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Matlab simulation of QPSK modulation and demodulation of the communication system, are simulated digital signal transmission in AWGN and Rayleigh fading channels, with content: QPSK modulation waveform and power spectrum AWGN channel output waveform and power spectrum signal in Rayleigh channel before and after the constellation diagram 6. using half-wave analysis simulation characteristics of AWGN channel and Rayleigh channel transmission errors