Computing For Nation Development, February 08 09, 2008 Bharati Vidyapeeth s Institute of Computer Applications and Management, New Delhi OFDM Systems For Different Modulation Technique Mrs. Pranita N. Palsapure Lecturer Y.C.C.E. Nagpur, pranita_palsapure@yahoo.co.in ABSTRACT This paper includes design of OFDM transmitter and receiver. The author has proposed the design of OFDM using Matlab 7.01. The digital modulation schemes such as BPSK, QPSK, 16PSK were selected to assess the performance of the designed OFDM system. From the simulation result it is observed that the BPSK allows BER to be improved in a noisy channel at the cost of maximum data transmission capacity. Use of QPSK and 16PSK allows higher transmission capacity but at the cost of slight increase the probability of error. The probability of error is more for 16PSK than QPSK. From the result author concluded that use of OFDM with QPSK, 16PSK is beneficial for long distance communication link where as short distance transmission link OFDM with BPSK will preferable.. KEYWORDS OFDM, QPSK, BPSK,16PSK,BER,SNR INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission technique, which divides the available spectrum into many carriers, each one being modulated by a low rate data stream. OFDM is similar to FDMA in that the multiple user access is achieved by subdividing the available bandwidth into multiple channels, which are then allocated to users. However, OFDM uses the spectrum much more efficiently by spacing the channels much closer together. This is achieved by making all the carriers orthogonal to one another, preventing interference between the closely spaced carriers. Coded Orthogonal Frequency Division Multiplexing (COFDM) is the same as OFDM except that forward error correction is applied to the signal before transmission. This is to overcome errors in the transmission due to lost carriers from frequency selective fading, channel noise and other propagation effects. For this discussion the terms OFDM and COFDM are used interchangeably, as the main focus of this thesis is on OFDM, but it is assumed that any practical system will use forward error correction, thus would be COFDM. OFDM overcomes most of the problems with both FDMA and TDMA. OFDM splits the available bandwidth into many narrow band channels (typically 100-8000). The carriers for each channel are made orthogonal to one another, allowing them to be spaced very close together, with no overhead as in the FDMA example. Because of this there is no great need for users to be time multiplex as in TDMA, thus there is no overhead associated with switching between users. The orthogonality of the carriers means that each carrier has an integer number of cycles over a symbol period. Due to this, 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 then to be spaced as close as theoretically possible. This overcomes the problem of overhead carrier spacing required in FDMA. Each carrier in an OFDM signal has a very narrow bandwidth (i.e. 1 khz), thus the resulting symbol rate is low. This results in the signal having a high tolerance to multipath delay spread, as the delay spread must be very long to cause significant inter-symbol interference (e.g. > 500 μsec). 1. OFDM GENERATION To generate OFDM successfully the relationship between all the carriers must be carefully controlled to maintain the orthogonality of the carriers. For this reason, OFDM is generated by firstly choosing the spectrum required, based on the input data, and modulation scheme used. Each carrier to be produced is assigned some data to transmit. The required amplitude and phase of the carrier is then calculated based on the modulation scheme (typically differential BPSK, QPSK, or QAM). The required spectrum is then converted back to its time domain signal using an Inverse Fourier Transform. In most applications, an Inverse Fast Fourier Transform (IFFT) is used. The IFFT performs the transformation very efficiently, and provides a simple way of ensuring the carrier signals produced are orthogonal. The Fast Fourier Transform (FFT) transforms a cyclic time domain signal into its equivalent frequency spectrum. This is done by finding the equivalent waveform, generated by a sum of orthogonal sinusoidal components. The amplitude and phase of the sinusoidal components represent the frequency spectrum of the time domain signal. The IFFT performs the reverse process, transforming a spectrum (amplitude and phase of each component) into a time domain signal. An IFFT converts a number of complex data points, of length that is a power of 2, into the time domain signal of the same number of points. Each data point in frequency spectrum used for an FFT or IFFT is called a bin. The orthogonal carriers required for the OFDM signal can be easily generated by setting the amplitude and phase of each frequency bin, then performing the IFFT. Since each bin of an IFFT corresponds to the amplitude and phase of a set of orthogonal sinusoids, the reverse process guarantees that the carriers generated are orthogonal.
Figure 1: Basic FFT, OFDM transmitter and receiver 2. ADDING A GUARD PERIOD TO OFDM One of the most important properties of OFDM transmissions is its high level of robustness against multipath delay spread. This is a result of the long symbol period used, which minimizes the inter-symbol interference. The level of multipath robustness can be further increased by the addition of a guard period between transmitted symbols. The guard period allows time for multipath signals from the pervious symbol to die away before the information from the current symbol is gathered. The most effective guard period to use is a cyclic extension of the symbol. If a mirror in time, of the end of the symbol waveform is put at the start of the symbol as the guard period, this effectively extends the length of the symbol, while maintaining the orthogonality of the waveform. Using this cyclic extended symbol the samples required for performing the FFT (to decode the symbol), can be taken anywhere over the length of the symbol. This provides multipath immunity as well as symbol time synchronization tolerance. Other variations of guard periods are possible. One possible variation is to have half the guard period a cyclic extension of the symbol, as above, an the other half a zero amplitude signal. Using this method the symbols can be easily identified. This possibly allows for symbol timing to be recovered from the signal, simply by applying envelop detection. The disadvantage of using this guard period method is that the zero period does not give any multipath tolerance, thus the effective active guard period is halved in length. An OFDM system was modelled using Matlab to allow various parameters of the system to be varied and tested. The aim of doing these simulations was to measure the performance of OFDM under different modulation technique and compare their result. 3. OFDM MODEL USED The OFDM system was modelled using Matlab and is shown in Figure 16. A brief description of the model is provided below Figure 2: OFDM Model used for simulations 3.1 SERIAL TO PARALLEL CONVERSION The input serial data stream is formatted into the word size required for transmission, e.g. 2 bits/word for QPSK, and shifted into a parallel format. The data is then transmitted in parallel by assigning each data word to one carrier in the transmission. 3.2 MODULATION OF DATA The data to be transmitted on each carrier is then differential encoded with previous symbols, then mapped into a Phase Shift Keying (PSK) format. Since differential encoding requires an initial phase reference an extra. Symbol is added at the start for this purpose. The data on each symbol is then mapped to a phase angle based on the modulation method. For example, for QPSK the phase angles used are 0, 90, 180, and 270 degrees. The use of phase shift keying produces a constant amplitude signal and was chosen for its simplicity and to reduce problems with amplitude fluctuations due to fading. 3.3 INVERSE FOURIER TRANSFORM After the required spectrum is worked out, an inverse fourier transform is used to find the corresponding time waveform. The guard period is then added to the start of each symbol. 3.4 GUARD PERIOD The guard period used was made up of two sections. Half of the guard period time is a zero amplitude transmission. The other half of the guard period is a cyclic extension of the symbol to be transmitted. This was to allow for symbol timing to be easily recovered by envelope detection. However it was found that it was not required in any of the simulations as the timing could be accurately determined position of the samples. After the guard has been added, the symbols are then
OFDM System For Different Modulation Technique converted back to a serial time waveform. This is then the base band signal for the OFDM transmission. 3.5 CHANNEL A channel model is then applied to the transmitted signal. The model allows for the signal to noise ratio, multipath, and peak power clipping to be controlled. The signal to noise ratio is set by adding a known amount of white noise to the transmitted signal. Multipath delay spread then added by simulating the delay spread using an FIR filter. The length of the FIR filter represents the maximum delay spread, while the coefficient amplitude represents the reflected signal magnitude 3.6 RECEIVER The receiver basically does the reverse operation to the transmitter. The guard period is removed. The FFT of each symbol is then taken to find the original transmitted spectrum. The phase angle of each transmission carrier is then evaluated and converted back to the data word by demodulating the received phase. The data words are then combined back to the same word size as the original data 4. SIMULATION RESULT FOR OFDM The OFDM model is simulated in Matlab 7.01 using communication tool box and related functions. OFDM model has been tested using different modulation technique such as BPSK, QPSK and 16PSK and their performance has been compaired. OFDM technique has been tested for different data type such as binary data, text file and.wav file and the result for one data type is comp aired for different modulation technique. 1 0.11905 0.24429 0.47619 2 0.08761 0.2381 0.4571 3 0.095238 0.21429 0.44714 4 0.071429 0.15905 0.4312 5 0.071429 0.15905 0.42857 6 0.047619 0.11905 0.412 7 0.0347 0.078619 0.41857 8 0.03 0.047619 0.387 9 0.02381 0.043619 0.35952 10 0.01381 0.02381 0.351 11 0.0108 0.02381 0.34714 12 0 0.01 0.321 13 0 0 0.30714 14 0 0 0.234 15 0 0 0.19048 16 0 0 0.1812 17 0 0 0.1781 18 0 0 0.12 19 0 0 0.095238 20 0 0 0.0645 Table 1:BER results of OFDM for binary file using 4.1 SIMULATION RESULT FOR BINARY FILE USING These are categorized as tabular results and graphical result. Signal to noise ratio also called as Eb/No, where Eb is bit energy and No is the noise energy. SNR values in db are varied and corresponding BER is noted for different modulation technique such as BPSK, QPSK and 16PSK. These results are tabulated as shown in Table 1.The graph also plotted to compaire the three modulation technique for binary data. The graph is as shown in Figure 3. Figure 3. Comparison of BPSK, QPSK and 16PSK for binary file
4.2 SIMULATION RESULT FOR TEXT FILE USING These result are tabulated as shown in Table 2.The graph also plotted to compare the three modulation technique for text file. The graph is as shown in Figure 4.. 1 0.089286 0.20833 0.3831 2 0.065476 0.19643 0.375 3 0.047619 0.185 0.35381 4 0.030667 0.17262 0.33667 5 0.020857 0.095238 0.32738 6 0.01381 0.083333 0.31762 7 0.9524 0.073571 0.30333 8 0.0039524 0.065476 0.28571 9 0.0029524 0.053333 0.23643 10 0 0.035714 0.21976 11 0 0.027619 0.20405 12 0 0.017857 0.1819 13 0 0.011905 0.17238 14 0 0.010857 0.15048 15 0 0.017 0.14833 16 0 0 0.1369 17 0 0 0.12667 18 0 0 0.11667 19 0 0 0.10881 20 0 0 0.10076 Table 2:BER results of OFDM for text file using 4.3 SIMULATION RESULT FOR.WAV FILE USING These result are tabulated as shown in Table 2.The graph also plotted to compare the three modulation technique for text file. The graph is as shown in Figure 4.. 1 0.085705 0.2192 0.39632 2 0.066654 0.18951 0.38308 3 0.049621 0.16299 0.36899 4 0.035778 0.13774 0.35634 5 0.025622 0.1127 0.34142 6 0.017741 0.092339 0.32802 7 0.011907 0.074143 0.31118 8 0.0079902 0.060154 0.29882 9 0.3381 0.048189 0.28434 10 0.003334 0.039193 0.2701 11 0.0022209 0.032567 0.2603 12 0.0014266 0.027354 0.24778 13 0.00090928 0.023696 0.23637 14 0.00069503 0.021245 0.22866 15 0.00040238 0.019176 0.2211 16 0.00020119 0.017446 0.21317 17 0.00012803 0.016532 0.20671 18 5.7483e- 0.015082 0.20323 19 3.3967e- 0.014616 0.19788 20 2.3516e- 0.013744 0.19512 Table 2:BER results of OFDM for.wav file using Figure 4. Comparison of BPSK, QPSK and 16PSK for text file Figure 5 Comparison of BPSK, QPSK and 16PSK for.wav file
OFDM System For Different Modulation Technique CONCLUSION OFDM makes efficient use of available spectrum by allowing overlapping among the carriers. It basically converts the high data rate stream in to several parallel lower data rate streams and their by eliminating the frequency selective fading. It has been seen that the OFDM is a power full modulation technique that is capable of high data rate and it able to eliminate ISI.It is computationally effective due to use of FFT technique to implement modulation and demodulation function The current status of research is that OFDM appears to be suitable modulation technique for high performance wireless communication. The digital modulation technique for OFDM system design are investigated which includes.however possible system performance gain may be obtained by dynamically choosing modulation technique. This is based on the user requirement parameter such as transmission data capacity and transmission distance. Using Matlab 7.01 and communication commands the performance of OFDM system was tested for three digital modulation technique namely BPSK, QPSK and 16PSK.From the observations conclusion drawn are as follows 1. It is observed that OFDM system with QPSK modulation scheme can tolerate transmission with SNR in excess of 13db for binary data. The result obtain for BER Vs SNR show low BER for larger value of SNR. 2. The result further show that BER rapidly increases as SNR below 7db. This is because of the fact that QPSK uses 2 bit per symbol and 16PSK uses 3 bit per symbol. Hence QPSK and 16PSK is easily effected by the noise.so OFDM with QPSK and 16PSK require larger transmit power. 3. In case of OFDM with BPSK the BER less for low SNR as compaired to QPSK and 16PSK.Thus BPSK allow the BER to be improved in the noisy channel at the cost of transmission data capacity. 4. Comparison of three plots drawn for BPSK, QPSK and 16psk for binary data, text file and.wav file clearly indicate that for same value of SNR larger BER will be there in QPSK and 16PSK compaired to BPSK. 5 Finally we concluded that OFDM system with BPSK scheme is suitable for low capacity short distance application while OFDM with QPSK schemes useful for large capacity long distance application at the cost of slight increase in the bit error rate. OFDM promises to be suitable modulation technique high capacity wireless communication sin future. [3] Comparison of orthogonal frequency multiplexing CDMA technique [4] MATLAB7.1 software communication commands. [5] Simon Haykin, Digital communication, Wiley publication Ltd, Singapore. [6] T.S.Rappaort, Wireless Communications Principal & practice second edition. [7] Dr. K. Feher, Wireless Digital communications Prentice- Hall of India private limited. [8] J.G. Prokis, M. Salehi, Contemporary communications systems using MATLAB. FUTURE SCOPE OFDM system can be implemented for different channel and for varying different channel condition such as peak power clipping and multipath condition. REFERENCES [1] Stefab Kaiser, OFDM code division multiplexing in Fading channel IEEE transaction on communication vol.50 no.8 AV2002 [2] Zovan Cvetkovic Modulating waveforms for OFDM