# Bit error rate simulation using 16 qam technique in matlab

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3 Fig 1(B): Receiver Fig1: Block diagram of OFDM Transceiver 2. Simulation Tool MATLAB (matrix laboratory) is a calculating environment and fourth-generation programming language. Developed by Math Works, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java. Matlab is an ideal tool for simulating digital communications systems, it is possible due to its easy language and excellent information revelation properties. Bit-error- rate testing of modems is most frequently simulation tasks in the field of digital communications. The BER (Bit-error-rate) performance of a receiver is a figure of merit which allows comparison of different designs in a blond style. Before we can performance bit-error-rate test, we must precisely understand the meaning of these samples. We must know the purpose of representation the signal values of these samples. We must also know the time interval between successive samples. For communications simulations, the numeric value of the sample represents the amplitude of the continuous-time signal at a specific instant in time. Ts is the time between successive samples. It shows us how often the sampling of continuous time signal has been performed. In place of Ts, we usually specify the sampling frequency fs, which is the inverse of Ts. 3. Working Methodology Orthogonal Frequency Division Multiplexing (OFDM) system has been considered as one of the strong standard candidates for the next generation mobile radio communication systems. Multiplexing a serial data symbol stream into a large number of orthogonal sub-channels makes the OFDM signals spectral bandwidth efficient. It has been shown that the performance of OFDM system over frequency selective fading channels is better than that of the single carrier modulation system. One of the major drawbacks of OFDM system is not well synchronized which brings on the OFDM signal distortion. Recently many works [1], [2], [3], [4], [5], [6], have been done in developing a method to reduce the effect of unsynchronization. The simple and widely used method is frequency synchronization. Block coding [3], the encoding of an input data into a codeword with low PAPR is another well known technique to reduce the effect of un-synchronization problem, but it incurs the rate decrease. Convolutional coding may be used with Viterbi decoding for synchronization. 3.1 Proposed method This proposed method use convolution decoding and pilot for synchronization in OFDM. Following diagram of proposed algorithm given below: ~ 61 ~

5 Parallel conversion, Cyclic Prefix Removal, IFFT, Pilot removal. Fig 4 represents OFDM signal input (graphical representation between amplitude and time) 4.6 Plotting the Result in terms of EbNo and BER Here we first find SNR by using the following formula ber=no_of_error/(nbitpersym*nsym); After calculating it, we move on to plot the result in terms of EbNo(energy per bit noise spectral density)and BER. 4.7 Trellis code generation at transmitter Here we generate the trellis code by using this code : trellis = poly2trellis(constlen, codegen); After generation we do interleaving and binary to decimal conversion QAM Modulation at transmitter We use the following code for 16-QAM y = qammod(dec,m); After QAM modulation we do pilot insertion, IFFT, Add cyclic extension at transmitter. 4.9 Starting of SNR loop and Addition of Additive White Gaussian Noise ofdm_sig=awgn(cext_data,snr,'measured'); Fig 4: OFDM Signal Fig 5 displays the scatter plot for QAM 16 point without interference of AWGN Run Receiver For receiving the transmitted data by verious processes we use the code given below rxed_sig(i)=ofdm_sig(i+16); After this we code for FFT, Pilot Synchronization, Demodulation, Decimal to binary conversion,de-interleaving and Decoding BER Calculation and End of SNR loop BER(si,o)=errors/length(data); 4.12 Plotting of BER vs SNR Curve semilogy(snr,ber(2,:),'.-'); 5. Results The main aim of this dissertation is to simulate the OFDM systems by using pilot insertion and cyclic prefix for the reduction of BER. The aim of doing the simulation is to measure the performance of OFDM with BER and SNR calculation under Additive White Gaussian Noise channel conditions, under 16 point QAM modulation scheme. All simulations are performed in MATLAB (R2010a). Fig 5: Scatter plot of 16 QAM without Interference Fig 6 displays a comparison of BER and SNR of proposed method and simple OFDM by 16-QAM modulation scheme with a number of data sub-carriers 58 and FFT size is Simulation Results Fig 3 represents the randomly generated transmitted data (showing data points and phase representation). Fig 3: Randomly Generated Transmitted Data ~ 63 ~ Fig 6: BER vs Ebno. Curve

6 Fig 7 displays graphical representation shows a comparison between BER and SNR using viterbi algorithm method and convolutional codes. 6. U. Tureli, H. Liu and M. D. Zoltowski, OFDM Blind Carrier Offset Estimation: ESPRIT, IEEE Trans. Commun., vol. 48, pp , September Wikipedia, Free Encyclopaedia, Article On Bit ErrorRate 8. B. Sklar, Digital Communications: Fundamentals And Applications, CH. 4, Englewood Cliffs, Nj: Prentice Hall, Wikipedia, Free Encyclopaedia, Article On Signal To Noise Ratio The Math Works, Inc., The Student Edition Of Matlab Version 7 User's Guide, Prentice Hall, ISBN , M. Jeruchim, Techniques For Estimating The Bit Error Rate In The Simulation Of Digital Communication Systems," IEEE J. Select. Areas Communication.,Vol.sac p , JAN Fig 7: BER vs SNR Curve 7. Conclusion The performance of OFDM systems depends on the signal quality seen by the receiver. The main advantage of the work done is as follows: The important parameters in viterbi algorithm for synchronization problem reduction have been studied through MATLAB simulation. Here the convolution method has been used to reduce the effect of error in OFDM. Viterbi algorithm is used for decoding purposes. Computer simulations have shown that: Error between simple OFDM method and convolution method in terms of bit error rate, taking different values of signal to noise ratio. Outputs are shown in graphical representation between BER and S/N ratio, which is known as bit error probability curve. Our algorithm improves the accuracy compare to simple OFDM by: 10-1 at 0db SNR for simple OFDM and 10-3 at 0db SNR for proposed method (Convolution OFDM). This method shows here the better result as compared to simple OFDM. 8. References 1. B. Ai et al, On the synchronization techniques for wireless OFDM systems, IEEE Transactions on Broadcasting, vol. 52, no. 2, pp , June C. R. N. Athaudage, K. Sathananthan and R. R. V. Angiras, Enhanced Frequency Synchronization for OFDM Systems using Timing Error Feedback Compensation, IEEE PIMRC 2004, September J.J. van de Beek, M. Sandell and P. O. B Orjesson, ML Estimation of Time and Frequency Offset in OFDM, IEEE Trans. Signal Processing, vol. 45, pp , July M. Morelli, C.-C. Kuo and M.-O. Pun, Synchronization techniques for orthogonal frequency division multiple access (OFDMA) A tutorial review, Proceedings of the IEEE, vol. 95, no. 7, pp , July S. A. Fechtel, OFDM carrier and sampling frequency synchronization and its performance on stationary and mobile channels, IEEE Transactions on Consumer Electronics, vol. 46, no. 3, pp , Aug ~ 64 ~

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