In this tutorial we show how to model QPSK communication system and how to analyze the BER(Bit Error Rate) Performance. This is the 15th tutorial on Modeling digital communication systems using Simulink.

The QPSK communication system is one of the digital modulation technique in digital communication. It is widely used digital modulation method in telecommunication and wireless communication systems. This Modeling and Analysis of BER performance of QPSK in Simulink tutorial will show you step by step how to create QPSK model in Simulink, how to set the parameters and how to calculate the Probability of Error or BER. We also show how to analyze the performance under AWGN channel assumption with the theoritical calculated BER. This allows you to know how to model QPSK digital modulation and then compare with other digital communication system such as BPSK under the same AWGN channel environment. If you want to learn how and where digital modulation systems are used see the following free books:

The QPSK modeled system is as shown below.

Starting from the source on the left side we have a Random integer generator. The random integer source specifies M=4 with a sample time=1 s.

The QPSK Modulator Parameters setting is shown below. For QPSK the M-ary number has to set to 4. The phase offset is pi/4, and integer type is Integer.

The AWGN channel setting is shown below. Again as in previous tutorial with BPSK(see Frame based BPSK modulation/demodulation with AWGN), the seed is set to 67 but now here the Eb/No is set to 6dB. The input signal power is still 1W and the symbol period is also still 1s.

If you look at the Scope 2, you will see the random source signal output and the noisy real and imaginary QPSK signals.

If you click on the two scatter blocks you will see the constellation diagram for the QPSK signal and the noisy QPSK signal as shown below.

In the figure above, on the left side, you will see the original QPSK signal at phase angles located

at +𝜋/4,3 𝜋/4,-3 𝜋/4,−𝜋/4. On the right side, you see multiple QPSK corrupted with noise due to the simulation time of 100,000 s.

Modeling and Analysis of BER performance of QPSK in Simulink is yet not complete. We now see how to calculate and analyze BER performance.

After the AWGN channel block you can see the QPSK demodulator whose setting is similar to the QPSK modulator. Then after the demodulator you can see we have used the Error Rate Calculation block that determines BER using the input and the output. After simulation you will find that the simualted probability of error, Ps, is 0.04541 for Eb/No of 6dB. The theoretical BER,P is 0.0455 which can be calculated by the following formula for QPSK.

where 𝛾b is the SNR per bit, Eb/No. Since QPSK symbols have two bits per symbol, the symbol SNR, Es/No =2Eb/No or 𝛾s = 2𝛾b. Then for 𝛾b = 3 dB or 𝛾s = 6 dB, the theoretical QPSK symbol error rate in AWGN is 0.0455. The simulated symbol error rate for 𝛾s = 6 dB is 0.04541 based on the 100,000 s simulation time and agrees reasonably with the theoretical symbol error rate.

This Modeling and Analysis of BER performance of QPSK in Simulink tutorial will help you in many of the other digital modulation/demodulation modeling and analysis. For using matlab programming language for modeling and analysis of QPSK modulation see matlab code for qpsk modulation and demodulation.

The QPSK communication system is one of the digital modulation technique in digital communication. It is widely used digital modulation method in telecommunication and wireless communication systems. This Modeling and Analysis of BER performance of QPSK in Simulink tutorial will show you step by step how to create QPSK model in Simulink, how to set the parameters and how to calculate the Probability of Error or BER. We also show how to analyze the performance under AWGN channel assumption with the theoritical calculated BER. This allows you to know how to model QPSK digital modulation and then compare with other digital communication system such as BPSK under the same AWGN channel environment. If you want to learn how and where digital modulation systems are used see the following free books:

The QPSK modeled system is as shown below.

Starting from the source on the left side we have a Random integer generator. The random integer source specifies M=4 with a sample time=1 s.

The QPSK Modulator Parameters setting is shown below. For QPSK the M-ary number has to set to 4. The phase offset is pi/4, and integer type is Integer.

The AWGN channel setting is shown below. Again as in previous tutorial with BPSK(see Frame based BPSK modulation/demodulation with AWGN), the seed is set to 67 but now here the Eb/No is set to 6dB. The input signal power is still 1W and the symbol period is also still 1s.

If you look at the Scope 2, you will see the random source signal output and the noisy real and imaginary QPSK signals.

If you click on the two scatter blocks you will see the constellation diagram for the QPSK signal and the noisy QPSK signal as shown below.

In the figure above, on the left side, you will see the original QPSK signal at phase angles located

at +𝜋/4,3 𝜋/4,-3 𝜋/4,−𝜋/4. On the right side, you see multiple QPSK corrupted with noise due to the simulation time of 100,000 s.

Modeling and Analysis of BER performance of QPSK in Simulink is yet not complete. We now see how to calculate and analyze BER performance.

After the AWGN channel block you can see the QPSK demodulator whose setting is similar to the QPSK modulator. Then after the demodulator you can see we have used the Error Rate Calculation block that determines BER using the input and the output. After simulation you will find that the simualted probability of error, Ps, is 0.04541 for Eb/No of 6dB. The theoretical BER,P is 0.0455 which can be calculated by the following formula for QPSK.

where 𝛾b is the SNR per bit, Eb/No. Since QPSK symbols have two bits per symbol, the symbol SNR, Es/No =2Eb/No or 𝛾s = 2𝛾b. Then for 𝛾b = 3 dB or 𝛾s = 6 dB, the theoretical QPSK symbol error rate in AWGN is 0.0455. The simulated symbol error rate for 𝛾s = 6 dB is 0.04541 based on the 100,000 s simulation time and agrees reasonably with the theoretical symbol error rate.

This Modeling and Analysis of BER performance of QPSK in Simulink tutorial will help you in many of the other digital modulation/demodulation modeling and analysis. For using matlab programming language for modeling and analysis of QPSK modulation see matlab code for qpsk modulation and demodulation.

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