Performance Comparison of QPSK and 16QAM under Rayleigh Channel and AWGN Channel

In this article, we will examine the performance comparison of QPSK and 16QAM modulation schemes under both Rayleigh fading channels and additive white Gaussian noise (AWGN) channels. First, let's understand the characteristics of these channel models. The Rayleigh channel represents a common wireless communication model that simulates multipath fading effects, where signals propagate through multiple paths to the receiver. This can be implemented in simulation code using Rayleigh fading generators that typically employ Doppler spectrum modeling and multiple delayed signal paths. In contrast, the AWGN channel serves as an idealized channel model that assumes only noise exists without other interferences, which can be simulated by simply adding Gaussian random noise to the transmitted signal using functions like randn() in MATLAB or random.gauss() in Python.

We will compare the performance differences between QPSK and 16QAM under these two channel conditions. QPSK (Quadrature Phase Shift Keying) is a modulation scheme that transmits two bits per symbol, typically implemented using four phase states (0°, 90°, 180°, 270°) in constellation diagrams. 16QAM (16-Quadrature Amplitude Modulation) transmits four bits per symbol, utilizing both amplitude and phase variations across 16 constellation points. In code implementations, QPSK modulation can be achieved through simple phase shifting operations, while 16QAM requires more complex mapping between input bits and constellation points.

Our investigation will focus on key performance metrics including bit error rate (BER), transmission rate, and spectral efficiency under different channel conditions. For BER calculation, we typically implement Monte Carlo simulations where we compare transmitted and received bits while gradually increasing signal-to-noise ratio (SNR) values. The simulation code would include modules for signal generation, modulation/demodulation, channel effects addition, and error counting. Through this comparative analysis, we can better understand the importance of selecting appropriate modulation schemes for different channel environments, particularly noting that while 16QAM offers higher data rates, it demonstrates greater sensitivity to channel impairments compared to the more robust QPSK scheme.