An I/Q (In-phase/Quadrature) scatter plot showing symbol positions of a digitally modulated signal. Ideal constellation points are displayed as reference markers with received symbols scattered around them, revealing modulation quality and signal impairments such as noise, phase offset, and amplitude distortion. This plot is the standard diagnostic tool for evaluating digital modulation schemes like 16-QAM.
""" anyplot.ai
scatter-constellation-diagram: Digital Modulation Constellation Diagram
Library: plotly 6.8.0 | Python 3.13.14
Quality: 93/100 | Updated: 2026-06-18
"""
import os
import numpy as np
import plotly.graph_objects as go
# Theme tokens — Imprint palette, theme-adaptive chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint sequential colormap for continuous error magnitude (single-polarity)
imprint_seq = [[0.0, "#009E73"], [1.0, "#4467A3"]]
# Data
np.random.seed(42)
ideal_values = np.array([-3, -1, 1, 3])
ideal_i, ideal_q = np.meshgrid(ideal_values, ideal_values)
ideal_i = ideal_i.flatten()
ideal_q = ideal_q.flatten()
n_symbols = 1200
snr_db = 20
snr_linear = 10 ** (snr_db / 10)
signal_power = np.mean(ideal_i**2 + ideal_q**2)
noise_std = np.sqrt(signal_power / snr_linear / 2)
symbol_indices = np.random.randint(0, 16, n_symbols)
noise_i = np.random.normal(0, noise_std, n_symbols)
noise_q = np.random.normal(0, noise_std, n_symbols)
# Phase offset impairment (~5 degrees carrier phase error)
phase_offset = np.deg2rad(5)
ref_i = ideal_i[symbol_indices]
ref_q = ideal_q[symbol_indices]
rotated_i = ref_i * np.cos(phase_offset) - ref_q * np.sin(phase_offset)
rotated_q = ref_i * np.sin(phase_offset) + ref_q * np.cos(phase_offset)
received_i = rotated_i + noise_i
received_q = rotated_q + noise_q
# Error vector magnitude (relative to ideal, not rotated)
error_vectors = np.sqrt((received_i - ref_i) ** 2 + (received_q - ref_q) ** 2)
evm_rms = np.sqrt(np.mean(error_vectors**2)) / np.sqrt(signal_power) * 100
# Plot
fig = go.Figure()
# Received symbols colored by error magnitude — Imprint sequential colormap
fig.add_trace(
go.Scattergl(
x=received_i,
y=received_q,
mode="markers",
marker={
"size": 9,
"color": error_vectors,
"colorscale": imprint_seq,
"opacity": 0.6,
"colorbar": {
"title": {"text": "Error<br>Magnitude", "font": {"size": 12, "color": INK_SOFT}},
"tickfont": {"size": 10, "color": INK_SOFT},
"thickness": 16,
"len": 0.45,
"y": 0.25,
"outlinewidth": 0,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
"cmin": 0,
"cmax": np.percentile(error_vectors, 97),
},
name="Received symbols",
hovertemplate="I: %{x:.3f}<br>Q: %{y:.3f}<br>Error: %{marker.color:.3f}<extra></extra>",
showlegend=True,
)
)
# Ideal constellation points — matte red X markers (semantic anchor for reference targets)
fig.add_trace(
go.Scatter(
x=ideal_i,
y=ideal_q,
mode="markers",
marker={"size": 20, "color": "rgba(0,0,0,0)", "symbol": "x", "line": {"width": 3, "color": "#AE3030"}},
name="Ideal points",
hovertemplate="I: %{x}<br>Q: %{y}<extra></extra>",
)
)
# Decision boundaries — theme-adaptive grid color
for boundary in [-2, 0, 2]:
fig.add_shape(
type="line", x0=boundary, y0=-4.8, x1=boundary, y1=4.8, line={"color": GRID, "width": 1, "dash": "dash"}
)
fig.add_shape(
type="line", x0=-4.8, y0=boundary, x1=4.8, y1=boundary, line={"color": GRID, "width": 1, "dash": "dash"}
)
# EVM annotation — theme-adaptive colors
fig.add_annotation(
x=0.98,
y=0.98,
xref="paper",
yref="paper",
text=f"<b>EVM = {evm_rms:.1f}%</b><br><span style='font-size:10px'>SNR = {snr_db} dB · Phase offset = 5°</span>",
showarrow=False,
font={"size": 12, "color": INK, "family": "Arial"},
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderwidth=1,
borderpad=10,
xanchor="right",
yanchor="top",
align="right",
)
TITLE = "scatter-constellation-diagram · python · plotly · anyplot.ai"
fig.update_layout(
autosize=False,
title={"text": TITLE, "font": {"size": 16, "color": INK, "family": "Arial"}, "x": 0.5, "xanchor": "center"},
xaxis={
"title": {"text": "In-Phase (I)", "font": {"size": 12, "color": INK, "family": "Arial"}},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [-4.8, 4.8],
"zeroline": True,
"zerolinewidth": 1.5,
"zerolinecolor": INK_SOFT,
"dtick": 1,
"showgrid": False,
"constrain": "domain",
"linecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Quadrature (Q)", "font": {"size": 12, "color": INK, "family": "Arial"}},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [-4.8, 4.8],
"scaleanchor": "x",
"scaleratio": 1,
"constrain": "domain",
"zeroline": True,
"zerolinewidth": 1.5,
"zerolinecolor": INK_SOFT,
"dtick": 1,
"showgrid": False,
"linecolor": INK_SOFT,
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
legend={
"font": {"size": 10, "color": INK_SOFT, "family": "Arial"},
"x": 0.02,
"y": 0.98,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
margin={"l": 80, "r": 100, "t": 80, "b": 60},
)
# Save — square 2400×2400 (equal aspect required for constellation geometry)
fig.write_image(f"plot-{THEME}.png", width=600, height=600, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Digital Modulation Constellation Diagram on anyplot.ai.