PPolySim OS

BER vs SNR

The waterfall curve at the heart of every digital link. Watch bit error rate plunge as signal-to-noise improves, and see why packing more bits per symbol costs you reliability.

BER vs SNR StudioLive

Controls

Schemes

Log-scale BER (1e-6…1) vs Eb/N0. Lines are the closed-form theory; dots are a live AWGN Monte-Carlo simulation.

Presets

▶ Run in Python

Data Inspector

Marker10 dB
BPSK/QPSK3.87e-6
16-QAM1.75e-3 (+3.9 dB)
64-QAM2.65e-2 (+8.2 dB)
BFSK7.83e-4 (+3.1 dB)

Governing equation

Reading this result: Each curve is a "waterfall": BER falls steeply once Eb/N0 clears a threshold. BPSK/QPSK is the most robust — its bits are the farthest apart. Packing more bits per symbol (16-QAM, then 64-QAM) crowds the constellation, so those schemes need several extra dB of Eb/N0 to hit the same BER. That is the core rate-vs-reliability trade: higher-order QAM carries more data per hertz but demands a cleaner channel. The dots are a live Monte-Carlo run (20,000 bits/point) and track the closed-form lines.

(+dB) = extra Eb/N0 versus BPSK/QPSK to reach BER = 1e-4 (coding-gain gap).

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How it works

Bit error rate (BER) versus Eb/N0 is how communications engineers judge a modulation scheme. Each curve is a 'waterfall': errors fall off a cliff once the signal-to-noise ratio clears a threshold. The solid lines are the closed-form results — BPSK and QPSK share P_b = Q(√(2Eb/N0)), while square M-QAM uses the standard Gray-coded approximation with the Q-function (built here from erfc). The dots are a live Monte-Carlo simulation: random bits are modulated, corrupted with additive white Gaussian noise, detected, and the errors counted — so the simulated points track the theory. Compare schemes to see the rate-versus-reliability trade-off: 16-QAM and 64-QAM carry more bits per symbol but need several extra dB of Eb/N0 to hit the same error rate.

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Frequently asked questions

Is this bit error rate SNR waterfall curve tool really free?
Yes. BER vs SNR runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.