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: altair 6.2.1 | Python 3.13.14
Quality: 91/100 | Updated: 2026-06-18
"""
import os
import sys
# Prevent self-import: remove the script's own directory from sys.path
# so that `import altair` resolves to the installed package, not this file.
_thisdir = os.path.dirname(os.path.realpath(__file__))
sys.path[:] = [p for p in sys.path if p not in ("", ".") and os.path.realpath(p) != _thisdir]
import altair as alt
import numpy as np
import pandas as pd
from PIL import Image
# Theme-adaptive chrome tokens (Imprint palette)
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"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint sequential colormap — low error (green) → high error (blue)
SEQ_LOW = "#009E73" # Imprint position 1
SEQ_HIGH = "#4467A3" # Imprint position 3
# Ideal point color — semantic matte red (Imprint position 5: reference/error anchor)
IDEAL_COLOR = "#AE3030"
# Data
np.random.seed(42)
ideal_vals = [-3, -1, 1, 3]
ideal_i, ideal_q = np.meshgrid(ideal_vals, ideal_vals)
ideal_i = ideal_i.flatten()
ideal_q = ideal_q.flatten()
n_symbols = 1000
symbol_indices = np.random.randint(0, 16, size=n_symbols)
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)
received_i = ideal_i[symbol_indices] + np.random.normal(0, noise_std, n_symbols)
received_q = ideal_q[symbol_indices] + np.random.normal(0, noise_std, n_symbols)
error_vectors = np.sqrt((received_i - ideal_i[symbol_indices]) ** 2 + (received_q - ideal_q[symbol_indices]) ** 2)
rms_signal = np.sqrt(signal_power)
evm_pct = np.sqrt(np.mean(error_vectors**2)) / rms_signal * 100
df_received = pd.DataFrame(
{
"I": received_i,
"Q": received_q,
"Error Magnitude": error_vectors,
"Nearest I": ideal_i[symbol_indices],
"Nearest Q": ideal_q[symbol_indices],
}
)
df_ideal = pd.DataFrame({"I": ideal_i, "Q": ideal_q})
# Decision boundaries at midpoints separating the 16-QAM symbol regions
boundary_vals = [-4, -2, 0, 2, 4]
boundary_h = pd.DataFrame([{"x": -5.2, "x2": 5.2, "y": v} for v in boundary_vals])
boundary_v = pd.DataFrame([{"y": -5.2, "y2": 5.2, "x": v} for v in boundary_vals])
df_evm = pd.DataFrame({"I": [4.0], "Q": [4.5], "label": [f"EVM = {evm_pct:.1f}%"]})
# Interactive selection — highlights nearest symbol on hover
nearest = alt.selection_point(on="pointerover", nearest=True, fields=["I", "Q"], empty=False)
# Equal symmetric domains for accurate constellation geometry (equal aspect ratio)
scale_x = alt.Scale(domain=[-5.5, 5.5], nice=False)
scale_y = alt.Scale(domain=[-5.5, 5.5], nice=False)
# Layer: dashed decision boundary grid lines
h_rules = (
alt.Chart(boundary_h)
.mark_rule(strokeDash=[8, 5], strokeWidth=1, opacity=0.45)
.encode(x=alt.X("x:Q", scale=scale_x), x2="x2:Q", y=alt.Y("y:Q", scale=scale_y), color=alt.value(INK_MUTED))
)
v_rules = (
alt.Chart(boundary_v)
.mark_rule(strokeDash=[8, 5], strokeWidth=1, opacity=0.45)
.encode(y=alt.Y("y:Q", scale=scale_y), y2="y2:Q", x=alt.X("x:Q", scale=scale_x), color=alt.value(INK_MUTED))
)
# Layer: received symbols, color-coded by error magnitude (imprint_seq)
received_layer = (
alt.Chart(df_received)
.mark_circle(size=40)
.encode(
x=alt.X("I:Q", title="In-Phase (I)", scale=scale_x),
y=alt.Y("Q:Q", title="Quadrature (Q)", scale=scale_y),
color=alt.Color(
"Error Magnitude:Q",
scale=alt.Scale(range=[SEQ_LOW, SEQ_HIGH]),
legend=alt.Legend(
title="Error Mag.", titleFontSize=10, labelFontSize=10, orient="right", gradientLength=100
),
),
opacity=alt.condition(nearest, alt.value(0.9), alt.value(0.35)),
size=alt.condition(nearest, alt.value(120), alt.value(40)),
tooltip=[
alt.Tooltip("I:Q", format=".3f"),
alt.Tooltip("Q:Q", format=".3f"),
alt.Tooltip("Error Magnitude:Q", format=".3f", title="Error"),
alt.Tooltip("Nearest I:Q", format=".0f", title="Ideal I"),
alt.Tooltip("Nearest Q:Q", format=".0f", title="Ideal Q"),
],
)
.add_params(nearest)
)
# Layer: ideal constellation points (cross markers, Imprint matte red semantic anchor)
ideal_layer = (
alt.Chart(df_ideal)
.mark_point(size=300, filled=False, strokeWidth=3.0)
.encode(
x="I:Q",
y="Q:Q",
color=alt.value(IDEAL_COLOR),
shape=alt.value("cross"),
tooltip=[alt.Tooltip("I:Q", format=".0f", title="Ideal I"), alt.Tooltip("Q:Q", format=".0f", title="Ideal Q")],
)
)
# Layer: EVM annotation
evm_label = (
alt.Chart(df_evm)
.mark_text(fontSize=13, fontWeight="bold", align="right", font="monospace")
.encode(x="I:Q", y="Q:Q", text="label:N", color=alt.value(INK))
)
chart = (
alt.layer(h_rules, v_rules, received_layer, ideal_layer, evm_label)
.properties(
width=460,
height=460,
background=PAGE_BG,
title=alt.Title(
"scatter-constellation-diagram · python · altair · anyplot.ai",
fontSize=17,
fontWeight="bold",
anchor="middle",
offset=10,
),
)
.configure_view(fill=PAGE_BG, stroke=None)
.configure_axis(
labelFontSize=10,
titleFontSize=12,
tickSize=4,
domainColor=INK_SOFT,
tickColor=INK_SOFT,
labelColor=INK_SOFT,
titleColor=INK,
grid=False,
)
.configure_title(color=INK)
.configure_legend(fillColor=ELEVATED_BG, strokeColor=INK_SOFT, labelColor=INK_SOFT, titleColor=INK)
)
# Save PNG then pad to exact 2400×2400 square canvas
chart.save(f"plot-{THEME}.png", scale_factor=4.0)
TW, TH = 2400, 2400
_img = Image.open(f"plot-{THEME}.png").convert("RGB")
_w, _h = _img.size
if _w > TW or _h > TH:
raise SystemExit(
f"altair vl-convert produced {_w}×{_h}, exceeds target {TW}×{TH}. "
f"Shrink chart .properties(width=, height=) values and re-render."
)
if _w < TW or _h < TH:
_canvas = Image.new("RGB", (TW, TH), PAGE_BG)
_canvas.paste(_img, ((TW - _w) // 2, (TH - _h) // 2))
_canvas.save(f"plot-{THEME}.png")
chart.save(f"plot-{THEME}.html")
Part of Digital Modulation Constellation Diagram on anyplot.ai.