Goals
According to the flow chart above, we need to generate a binary sequence of 0's and 1's, the length of which is 2N bits, that occur with equal probability and are mutually independent for which a ‘rand’ function is used. The data is then passed through a QPSK modulator to produce N complex symbols of {±1 , ±1j}. At the receiver, noise is added to the transmitted signal and the resultant signal is then passed through the QPSK demodulator to produce estimates of the transmitted binary data. After that, the demodulator output is compared with the original sequence, and finally an error counter is used to count the number of bit errors. The above procedure is repeated for various values of noise power. In other words, the signal-to-noise ratio (SNR), i.e. Eb/No is varied indefinitely.
Requirement
Using the above …show more content…
The analytical curve is a uniform degradation as a function of BER in the y-axis and SNR in the x-axis.
We infer from graph 3.5 that with the number of bits N= 10^7, ymin = 10^-5 and ymax = 0.5, the simulated curve coincides with the analytical curve at all instances ranging from 10^-1 to 10^-5.
The simulation is complete with the curve uniformly degrading along the x-axis. The simulation curve is depressing along the analytical curve, thereby producing an almost ideal BER Curve.
We can also conclude that if the number of bits is increased and a less number of instances are chosen along the y-axis, the BER to SNR curve can be ideal.
The QPSK performance along the x and y axis is seen to be ideal when the number of bits N is increased to 10^7 and ymin is limited to 10^-5.
4 Conclusion
To determine the BER performance of a QPSK signal as a function of Bit Error Rate and Signal to Noise Ratio, the analytical and simulated curves of the QPSK signals are
According to the flow chart above, we need to generate a binary sequence of 0's and 1's, the length of which is 2N bits, that occur with equal probability and are mutually independent for which a ‘rand’ function is used. The data is then passed through a QPSK modulator to produce N complex symbols of {±1 , ±1j}. At the receiver, noise is added to the transmitted signal and the resultant signal is then passed through the QPSK demodulator to produce estimates of the transmitted binary data. After that, the demodulator output is compared with the original sequence, and finally an error counter is used to count the number of bit errors. The above procedure is repeated for various values of noise power. In other words, the signal-to-noise ratio (SNR), i.e. Eb/No is varied indefinitely.
Requirement
Using the above …show more content…
The analytical curve is a uniform degradation as a function of BER in the y-axis and SNR in the x-axis.
We infer from graph 3.5 that with the number of bits N= 10^7, ymin = 10^-5 and ymax = 0.5, the simulated curve coincides with the analytical curve at all instances ranging from 10^-1 to 10^-5.
The simulation is complete with the curve uniformly degrading along the x-axis. The simulation curve is depressing along the analytical curve, thereby producing an almost ideal BER Curve.
We can also conclude that if the number of bits is increased and a less number of instances are chosen along the y-axis, the BER to SNR curve can be ideal.
The QPSK performance along the x and y axis is seen to be ideal when the number of bits N is increased to 10^7 and ymin is limited to 10^-5.
4 Conclusion
To determine the BER performance of a QPSK signal as a function of Bit Error Rate and Signal to Noise Ratio, the analytical and simulated curves of the QPSK signals are