Convert bit energy, symbol energy, and sample SNR for a chosen modulation. Built for BER simulation setup — unit-energy complex baseband noise variance included.
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How to use this with GaussianWaves articles
Pick the modulation, decide whether you are sweeping Eb/N0, Es/N0, or sample SNR, then copy the shareable link or the Python noise snippet into your lab notebook.
- Full derivation: Eb/N0, Es/N0 and SNR conversions
- Check the BER curve: BER vs Eb/N0 calculator
- BPSK Monte Carlo: BPSK BER simulation (Python/Matlab)
- OFDM BER: OFDM performance in AWGN — set noise from Es/N0, not raw Eb/N0
FAQ
Why is Es/N0 higher than Eb/N0 for QPSK? Each QPSK symbol carries two bits, so symbol energy is twice bit energy: Es/N0 = Eb/N0 + 3.01 dB.
When does SNR equal Es/N0? When you have one complex sample per symbol (L = 1) and unit-energy symbols. That is the usual textbook Monte Carlo loop.
What if I oversample before the matched filter? Set L to your samples per symbol. SNR per sample drops by 10·log10(L) while Es/N0 (after matched filtering) stays the design target.
Why split noise power by 2 on I and Q? Circular complex noise needs total variance σ² with half on each real dimension. Skipping the √(1/2) makes the curve look about 3 dB too bad.
What this converter computes
Digital communication theory almost always plots bit error rate against Eb/N0. Simulators add noise against symbol energy Es. This tool applies the exact relations:
- $$E_s/N_0 = k\, E_b/N_0$$ with $$k = \log_2 M$$ for an M-ary alphabet (or a coded bits-per-symbol rate)
- In decibels: $$(E_s/N_0)_{\mathrm{dB}} = (E_b/N_0)_{\mathrm{dB}} + 10\log_{10} k$$
- Symbol-rate sample SNR: $$\mathrm{SNR} = E_s/N_0$$ when $$L=1$$; otherwise $$\mathrm{SNR}_{\mathrm{sample}} = (E_s/N_0)/L$$
- Unit-energy complex noise: $$\sigma^2 = 1/(E_s/N_0)$$, each of I and Q scaled by $$\sqrt{\sigma^2/2}$$
Use the shareable link when you ask a classmate or colleague to reproduce the same operating point. Use the Python snippet to avoid the classic “BER 3 dB off” bug.