This is the 13th tutorial on Modeling digital communication systems using Simulink where we will show how to use another noise channel other than AWGN. In the previous tutorials Determination of BPSK BER performance under AWGN and afterwards Comparison of Simulated and Theoretical BPSK BER we used the AWGN noise channel and plotted the BER performance vs the Bit Energy per Noise for binary modulated BPSK digital communication system. Here we want to use a direct method of adding gaussian noise as the communication channel.

The following shows how to model a BPSK communication system with Gaussian Noise Generator instead of AWGN.

In this modeling, most of the parameter are same as that in AWGN case. The random integer generator has seed of 37. The sample time and symbol period both are set to 1s. The run time is 100000s and the input signal power is 1W.

For the two Gaussian noise generator, the gauss random noise seeds are 43 and 37. The variances are 0.25 and mean is 0. The Gaussian noise is a complex signal of the form a+jb, where a the real part has different seed then the b, the imaginary part, which has different seed number. This is to ensure that the real and imaginary part of the noise signal are statistically independent. See figure below.

In the figure you can see that we have used several running variance blocks. These are used to compute the power of the different signals. The Display 1 displays the BPSK modulated signal power which is 1. The Display 2 displays noise power which is 0.4994. These together gives Eb/No of 3dB. The Display 3 is showing the noisy BPSK signal power level which is 1.246. The simulated BER is 0.02266, and is close to the theoretical BER=0.0229 for 𝛾b =3 dB. The figure below illustrates the real and imaginary parts of the Gaussian noise generator for a variance equal to 0.25 used in both the real and imaginary Gaussian noise blocks.

The following shows how to model a BPSK communication system with Gaussian Noise Generator instead of AWGN.

In this modeling, most of the parameter are same as that in AWGN case. The random integer generator has seed of 37. The sample time and symbol period both are set to 1s. The run time is 100000s and the input signal power is 1W.

For the two Gaussian noise generator, the gauss random noise seeds are 43 and 37. The variances are 0.25 and mean is 0. The Gaussian noise is a complex signal of the form a+jb, where a the real part has different seed then the b, the imaginary part, which has different seed number. This is to ensure that the real and imaginary part of the noise signal are statistically independent. See figure below.

In the figure you can see that we have used several running variance blocks. These are used to compute the power of the different signals. The Display 1 displays the BPSK modulated signal power which is 1. The Display 2 displays noise power which is 0.4994. These together gives Eb/No of 3dB. The Display 3 is showing the noisy BPSK signal power level which is 1.246. The simulated BER is 0.02266, and is close to the theoretical BER=0.0229 for 𝛾b =3 dB. The figure below illustrates the real and imaginary parts of the Gaussian noise generator for a variance equal to 0.25 used in both the real and imaginary Gaussian noise blocks.

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