This is the 11th simulink tutorial of Modeling digital communication systems using Simulink where we will show how to create simulink model for the determination of BPSK BER performance under AWGN. Also we show how to observe real and imaginary part of a signal like the BPSK modulated signal. Calculation of BER is important in digital communication system because it allows us to calculate the performance of the modulation/demodulation scheme. See Probability of Error and channel capacity vs SNR/bit for BPSK modulation where we have discussed this for BPSK system.

Before continuing reading this tutorial you might want to visit the previous tutorial Basic BPSK digital communication system with AWGN in Simulink. In the previous tutorial we had added the AWGN block and observed the errors in received symbols. Below is the simulink model figure of previous tutorial.

To this model we will now add the complex to real imaginary block at the output of BPSK block and at the output of the AWGN block and additional scope 2 and scope 3. This is shown below.

To view the BPSK modulator output signal as real and imaginary click on the scope 2. You can see that real part of the BPSK signal is antipodal signal with ±1 amplitude corresponding to random source outputs 0 and 1.

Similarly, the scope 3 displays the real and imaginary parts of the output of the AWGN block. The AWGN was set to Eb/No =4 dB.

You can compare the signals out from the BPSK modulator and AWGN output to observe how AWGN introduces errors.

Now the figure below displays the input to the BPSK modulator and the output from the BPSK demodulator on Scope 1. It is observed that with Eb/No =4 dB few demodulation errors are made so that the input and output sequences are the same; if the simulation time were extended, errors would be apparent.

Now add the error rate calculation block and its associated display as shown in figure below.

Double click on the Error Rate Calculation block to view/modify its parameter as shown below.

The receive delay and computation delay are both set to zero in this example.

The display block indicates the estimated error rate, the number of errors, and the total number of symbols used in the simulation The upper number in display block displays a BER = 0.0127 for the specified Eb/No of 4dB.

So in this way you can model BPSK modulation scheme and determine the BER for given Energy bit/noise ratio using AWGN channel.

Optionally one can also model BPSK modulation using matlab function block which is shown in Simulink BPSK model. We could have used pure matlab programming language also for modeling BPSK/ QPSK digital communication. For example in matlab code for qpsk modulation and demodulation we show how to write such modulation/demodulation scheme.

For book explaining different digital modulation/demodulation communication systems see books like Download Digital Modulation Techniques pdf free.

Before continuing reading this tutorial you might want to visit the previous tutorial Basic BPSK digital communication system with AWGN in Simulink. In the previous tutorial we had added the AWGN block and observed the errors in received symbols. Below is the simulink model figure of previous tutorial.

### Observing Real and Imaginary part of Signal

To this model we will now add the complex to real imaginary block at the output of BPSK block and at the output of the AWGN block and additional scope 2 and scope 3. This is shown below.

To view the BPSK modulator output signal as real and imaginary click on the scope 2. You can see that real part of the BPSK signal is antipodal signal with ±1 amplitude corresponding to random source outputs 0 and 1.

Similarly, the scope 3 displays the real and imaginary parts of the output of the AWGN block. The AWGN was set to Eb/No =4 dB.

You can compare the signals out from the BPSK modulator and AWGN output to observe how AWGN introduces errors.

Now the figure below displays the input to the BPSK modulator and the output from the BPSK demodulator on Scope 1. It is observed that with Eb/No =4 dB few demodulation errors are made so that the input and output sequences are the same; if the simulation time were extended, errors would be apparent.

### Determining BPSK BER Performance

Now add the error rate calculation block and its associated display as shown in figure below.

Double click on the Error Rate Calculation block to view/modify its parameter as shown below.

The receive delay and computation delay are both set to zero in this example.

The display block indicates the estimated error rate, the number of errors, and the total number of symbols used in the simulation The upper number in display block displays a BER = 0.0127 for the specified Eb/No of 4dB.

So in this way you can model BPSK modulation scheme and determine the BER for given Energy bit/noise ratio using AWGN channel.

Optionally one can also model BPSK modulation using matlab function block which is shown in Simulink BPSK model. We could have used pure matlab programming language also for modeling BPSK/ QPSK digital communication. For example in matlab code for qpsk modulation and demodulation we show how to write such modulation/demodulation scheme.

For book explaining different digital modulation/demodulation communication systems see books like Download Digital Modulation Techniques pdf free.

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