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Effect of Noise on QPSK Constellation - Simulation


QPSK Constellation with AWGN

Visualizing modulation symbols under different SNR conditions

Input Parameters

Theory

In 4-Phase Shift Keying (4-PSK), each symbol encodes 2 bits using one of four possible phases: 0, Ī€/2, Ī€, 3Ī€/2. The transmitted complex baseband signal is:

x[n] = A · exp(jθ_n)

where A is the symbol amplitude, and θ_n ∈ {0, Ī€/2, Ī€, 3Ī€/2} is the phase corresponding to the transmitted bits. When the signal passes through an additive white Gaussian noise (AWGN) channel, the received signal is:

r[n] = x[n] + w[n]

where w[n] ~ N(0, Īƒ²) is the complex AWGN. The signal-to-noise ratio (SNR) in decibels is defined as:

SNR (dB) = 10 · log10 (P_signal / P_noise)

Constellation Diagram

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