16-QAM constellation diagram with AWGN noise

Python Code

"""Digital Comms — 16-QAM constellation diagram with AWGN noise."""


import numpy as np
import plotly.graph_objects as go


def generate():
    RNG = np.random.default_rng(42)

    # ── 16-QAM ideal constellation points ────────────────────────────────────────
    # Gray-coded 16-QAM: I,Q ∈ {-3,-1,+1,+3}/sqrt(10)
    levels = np.array([-3, -1, 1, 3]) / np.sqrt(10)
    I_ideal, Q_ideal = np.meshgrid(levels, levels)
    I_ideal = I_ideal.ravel()
    Q_ideal = Q_ideal.ravel()

    # ── Generate ~2000 random symbols with AWGN ───────────────────────────────────
    N = 2000
    idx = RNG.integers(0, 16, size=N)
    I_tx = I_ideal[idx]
    Q_tx = Q_ideal[idx]

    # AWGN: Es=1, SNR_dB=15
    SNR_dB = 15
    Es = 1.0
    sigma = np.sqrt(Es / (2 * 10 ** (SNR_dB / 10)))  # per-dimension std
    I_noisy = I_tx + RNG.normal(0, sigma, N)
    Q_noisy = Q_tx + RNG.normal(0, sigma, N)

    # ── Build figure ──────────────────────────────────────────────────────────────
    fig = go.Figure()

    fig.add_trace(go.Scattergl(
        x=I_noisy,
        y=Q_noisy,
        mode="markers",
        marker=dict(size=4, opacity=0.45, color=VIOLET),
        name="Received symbols",
    ))

    fig.add_trace(go.Scatter(
        x=I_ideal,
        y=Q_ideal,
        mode="markers",
        marker=dict(size=12, symbol="x", color="#e03030", line=dict(width=2)),
        name="Ideal points",
    ))

    fig.update_layout(
        xaxis=dict(
            title="In-phase (I)",
            scaleanchor="y",
            scaleratio=1,
            constrain="domain",
            zeroline=True,
            zerolinecolor="#cccccc",
            range=[-1.1, 1.1],
        ),
        yaxis=dict(
            title="Quadrature (Q)",
            zeroline=True,
            zerolinecolor="#cccccc",
            range=[-1.1, 1.1],
        ),
        legend=dict(x=0.01, y=0.99),
    )

    return fig


if __name__ == "__main__":
    generate()

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