See how bits become radio waves. Modulate a random bit stream, send it through a noisy channel, and watch the constellation scatter and the errors climb.
Digital Modulation StudioLive
QAM / PSK constellations over an AWGN channel
Modulated waveform (first symbols)
Received constellation — ideal points ✕, decision boundaries dashed
Controls
Modulate a random bit stream, push it through a Gaussian (AWGN) channel, and decode each symbol to its nearest constellation point. Watch the noise cloud and error rate grow as Eb/N₀ drops.
Reading this result: QPSK carries 2 bits/symbol. At Eb/N₀ = 10 dB the noise standard deviation is 0.158 per axis, so the received cloud has no visible overlap with neighbouring decision regions. Its widely-spaced points tolerate a lot of noise before errors appear — the price is only 1 bit per symbol. Switch to 16-QAM at the same Eb/N₀ to see the crowded points start colliding.
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How it works
Each modulation scheme maps groups of bits to points in the I/Q plane and transmits s(t) = I·cos(2πf_c t) − Q·sin(2πf_c t). An additive white Gaussian noise (AWGN) channel then blurs every point into a cloud whose spread is set by Eb/N₀. A nearest-symbol decision recovers the bits, and comparing against what was sent gives the measured symbol and bit error rate. Higher-order schemes such as 16-QAM pack more bits per symbol, but their points sit closer together, so at the same Eb/N₀ they make more errors — the fundamental rate-versus-reliability trade of digital communications.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this QAM PSK constellation modulation tool really free?▾
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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.