# International Journal of Emerging Technologies in Computational and Applied Sciences(IJETCAS)

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4 V. Probability of Error and Bit Error Rate Probability of error P(e) and bit error rate (BER) are often used interchangeably. Probability of error is a function of the carrier-to-noise power ratio (or, more specifically, the average energy per bit-to-noise power density ratio) and the number of possible encoding conditions used (M-ary). Carrier-to-noise power ratio is the ratio of the average carrier power (the combined power of the carrier and its associated sidebands) to the thermal noise power Carrier power can be stated in watts or dbm. Where C(dBm) = 10 log [C(watts) / 0.001] VI. Simulation Model With increase in number of bits there is increment in number of symbols to be transmitted. It results in decrement in distance between symbols so increase in probability of error. The constellation diagram for 32 QAM is simulated in MATLAB 2013 and shown in fig. 3. Figure 3: Constellation Diagram of 32-QAM In figure 4 the simulation results of SNR vs BER are shown using MATLAB Figure 4: Simulated SNR vs BER for General M-QAM VI. Conclusion Theoretically with increase in order of M-ary QAM the BER must be increased with increasing the M value for a particular level of signal to noise ratio because and the simulation results also follows it. So it is concluded that to increase the rate of transmission in digital communication using OFDM if it is implemented using higher order QAM then it will result in increase in error probability because the distance between the transmitted symbols is decreased which cause the fading between these symbols. VII. References [1] K.Jasbir and V.S.Anant, Implementation and performance evaluation of OFDM Transceiver IJSRD, pp , vol.2, issue 4, june [2] S. Zhang, S. C. Liew, and P. P. Lam, Hot topic: Physical-layer network coding, in Proc. ACM MobiCom, Sep. 2006, pp [3] P. Popovski and H. Yomo, The anti-packets can increase the achievable throughput of a wireless multi-hop network, in Proc. IEEE ICC, Jun. 2006, pp IJETCAS ; 2014, IJETCAS All Rights Reserved Page 227

5 [4] K. Lee and L. Hanzo, Resource-efficient wireless relaying protocols, IEEE Wireless Commun. Mag., vol. 17, no. 2, pp , Apr [5] M. Noori and M. Ardakani, On symbol mapping for binary physicallayer network coding with PSK modulation, IEEE Trans. WirelessCommun., vol. 11, no. 1, pp , Jan [6] H. J. Yang, Y. Choi, and J. Chun, Modified high-order PAMs for binary coded physical-layer network coding, IEEE Commun. Lett., vol. 14, no. 8, pp , Aug [7] M. P. Wilson, K. Narayanan, H. D. Pfister, and A. Sprintson, Joint physical layer coding and network coding for bidirectional relaying, IEEE Trans. Inf. Theory, vol. 56, no. 11, pp , Nov [8] W. Nam, S.-Y. Chung, and Y. H. Lee, Capacity of the gaussian twoway relay channel to within 1/2 bit, IEEE Trans. Inf. Theory, vol. 56, no. 11, pp , Nov [9] A. Goldsmith and S. G. Chua, Variable-rate variable-power M-QAM for fading channels, IEEE Trans. Commun., vol. 45, pp , Oct IJETCAS ; 2014, IJETCAS All Rights Reserved Page 228

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