Channel Estimation in Wireless OFDM Systems

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2 Fourier transform (DFT) to replace the banks of sinusoidal generators and the demodulators was suggested by Weinstein and Ebert [5] in 1971, which significantly reduces the implementation complexity of OFDM modems. Hirosaki [8], suggested an equalization algorithm in order to suppress both inter symbol and inter sub carrier interference caused by the channel impulse response or timing and frequency errors. Simplified model implementations were studied by Peled [9] in Cimini [6] and Kelet [10] published analytical and early seminal experimental results on the performance of OFDM modems in mobile communication channels. carriers. The waveform of some carriers in a OFDM transmission is illustrated in Fig. 2. II. OFDM OFDM is simply defined as a form of multi-carrier modulation where the carrier spacing is carefully selected so that each sub carrier is orthogonal to the other sub carriers. Two signals are orthogonal if their dot product is zero. That is, if you take two signals multiply them together and if their integral over an interval is zero, then two signals are orthogonal in that interval. Orthogonality can be achieved by carefully selecting carrier spacing, such as letting the carrier spacing be equal to the reciprocal of the useful symbol period. As the sub carriers are orthogonal, the spectrum of each carrier has a null at the center frequency of each of the other carriers in the system. This results in no interference between the carriers, allowing them to be spaced as close as theoretically possible. Mathematically, suppose we have a set of signals ψ then 0 T ψ p t ψ q t = k for p = q = 0 for p q (1) Where and ψ q are pth and qth elements in the set. The signals are orthogonal if the integral value is zero. where T is a symbol period. Since the carriers are orthogonal to each other the nulls of one carrier coincides with the peak of another sub carrier. As a result, it is possible to extract the sub carrier of interest OFDM transmits a large number of narrowband sub channels. The frequency range between carriers is carefully chosen in order to make them orthogonal one another. In fact, the carriers are separated by an interval of 1/T, where T represents the duration of an OFDM symbol. The frequency spectrum of an OFDM transmission is illustrated in Fig.2. Each sinc of the frequency spectrum, in the Fig. 3 corresponds to a sinusoidal carrier modulated by a rectangular waveform representing the information symbol. One could easily notice that the frequency spectrum of one carrier exhibits zerocrossing at central frequencies corresponding to all other carriers. At these frequencies, the intercarrier interference is eliminated, although the individual spectra of subcarriers overlap. It is well known; orthogonal signals can be separated at the receiver by correlation techniques. The receiver acts as a bank of demodulators, translating each carrier down to baseband, the resulting signal then being integrated over a symbol period to recover the data. If the other carriers all beat down to frequencies which, in the time domain means an integer number of cycles per symbol period (T), then the integration process results in a zero contribution from all these Fig. 2 Spectrum of Orthogonal carriers Fig. 3 Time domain representation oforthogonal carriers The figure indicates the spectrum of carriers significantly over laps over the other carrier. This is contrary to the traditional FDM technique in which a guard band is provided between each carrier. From the figures illustrated, it is clear that OFDM is a highly efficient system and hence is often regarded as the optimal version of multi-carrier transmission schemes. The number of sub channels transmitted is fairly arbitrary with certain broad constraints, but in practical systems, sub-channels tend to be extremely numerous and close to each other. For example, the number of carriers in wireless LAN is 48 while for Digital Video Broadcast (DVB) it is as high as 6000 subcarriers. If we consider a single OFDM carrier, we can model the transmitted pulse as a sinusoid multiplied by a RECT function. In the frequency domain, the resulting spectrum has a sin(x)/x shape centered at the carrier frequency as shown in the Fig. 4. Fig. 4 A Single carrier of OFDM III. GENERATION OFOFDM SYMBOLS A baseband OFDM symbol can be generated in the digital domain before, modulating on a carrier for transmission. To generate a baseband OFDM symbol, a serial digitized data RES Publication 2012 Page 22

5 Fig. 11 estimation with M-PSK Fig. 9Comb type pilot arrangement In block-type pilot based channel estimation, OFDM channel estimation symbols are transmitted periodically, in which all sub-carriers are used as pilots. If the channel is constant during the block, there will be no channel estimation error since the pilots are sent at all carriers. The estimation can be performed by using either LSE or MMSE [11], [12]. In comb-type based channel estimation, the n p pilot signal is uniformly inserted into X(k) according to following equation: X k = X ml + l = {X p k l = 0 (12) = {inf data l = 1,2,, L 1 Where L is number of carrier/n p. VII. RESULTS In the simulation we consider a system operating with a bandwidth of 500 khz, divided into 64 tones with total symbol period of 138 Cs, of which 10 Cs is a cyclic prefix. Sampling is performed with a 500 khz rate. A symbol thus consists of 40 samples, five of which are contained in the cyclic prefix. 10,000 channels are randomized per average SNR. Fig. 10 estimation with M-QAM VIII. CONCLUSION In this work, studied of LSE and MMSE estimators for both block type and comb type pilot arrangement. The estimators in this study can be used to efficiently estimate the channel in an OFDM system given certain knowledge about channel statistics. The MMSE estimators assume a priori knowledge of noise variance and channel covariance. Moreover, its complexity is large compare to the LSE estimator. REFERENCES [1] Rappaport, T., Wireless Communication: Principles and Practice. New Jersey: PrenticeHall, [2] Chang, R., Synthesis of band limited Orthogonal Signals for multichannel datatransmission. Bell System Technical Journal. vol. 46, (December 1996): pp [3] Proakis, J., Digital Communications. New York: McGraw-Hill, [4] Torrance, J., and Hanzo, L., Comparative study of pilot symbol assisted modem systems. Proceedings of IEEE conference on Radio Receivers and Associated Systems, Bath UK, (September 1995): pp [5] Weinstein, S. and Ebert, P., Data Transmission by Frequency Division Multiplexing using the Discrete Fourier Transform. IEEE Transaction Communication Technology. vol. COM-19, (October 1971): pp Current version 06 January 2003 [6] Bello, P. A., Selective Fading limitations of the KATHRYN modem and some systemdesign considerations. IEEE Transaction Communication Technology. vol.com-13,(1965): pp [7] Zimmerman, M. and Krisch, A., The AN/GSC-10/KATHRYN/ variable rate datamodem for HF radio. IEEE Transaction Communication Technology. vol.ccm-15,(april 1967): pp [8] Hirosaki, B., An analysis of automatic equalizers for orthogonally multiplexed QAMsystems, IEEE Transaction Communication Technology. vol. COM-28, (January 1980):pp [9] Peled, A. and Ruiz, A., Frequency Domain Data Transmission using ReducedComputational Complexity Algorithms. Proceedings of International Conference onacoustics. vol. 3, (April 1980): pp [10] Ketel, I., The Multitone. IEEE Transaction on Communication. vol. 37, (February 1989): pp [11] Coleri, S., Ergen, M., Puri, A. and Bahai, A., Estimation Techniques based on Pilot Arrangement in OFDM systems, IEEE Transaction on Broadcasting. (September 2002). [12] Bahai, A. R. S. and Saltzberg, B. R., Multi-Carrier Digital Communications: Theory and Applications of OFDM. Kluwer Academic/Plenum, RES Publication 2012 Page 25

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