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INTERNATIONAL and Communication Engineering & Technology (IJECET), International Journal of Electronics JOURNAL OF ELECTRONICS AND ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) IJECET Volume 4, Issue 3, May – June, 2013, pp. 162-176 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) ©IAEME www.jifactor.com SIMULATION OF OFDM MODULATION ADAPTED TO THE TRANSMISSION OF A FIXED IMAGE ON DISTURBED CHANNEL Louis Paul Ofamo Babaga, Ntsama Eloundou Pascal Physics Department, Faculty of Sciences/ University of Ngaoundere, P. O; Box 454 Ngaoundere, Cameroon ABSTRACT In recent years, the speed in the transmission of audio and video data is a major concern. Thus, in this paper we present the results of the modulated OFDM (Orthogonal Frequency Division Multiplexing) still images that is based on the fast Fourier transform (FFT: Fast Fourier Transform) digital transmission. These results are obtained from a chain of communication developed in MATLAB. We evaluate the performance of the transmission system in terms of visual quality of the image reception (98% of the original image). We also obtain the different values of SNR, TEB, and other important parameters relying on the classic OFDM with a guard interval of time corresponding to 25% of the useful symbol period, and the modified OFDM, by just reducing that interval. The results are presented according to three patterns of M-PSK modulation frequency used in simulation. Namely: BPSK, QPSK and 16PSK and by extension, 256PSK modulation. It should be noted that convolutional coding is used to improve transmission quality. Keywords: Digital transmission, Orthogonal Frequency Division Multiplexing (OFDM), FFT, cyclic time guard. I. INTRODUCTION Future mobile radio communication systems that can provide diverse transmission services such as video, voice, image and other data, with high transmission rate and low power transmission, are of great interest. The problem of transmitting high data rates on the frequency of a fading channel is inter-symbol interference (ISI), which severely degrades system performance. OFDM digital subcarriers in multiple form by the orthogonal frequency division transmission, is a solution that can effectively combat ISI [1,2]. OFDM scheme, a bit stream is converted to high-speed trains with parallel low bit rate. Parallel streams are 162 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME modulated on orthogonal subcarriers. Spectrum of these subcarriers are closely spaced and covered with a high efficiency of bandwidth. The bandwidth of these subcarriers is small compared to the coherence bandwidth of the channel that is the sub-carriers are not subject to flat fading. OFDM also uses a time guard duty at the beginning of each symbol to remove any shorter than its length [3] ISI. In this paper, a study on combined use of convolutional coding and OFDM technique for the transmission of fixed images, simulated with Matlab is presented in four modulation formats (BPSK, QPSK, 16PSK and 256PSK). Thus, we propose a new division of time Guard in OFDM system (below 25% of a useful symbol period). This system will provide better picture quality reception. The paper is organized as follows: Section 2 provides background information on the OFDM modeling classic system, Section 3 presents the OFDM implemented modulator, Section 4 presents the disturbed channel, the overview of the demodulation is given in Section 5, and the results are given in Section 6. II. OFDM MODELING OFDM is a combination of modulation and multiplexing. We use DPSK modulation. In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard bands are not required. According [4], in an OFDM system, the carrier spacing 1/NT is f, where N is the number of carriers, and 1/T is the symbol rate [5]. With this carrier spacing, sub-channels can maintain orthogonality, although they overlap. Therefore, there is no inter-carrier interference (ICI) with ideal OFDM systems. The transmitted signal through the system for an OFDM symbol period is of following form: s (t ) = Re ∑ an h(t )e j 2π f nt +φ (1) n Where an is the data symbol transmitted on the n-th subcarrier, h(t) is the pulse shaping filter response. fn is the n-th subcarrier frequency fn = f + N∆f. As the number of OFDM subcarriers increases, the complexity of the modulator and demodulator is increased accordingly. However, the OFDM modulator and the demodulator can be implemented easily by use of inverse discrete Fourier transform (IDFT) and discrete Fourier transform (DFT), respectively. In practice, the couple IFFT/FFT (fast Fourier transforms inverse and direct) is used for its efficiency and speed. The time-domain coefficients Cm can be calculated by: N −1 2π nm 1 −j Cm = N ∑ an e n =0 N (2) Where an is the input to the IDFT block which is the data symbol for n-th subcarrier. Cm is the m-th output of IDFT block. After this operation, the parallel output of IDFT block Cm (m = 1, …, N - 1) is converted into a serial data stream. Figure 1 shows a block diagram of the OFDM transmitter. In equation (2), the data symbols of the frequency domain are converted to a series of samples in the time domain. 163 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME OFDM modulator DPSK Binary input Convolutional Serial IFFT Cyclic Parallel Modulation data (image) encoder to (IDFT) extension to (1, 2, 4 or 8 Parallel bits) addition Serial Communication Noise channel DPSK Binary Convolutional Parallel Demodulation FFT Cyclic Serial output data decoder to (1, 2, 4 or 8 bits) (DFT) extension to (image) Serial removal Parallel OFDM demodulator Figure 1. OFDM transmission and reception scheme * Preservation of orthogonality (Guard Interval) Following the same symbol arriving at a receiver by two paths will add causing two types of defects: • The intra symbol interference: addition of a symbol with itself slightly out of phase. • The inter symbol interference: adding a symbol with the following over the preceding slightly out of phase. Between each transmitted symbol, inserting a guard interval called "dead zone". In addition, the useful symbol duration is greater than the spread echoes. These two precautions will limit the inter-symbol interference. The time you issue differs from the information symbol period because it must take into account relevant periods between a "call time", which aims to eliminate the ISI continues despite the carrier orthogonality. Between the symbol periods (Ts), the useful (Tu) and the guard interval (Tg), therefore establish the relationship: Ts = Tu + Tg (3) Guard period IFFT output Tg Tu Ts Figure. 2. Time guard interval (cyclic prefix) Figure 2 shows the addition of a guard interval. The symbol period is extended so as to be greater than the integration period Tu. All carriers are cyclical inside you; it is the same for the entire modulated signal. The length of the interval is selected to match the expected level of multipath. It should not be too much of you, not to sacrifice too much data capacity (and spectral efficiency). For DAB (Digital Audio Broadcasting), a guard about you Tu/4 is 164 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME used; DVB (Digital Video Broadcasting) has more options, the largest being Tu/4 where OFDM modified guard interval ≤ Tu/4; we also simulated and compared with the results for Tg=Tu/4. At the receiver, the signal is converted to base band and sampled at the symbol rate 1/T. Then, N serial samples are converted to parallel data and passed to a DFT which converts the signal from time domain to frequency domain. To decrease the SNR required to achieve the required quality of the received image, a convolutional coding [5, 6, 7] is applied to the OFDM system. OFDM coding is the concatenation of the OFDM system with convolutional encoding. As seen, the convolutional coding is integrated into the OFDM system to improve the performance in noisy channels [5, 8]. The binary input information are first encoded using any encoding of convolutional code rate, then, they are modulated and transmitted through a channel with additive noise. In this model consider frequency selective time varying fading channel with additive noise, where the channel impulse response can be represented by the formula: L 1 h(t ) = L ∑ e (θ m =1 j m + 2π f Dm t ) δ (t −τ m ) (4) Where L is the number of reflected multipaths, τm is the delay, θm is the phase rotation and fDm is the Doppler frequency offset of the mth path. III. OFDM MODULATION Conventional OFDM can be modified by adjusting certain sensitive parameters and/or adding new elements that can improve the system. Thus, conventional time guard 25% of symbol period can be reduced to a reasonable value to avoid inter-symbol interference. In the classic OFDM, we could associate a convolutional coding to improve the visual quality of the image reception (See figure 1) 3.1 Convolutional coding According [4], simulation studies have been performed using convolutional coding with OFDM systems considered in figure 1. The parameters of the convolution coding are code rate (r) equal 1/2 and 1/3 with constraint lengths (K) equal 3 and 7 for each of them. For rate 1/2 the function generators are [6,7] for constraint length 3 and [133,171] for the constraint length 7, while for rate 1/3 are [6,7,7] for the constraint length 3, and [133,145,175] for the constraint length 7. All these generator vectors are represented in octal form. 3.2 Type of OFDM modulation implemented The flow of serial input data to be converted in parallel, the modulator has to add a number of zeros at the end of the data stream in order to adapt the data flow to enter a 2-D matrix [9]. Suppose a frame of data with 11530 symbols is being transmitted by 400 carriers with a capacity of 30 symbols/carrier, 470 zeros are padded at the end in order for the data stream to form a 30-by-400 matrix, as shown in Figure 3. Each column in the 2-D matrix represents a carrier while each row represents one symbol period over all carriers. 165 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME 400 30 Data Figure 3. Data transmission matrix 3.2.1 Differential Phase Shift Keying (DPSK) modulation The DPSK Baseband Modulator block modulates the signal using the differential phase shift keying method. The output is a baseband representation of the modulated signal. Before, differential encoding can be operated on each carrier (column of the matrix), an extra row of reference data must be added on top of the matrix [10]. The modulator creates a row of uniformly random numbers within an interval defined by the symbol size (order of PSK chosen) and patches it on the top of the matrix. Figure 4 shows a 31 by 400 resulted matrix. 400 Reference Row 31 Data Figure 4. Differentiated matrix For each column, starting from the second row (the first actual data symbol), the value is changed to the remainder of the sum of its previous row and itself over the symbol size (power 2 of the PSK order). Figure 5 show the signal modulated on a carrier; modulated in a symbol period. The DPSK modulator generates a matrix filled with complex number whose phases are translated into small amplitudes [11]. These complex numbers are then converted into a rectangular shape for further processing. The BPSK (symbol size is 2), 16PSK (symbol size is 24) and 256PSK (28) just follow the same principle. Figure 5. OFDM time signal (one symbol period in one carrier) 166 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME 3.2.2 Bloc of Inverse Fast Fourier Transform For a vector of length N, direct and inverse Fast Fourier transforms are given by formulas (5) and (6): N X ( k ) = ∑ x ( j )wNj −1)( k −1) ( (5) j =1 N 1 x( j) = N ∑ X ( k )w ( k =1 − j −1)( k −1) N 6) 2π i − With wN = e N Figure 6, shows an enlarged to a certain size of the IFFT matrix (e.g. size of the IFFT = 1024) and becomes a matrix 31×1024. Since each column of the matrix represents a DPSK support, their values are stored in the columns of the matrix where the IFFT their corresponding carriers should reside. Their combined values are stored in the columns corresponding to the locations of carriers combined. 1024 Data 31 Data conjugate 400 400 Figure 6. IFFT matrix All other columns in the IFFT matrix are set to zero. The matrix for signal transmission, Inverse Fast Fourier Transform (IFFT), and only the real part of the result is valuable, so that the imaginary part is eliminated [12]. 3.2.3 Insert periodic time guard An exact copy of the last portion of 25% of each symbol period (row of the matrix) is inserted at the beginning of the classic OFDM [13, 14]. The time of periodic care, is synchronization to the receiver for each symbol period demodulation signal reception [7]. The guard time is changed during the simulation. Modified OFDM has a guard interval of 20% of symbol period; Figure 7 shows a time domain representation of an OFDM Signal. Figure (7.a) shows a time domain representation of the conventional OFMD signal, where the guard period is fixes during all the frame of the data file of the image. Figure (7.b) shows a time domain representation of the new guard period where, Tg ≥ Tgm et Tu ≥ Tum 167 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME Copy Guard Period Guard Period a) IFFT IFFT output IFFT Tg Tu Symbol Symbol N-1 N+1 Ts Symbol N Copy Guard Guard b) IFFT Period IFFT output Period Tgm Tuu Symbol Symbol N-1 TS N+1 Symbol N Figure.7. Integration of the signal with guard interval The matrix becomes a matrix of modulation when converted to serial. A time- modulated in a data frame signal is generated. IV. COMMUNICATION CHANNEL Two properties of a typical communication channel are modelled. First, a variable clipping (off peak power) to MATLAB program is set by the user. The root mean square powers of the transmitted (RMSP) before and after the channel signal are indicated. Secondly, the channel noise is modeled by adding white Gaussian noise (AWGN) defines by: var iance of the mod ulated signal σ= (7) linear SNR SNRdB With linear SNR = 10 10 It has a mean of zero and a standard deviation equaling the square root of the quotient of the variance of the signal over the linear Signal-to-Noise Ratio, the dB value of which is set by the user as well. 168 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME V. OFDM DEMODULATION The DPSK Baseband Demodulator block demodulates a signal that was modulated using the differential phase shift keying method. The input is a baseband representation of the modulated signal. The input must be a discrete-time complex signal. The input can be either a scalar or a frame-based column vector. As any type of modulation/demodulation, the OFDM demodulation process is essentially an inverse of the OFDM modulation. And as the modulator, the OFDM demodulator demodulates the received data frame with respect to the transmitted image unless the data have a length less than the total number of symbols per frame designed [15]. For remove a periodic time guard, the previous example used in section 3.2 should continue to be used for illustrative purposes. Figure 8 shows that after converting a frame of discrete time signal from serial to parallel, a length of 25% of a symbol period is discarded from all rows. Thus the remaining is then a number of discrete signals with the length of one symbol period lined up in parallel. 1280 400 1024 400 31 30 31 30 Data Data Data Data Figure 8. Time Guard Removal VI. SIMULATION RESULTS The performance evaluation is done by measuring the quality of the received image. There are two ways to measure quality image: subjective based and objective based. The root mean square error (RMSE) and SNR are the most commonly objective based measure used due to their simplicity and ease of calculation. Root mean square error between the original and reconstructed image frame defined by: M −1 N −1 1 ∑ ∑ ( g ( x , y ) − f ( x, y ) ) 2 RMSE = (8) M ×N x =0 y =0 Where f(x,y) is the original image frame g(x,y) is the reconstructed image frame after the decompression process. M x N is dimensions of image frame In this paper objective and subjective criteria are used. The different values of BER (Bit Error Rate) and other parameters are presented in terms of four modulation formats used in the simulation. Namely: BPSK, QPSK, 16-PSK and 256-PSK. The performances of conventional OFDM system are evaluated by the following parameters: • Root Mean Square Power at the input of transmission channel (RMSPi), define by: 169 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME 1 −τs e if τ ≥ 0 RMSPi = s (9) 0 other • Root Mean square Power at the output of transmission channel (RMSPo), define by: 2 (τ −τ ) 1 − 2 s2 RMSPo = 2π s e si τ ≥ 0 (10) 0 other Where s is the RMS delay (root mean square) transmission. τ is the average delay introduced by the noisy channel and τ is the delay in the entrance channel. • Bit Error Rate define by: 1 BERBPSK, QPSK = 2 erfc ( SNRdB ) (11) The simulation is performed for two cases: the classical OFDM and modified OFDM. Simulation results are presented through the measurement of the quality of picture. The simulation parameters chosen are shown in Table 1. Table1. Parameters of simulation Parameters Values Source Image 256x256 Size IFFT size 2048 Number of 1009 Carriers Modulation BPSK, QPSK, 16PSK or Method 256PSK Peak Power 10 dB Clipping Signal-to-Noise [0….25] dB Ratio Information in table 1 can be modified depending on the configuration of OFDM system desired. The size of IFFT is 2048 and offers a channel bandwidth wide (20 MHz). Table 2 shows input images for four modulation formats and guard interval of 25% of useful symbol period. We observe that, for a SNR of 25 dB, reconstructed images are almost identical to the original image for BPSK and QPSK. For 16PSK and 256PSK modulations, the reconstructed images are noisy. A table 3, 4 and 5 shows the variation of different parameters. We find that the values of RMSPo are less than the RMSPi. For BPSK modulation, the BER is much reduced. For BPSK modulation with a SNR 25 dB, the quality of reconstructed image is 95.8%. 170 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME Table 6 shows the results of the modified OFDM. For OFDM modified, the image quality improves with SNR smaller and guard intervals of 20% of a useful symbol period. With a convolutional code rate of 1/3, a guard interval of 20% and a SNR of 16dB, received image are identical to the original image. Table 2. OFDM simulated classic transmission, original and received images with a guard time of 25% of the useful symbol period (without convolutional coding) Original image Received Received Received Received image image image image SNR = 0dB SNR = 5dB SNR = 10dB SNR = 25dB BPSK modulation with guard time interval 25% QPSK modulation with guard time interval 25% 16PSK modulation with guard time interval 25% 256PSK modulation with guard time interval 25% 171 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME Table 3. Numerical results for a BPSK SNR RMSPi RMSPo BER Image quality (dB) (dB) (dB) (%) (%) 0 15.32 13.34 17.31 23.00 5 14.75 11.86 2.03 84.91 10 15.11 10.95 0.16 91.50 25 17.30 9.10 0.00001 95.80 Table 4. Numerical results for a QPSK SNR RMSPi RMSPo BER Image quality (dB) (dB) (dB) (%) (%) 0 14.02 13.02 46.31 8.38 5 14.61 11.91 18.85 43.91 10 14.35 10.09 2.28 91.22 25 14.61 7.16 0.0001 93.80 Table 5. Numerical results for a 16PSK SNR RMSPi RMSPo BER Image quality (dB) (dB) (dB) (%) (%) 0 15.18 13.33 84.86 2.32 5 16 12.74 72.61 7.56 10 14.03 10.3 56.39 19.16 25 15.18 7.53 9.59 81.75 Table 6 clearly shows that changing the guard interval keeps below 25% of the symbol period; we get sharper images with SNR lower than those used by conventional OFDM. 172 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME Table 6. Modified OFDM: performances of image transmission with guard time intervals equal to 20% and a convolutional coding Original Image SNR guard image (dB) Interval Quality Image received modified (%) (%) Uncoded OFDM (QPSK) 19.00 20.00 97.05 Coded OFDM 17.00 20.00 97.90 r=1/2 (QPSK) Coded OFDM 16.00 20.00 98.90 r=1/3 (QPSK) Table 7 shows a comparison between conventional OFDM and modified OFDM. For a QPSK modulation format, comparisons show that the addition of a convolutional coding, and the modified of time guard of 25% to 20% of useful symbol period, we obtains reconstructed images identical to the original image. This shows the improvement of our system; hence the advantage of our modified OFDM system. The choice of QPSK format for the comparison is interesting. Table 7 shows the best image quality of modified OFDM for different values of SNR, to be compared with the results obtained from convolution OFDM. Compared to the work of [3, 4], obtained results are satisfactory and improved 173 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME Table 7. Comparison of results between conventional OFDM and OFDM modified conventional OFDM Modified OFDM Received image SNR 25 dB 25 dB Type of QPSK Without QPSK Without modulation convolutional coding convolutional coding Guard 25% 20% interval Image quality 94,80% 96.82% Received image SNR 20 dB 20 dB Type of QPSK Without QPSK With convolutional modulation convolutional coding coding r =1/2 Guard 25% 20% interval Image quality 93.50% 97.90% Received image SNR 17 dB 17 dB Type of QPSK Without QPSK With convolutional modulation convolutional coding coding r =1/3 Guard 25% 20% interval Image quality 92.2% 98.90% 174 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME VII. CONCLUSIONS In this study, we developed a simulation model of the transmission of fixed images in a noisy modified by the OFDM channel, using four modulation formats in Matlab. We have shown the interest of a guard interval time modification below 25% of the useful symbol period in order to recover a high quality signal transmitted. The addition of convolutional coding further improves the quality reception. The results obtained using three modulation formats (BPSK, QPSK, 16PSK) are acceptable, we get very close to 10-5 % for BPSK bit error rate. The simulation consisted in comparing the conventional OFDM transmission system (guard time of 25% of useful symbol period), and the modified OFDM with DPSK modulation (guard time of 20% of useful symbol period). The modified OFDM provides a better quality image than the classic reception system. Here the choice of the QPSK format for comparison is very important. However, in our future researches, we would to implement this OFDM modulation technique with QAM modulation format, and short guard time interval, so as to further clarify the received image. REFERENCES [1] J. Wang, "Broadband Wireless Communications: 3G and wireless LAN", Kluwer Academic Publishers 2001. [2] J. C. I. Chuang, "The Effects of Time Delay Spread on portable Radio Communications Channels with Digital Modulation", IEEE Journal on Selected Areas in Communications, Vol.5, No. 5, pp. 879-889, June 1987. [3] M. M. Salah, A. A. Elrahman, M. M. Mokhtar, "Performance Enhancement of Image Transmission using UEP overlayed UTG_OFDM scheme", 25th NRSC 2008, March 2008, Tanta Univ., Egypt. [4] M. M. Salah, A. A. Elrahman, A. Elmoghazy, "Unequal power allocation of image transmission in OFDM systems", 13th International Conference and technology, ASAT-13, May 26-28, 2009, Cairo, Egypt. [5] F. Al-Zuraiqi, "Analysis, Simulation and Modeling of mobile and fixed fading channel", B.S. thesis, Eastern Mediterranean University, June 2004. [6] A. R. S. Bahai, R. S. M. Burton, Ergen, "Multi-carrier Digital Communications: Theory and Applications of OFDM", Springer Science, Inc.2004. [7] W. Xiang, D. Waters, J. Barry, B. Walkenhorts, "Implementation and Experimental Results of a Three-Transmitter Tree-Receiver OFDM/ BLAST Testbed", IEEE Communication Magazine, December, 2004. [8] H. Schulze, L. Christian, "Theory and Applications of OFDM and CDMA", John Wiley & Sons, Ltd, 2005 [9] Y. Louët, "Mise en œuvre et performances des codes de Reed-Muller pour la réduction du facteur de crête dans la modulation O.F.D.M", Thèse présentée devant l’Université de Rennes 1. 2000. [10] E. Lawrey, "Adaptive Techniques for Multiuser OFDM", Ph.D. Thesis, James Cook University 2001. [11] L. Hui, L. Guoqing, "OFDM-Based Broadband Wireless Networks Design and Optimization Wiley", Interscience 2005. [12] L. Louis, P. Michael, "The Principles of OFDM", 2001. 175 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME [13] H., Juha, T. John, " OFDM Wireless LANs: A Theoretical and Practical Guide", SAMS 2001. [14] S. A. FECHTEL, "Ofdm carrier and sampling frequency synchronization and its performance on stationary and mobile channels", IEEE Trans. on Consumer Electronics, 46(3):438–441, Aug. 2000 [15] S. Gayatri, P. Prabhu, M. Shankar, "Simulation of Flat Fading Using MATLAB for Classroom Instruction", IEEE Transactions on education, vol. 45, no. 1, February 2002. [16] S.D.Giri and Prof.A.R.Salunke, “OFDM Based Wireless Lan Transmitter”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 4, Issue 2, 2013, pp. 469 - 476, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472. [17] Haritha.Thotakura, Dr. Sri Gowri .Sajja and Dr. Elizabeth Rani.D, “Performance of Coherent OFDM Systems against Frequency Offset Estimation under Different Fading Channels”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 3, Issue 1, 2012, pp. 244 - 251, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472. 176

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