of more pilots or equivalent pilots to operate IFFT-based estimator. In this paper, we propose a novel transmit scheme for OFDM systems with virtual subcarriers without changing pilot structure and usage bandwidth (3dB bandwidth). This scheme with comb-type pilots is based on the double-repetition structure in the frequency domain and the proper pulse shaping filter in the time domain. It can provide additional feasibility to reduce the IFFT-based channel estimation error at the band edges without high computational complexity. And the advantages of the proposed scheme are confirmed by simulation results. The remaining parts of this paper are organized as follows. In Section 1, a review of the conventional OFDM model and IFFT-based channel estimator is presented. Then the proposed transmit scheme for OFDM systems with virtual subcarriers and relevant receiver schemes are presented in Section. Some simulation results are then presented in Section 3. Finally, some conclusions are drawn in Section 4. 1 Conventional OFDM Model and IFFT-based Channel Estimator 1.1 OFDM Signal Model with Comb-type Pilots We consider an OFDM system that consists of N subcarriers among which only U subcarriers are used for transmission. Notice that residual N U subcarriers, namely virtual carriers at the edges of the spectrum, are used as guard band to suppress outer-band emission. Each data subcarrier is modulated as X where represents the subcarrier index and the OFDM symbol index is dropped for simplicity. After an IFFT, every OFDM symbol is added by a cyclic prefix (CP) with the length N g to avoid intersymbol interference (ISI) caused by multipath fading channels. The multipath channel can be characterized by L 1 h(n)= h l δ(n l), (1) l=0 where h l is the complex path gain with time delay l; and L is the maximum time delay which is no larger than N g. Then at the receiver, with perfect synchronization the th received subcarrier after FFT can be represented by Y = X H + W, =0,..., N 1, () where W is the white complex Gaussian noise with varianceσ ; and H is the channel response in the frequency domain given by L 1 H = h l e jπl/n, =0,..., N 1. (3) l=0 In order to estimate the multipath fading channel, M pilots are inserted into N subcarriers, and the distance of adjacent pilots in frequency domain is B= N/M (B is an integer). Then we can only use the M P + 1 comb-type pilots involved among the U transmission subcarriers to perform channel estimation, where M P is an even number. Let{P m, m=0,..., M} denote all M pilots, in which if m [ M P + 1, M 1 M P ], then P m = 0, and if m is others, then P m is a nown QPSK symbol with P m =1. Then the pilots inserted into the transmission subcarriers are as follows: X mb = P m, m=0,..., M. (4)

3 1. IFFT-based Channel Estimator Frequency Domain Time Domain Frequency Domain LS estimate M-point IFFT Zero-Padding to N points N-point FFT Fig. 1. IFFT-based chanel estimator diagram. The IFFT-based channel estimator is shown in Fig. 1. The comb-type pilots can be used to obtain the least squares (LS) estimates of the channel responses at the pilot subcarriers as: H mb = 0, m [ M P + 1, M 1 M P ], H mb = Y mb P m = H mb + W mb P m, m=others. (5) Then M-point IFFT is performed to transform the frequency response H P at the pilot subcarriers into the time domain. After padding N M zeros to the time response, an N-point FFT is performed to transform the results of the time domain into the frequency domain Ĥ. The different performance of MSE vs. subcarrier index is given [7] by: L 1 L 1 MSE()=σ [D 1 ] m,n e jπ(n m)/n, (6) m=0 n=0 where ( ) 1 denotes matrix inverse,σ is the noise variance, D is a L Lmatrix with its entry [D] p,q as follows: M P [D] p,q = e jπ(p q)im/n, 0 p, q L 1, (7) m=0 where{i m ; 0 m M P } is the subcarrier index of the M P + 1 pilots involved among the U transmission subcarriers. Without virtual subcarriers as mentioned in [4], the optimal pilots locations are uniformly distributed among all N subcarriers. But when virtual subcarriers are considered, this condition is not satisfied anymore. Then the only way to determine the optimal pilots location is through exhaustive search [8]. However, from (6) we can see an interesting phenomenon by numerical simulations in Fig.. The parameters used in Fig. are: N = 51, U = 193, B = 8, S NR=10dB. It is seen that MS E() is almost flat in the middle of the signal bandwidth (as shown on both sides in Fig. ), but grows rapidly at the edges. Even as the growth of channel length L near the number of pilots, the MS E performance at the edges will become worse. Considering the higher channel estimate errors, the data transmission on these subcarries will not be so reliable. 0 4 L=10 L=15 L=0 MSE(dB)

4 Fig.. MSE vs. subcarrier index by IFFT-based estimator. In order to suppress the channel estimate errors at the band edges for IFFT-based channel estimator, we propose a simple transmit scheme without changing pilot structure and usage bandwidth (3dB bandwidth) in the next section. Proposed Transmit Scheme.1 Novel Transmit Scheme The operations of novel transmit scheme in Fig. 3 can be summarized as follows: (1) Data and pilots are firstly multiplexed and mapped into the proper positions in U subcarriers with N U virtual subcarriers. Pilot pattern is designed as comb-type in []. () Then repetition and expansion in the frequency domain are performed as Fig. 3 shows, where both data subcarriers and pilot subcarriers are repeated and expanded. The transmitting sequence size U is transformed into U+ V. Now the number of virtual subcarriers is reduced to N U V. (3) An N-point IFFT is performed. (4) CP is inserted to each OFDM symbol. (5) Finally, a spectrum-shaping filtering in the time domain, which is designed to eep the whole usage 3dB bandwidth the same as the original bandwidth with U transmission subcarriers, is performed. Data Pilot Multiplexing Subcarrier Mapping Repearting & expanding IFFT N-point +CP filter in time domain EB, EB 1 V EB 1,1 U+V U EB V EB,1 EB 1, Fig. 3. Novel transmit scheme for OFDM systems. Note in Fig. 3, EB i (i = 1, ) means the extended bandwidth, which is repeated at both edges of the usage bandwidth U to form EB i, j (i, j = 1, ). In Step (), the length V of repetition sequences should be settled for V < min( 1 (N U), 1 U). Thereout, the pilots in EB i(i=1, ) are also repeated. The filter used in Step (5) should be designed with the same 3dB bandwidth as conventional OFDM scheme (i.e., the usage bandwidth remains U ). A design example of the filter and its relative frequency response will be shown in Section 3. After filtered in the time domain, the transmitting sequences including the pilots in the repeated bands (from innerband to outer-band) will have a continuous slow roll-off at both edges. Accordingly, the proposed scheme involving Step () and (5) can provide feasibility to reduce the channel estimation errors at the band edges without changing the basic structure of the IFFT-based channel estimator. At the same time, the usage bandwidth (3dB bandwidth) of transmitted signals will not be changed, either. 4

5 . Relevant Proposed Receiver Scheme In order to achieve good performance at the band edges, we present a simplified receiver scheme relative to the proposed transmit scheme in Fig. 4. y(n) Remove CP and FFT DeMultiplexing Data Subcarriers (U+V)*(B-1)/B Combination Pilot Subcarriers (U+V) (U+V)*(B-1)/B IFFT-Based Getting CIR relative ChannelEstimator to data suncarriers Combination (U+V)/B 1/H(K) Output EB, V EB 1,1 EB 1 U EB,1 EB EB 1, V Fig. 4. Receiver scheme for proposed transmit scheme. In Fig. 4, the number of pilots input into the conventional IFFT-based channel estimator is (U + V)/B instead of original U/B. Also the IFFT-based estimator outputs the channel responses of U +V subcarriers instead of U subcarriers. Compared with the conventional receiver, the proposed receiver only adds direct combination from outer-band to innerband with V subcarriers at each band edge, respectively, before the one-tap equalizer. This combination is performed to both the data (see the upper data stream in Fig. 4) and the channel responses (see the lower channel response stream in Fig. 4) at these V subcarriers at each band edge, respectively. In order to show the direct combination in details, let Y (EB i, j) (i,, ) denote the received signals in extended bandwidth, H (EB i, j) (i,, ) denote the relative channel estimates obtained by IFFT-based channel estimator, W (EB i, j) (i,, ) denote the relative noise terms, X (EB i) (i=1, ) denote the data transmitted in EB i respectively, then: Direct combination is performed as follows: Y (EB i, j) = H (EB i, j) X (EB i) + W (EB i, j), i,,. (8) Y (EB i, j) = ( H (EB i, j) ) X (EB i) + W (EB i, j), i=1,. (9) Then, the transmitted data X (EB i) can be detected by conventional one-tap equalizer. It should be noted that direct combination can be also replaced by other preferred combination schemes, such as coherent combination as follow: 3 Simulation Results X (EB i) = ((H (EB i, j) ) Y (EB i, j) )/ H (EB i, j), i=1,. (10) Some simulation results will be given to verify the proposed transmit scheme. Table 1 summarizes the parameters used in the simulations. 5

6 N 048 U 1537 V 80 N g 330 B 8 Modulation 16QAM Channel Code: Turbo Code Rate=1/, Length=9000 Table 1. Simulation parameters. As mentioned in Section.1, here we will present an illustrational filter (a raised cosine function FT rcos combined with a complementary error function-er f c function FT er f c ) in the time domain. The roll-off factorα=0., the tap length of FT rcos is defined as F+ 1=81, the tap length of FT er f c is defined as N f ilter = 56. Given i [1 : N f ilter ], then the filter coefficients are generated by the following pseudo codes: FT rcos (i): FT rcos (i)= sqrt( cos(π i N f ilter 1 )), i [ N f ilter F FT rcos (i)=0, i=others. F+ 1 : N f ilter + F+ 1]; FT er f c (i): when i [1 : 1 N f ilter] : when i [ 1 (1 α)n U f ilter N : 1 (1+α)N U f ilter N ] : when i [1 : 1 (1 α)n U f ilter N ] : when i=others : FF er f c (i)=0; FF er f c(i)=1; FF er f c(i)= 1 e f rc(4.5 i N f ilter 1 U N 1 U N ); when i [ 1 N f ilter+ 1 : N f ilter ] : FF er f c (i)= FF er f c (N f ilter i+1); then, FT er f c = i f f tshi f t(sqrt(ff er f c )). Finally, the filter used in Step (5) is generated by: FT(i)= FT er f c (i) FT rcos (i). (11) In the above pseudo codes, sqrt(x) denotes the square root of some element X; er f c(x) denotes complementary error function which is defined as er f c(x)= inf π X e t dt; i f f tshi f t(x) denotes the inverse FFT shift which swaps the left and right halves of X. As the pseudo codes mentioned above, we can see that the tap length of the filter is actually F+ 1. The frequency response of this filter is shown in Fig. 5. From Fig. 5, it can be seen that the usage 3dB bandwidth after filtering occupies still U = 1537 subcarriers. 3dB point of usage bandwidth 6

7 Fig. 5. Frequency response of the designed filter example. First, we give the distortion performance comparison between the novel OFDM transceiver schemes and the conventional scheme in Fig. 6. The distortion metric is defined as follows: E{ X } Output S INR=10log 10 ( )(db), (1) E{ ˆX X } where ˆX is the estimated data after one-tap equalizing. This simulation was performed without channel coding in 6-Tap bloc fading channels. Twenty thousand independent runs were performed for different SNRs to calculate the averaged distortion. At the receiver, two combination schemes including direct combination and coherent combination are considered, respectively. From Fig. 6, we can see that the receiver with direct combination for the novel transmit scheme can outperform the conventional scheme with 1-dB in high SNR region, the coherent combination receiver can even outperform the direct combination receiver with 1-dB. While in low SNR region (e.g. 10dB), the performance of all three schemes seems to be similar because the combination (either direct or coherent combination) from outer-band into inner-band will increase additional noise, which will degrade the performance improvements of the proposed schemes. Fig. 7 shows the BER performance in the 6-Tap-Rayleigh fading channels (The time delay profiles are described as ITU-R M.15 Vehicle-A, velocity=10m/h). Not only the direct combination receiver, but also the coherent combination receiver can outperform the conventional OFDM scheme in high SNR region. From Fig. 7, it can be also seen that the novel transmit scheme can provide additional diversity than the conventional OFDM scheme. Fig. 6. Distortion performance comparison. 7

8 Fig. 7. BER performance comparison. 4 Conclusion In this paper, we propose a novel transmit scheme for OFDM systems with comb-type pilots and virtual subcarriers. Moreover, the relative receiver schemes with conventional IFFT-based channel estimator to the proposed transmit scheme are presented to obtain the performance gain. Simulation results show that the proposed schemes can reduce the performance degradation at the edges of transmission bandwidth and provide additional diversity gain without changing the usage bandwidth (3dB bandwidth). References [1] Li Y, Cimini L. Robust channel estimation for ofdm systems with rapid dispersive fading channels[j]. IEEE Trans. Commun., 1998, 46(7): [] Edfors O, Borjesson P. Analysis of dft-based channel estimation for ofdm[j]. Wireless Personal Communications, 000, 1(1): [3] Hsieh M, Wei C. Channel estimation for ofdm systems based on comb-type pilot arrangement in frequency selective fading channels[j]. IEEE Trans. Consumer Electron., 1998, 44(1):17 5. [4] Negi R, Cioffi J. Pilot tone selection for channel estimation in a mobile ofdm system[j]. IEEE Trans. Consumer Electron., 1998, 44(3): [5] Yang B, Cao Z, Letaief K B. Analysis of low-complexity windowed dft-based mmse channel estimator for ofdm systems[j]. IEEE Trans. Commun., 001, 49(11): [6] Kim J, NAM S, Hong D. Channel estimation in comb-type pilot arrangements for ofdm systems with null subcarriers[j]. IEICE Trans. Commun., 006, e89(1): [7] Morelli M, Mengali U. A comparison of pilot-aided channel estimation methods for ofdm systems[j]. IEEE Trans. Sig. Process., 001, 49(1): [8] Hu D, Yang L, Shi Y, et al. Optimal pilot sequence design for channel estimation in mimo ofdm systems[j]. IEEE Commun. Lett., 006, 10(1):1 3. 8