Simulation of QPSK Modulation and Demodulation

This document presents a detailed QPSK modulation and demodulation simulation program, comprising the following components: 1. Baseband input waveform and its power spectral density The simulation generates baseband input waveforms representing unmodulated information-bearing signals. Through code implementation using MATLAB's signal processing toolbox, the program computes power spectral density using FFT-based methods with proper windowing techniques to analyze frequency domain characteristics. 2. QPSK modulated signal and its power spectral density The baseband signal undergoes QPSK modulation, where two bits are mapped to one complex constellation point using Gray coding for optimal bit error performance. The implementation utilizes I/Q modulation with carrier frequency shifting, followed by power spectral analysis to examine bandwidth efficiency and spectral properties. 3. AWGN channel output and its power spectral density The modulated signal passes through an Additive White Gaussian Noise (AWGN) channel implemented using random number generation with specified signal-to-noise ratio (SNR). The received signal's spectral characteristics are analyzed to observe noise impact on signal quality. 4. Signal constellation diagrams before and after Rayleigh channel transmission Beyond AWGN conditions, the simulation incorporates Rayleigh fading channel effects using complex Gaussian random variables. Constellation diagrams are plotted using scatter plots to visualize signal distortion and phase rotation introduced by multipath fading, enabling qualitative assessment of channel impairment. 5. Bit error rate performance under AWGN and Rayleigh fading channel conditions The system's error performance is quantitatively evaluated through Monte Carlo simulations across varying SNR values. The implementation includes symbol detection algorithms (maximum likelihood detection) and error counting routines to generate BER curves for both channel models. 6. Theoretical AWGN performance curves For validation purposes, theoretical BER curves for QPSK under AWGN conditions are derived using the Q-function and plotted alongside simulation results. This comparative analysis, implemented with consistent axis scaling, verifies simulation accuracy and demonstrates performance degradation in fading environments. Each section includes detailed implementation methodologies using appropriate digital communication algorithms, signal processing techniques, and performance evaluation metrics to provide comprehensive insights into QPSK system behavior under different channel conditions.