In the previous article we saw about how QPSK modulation and demodulation can be done. This concept is extended further to simulate the performance of QPSK modulation technique over an AWGN. Transmitter: For the QPSK modulation , a series of binary input message bits are generated. In QPSK, a symbol contains 2 bits. The generated binary bits are combined in terms of two bits and QPSK symbols are generated. From the constellation of QPSK modulation the symbol ’00′ is represented by 1, ’01′ by j (90 degrees phase rotation), ’10′ by -1 (180 degrees phase rotation) and ’11′ by -j (270 degrees phase rotation). In pi/4 QPSK, these phase rotations are offset by 45 degrees. So the effective representation of symbols in pi/4-QPSK is ’00′=1+j (45 degrees), ’01′=-1+j (135 degrees), ’10′ = -1-j (225 degrees) and ’11′= 1-j (315 degrees). Here we are simulating a pi/4 QPSK system.Once the symbols are mapped, the power of the QPSK modulated signal need to be normalized by \(\frac{1}{\sqrt{2}}\). AWGN channel: For QPSK modulation the channel can be modeled as $$ y=ax+n $$ where y is the received signal at the input of the QPSK receiver, x is the complex modulated signal transmitted through the channel , a is a channel amplitude scaling factor for the transmitted signal usually 1. ‘n’ is the Additive Gaussian White Noise random random variable with zero mean and variance \(\sigma^2 \). For AWGN the noise variance in terms of noise power spectral density \(N_0\) is given by, $$ \sigma^{2}=\frac{N_{0}}{2} $$ For M-PSK modulation […]
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