How to use this with GaussianWaves articles
Set Eb/N0 and modulation, then copy the shareable link (URL updates as you type). Paste it into notes, Slack, or a lab write-up so others open the same operating point.
- Unit converter: Eb/N0 ↔ Es/N0 ↔ SNR before you set noise variance.
- BPSK theory: derive optimum BPSK BER in AWGN, then match the curve here.
- Sim check: compare Monte Carlo points from the BPSK Python/Matlab BER sim to the red marker.
- Fading: AWGN curves are the floor—see BPSK BER on Rayleigh vs AWGN.
- Eb/N0 ↔ SNR: unit conversions in Eb/N0, Es/N0, SNR.
Related tutorials
Shareable Eb/N0 and modulation stay in the URL.
- BPSK: optimum receiver derivation
- BPSK BER sim: Monte Carlo check
- Eb/N0 conversions: unit hygiene
FAQ
Why do BPSK and QPSK share an Eb/N0 curve? QPSK is two orthogonal BPSK streams; bit energy is unchanged when SNR is normalized per bit.
Is this AWGN only? Yes — fading needs an average over the channel gain; see the Rayleigh BER articles.
Understanding Bit Error Rate (BER) vs $E_b/N_0$ Curves
In digital communication system analysis, Bit Error Rate (BER) curves plot the probability of bit error ($P_b$) on a logarithmic vertical axis against normalized signal energy ($E_b/N_0$ in decibels) on a linear horizontal axis. These curves establish the theoretical upper bound of performance for digital modulation schemes operating over Additive White Gaussian Noise (AWGN) channels.
Key Observations from the Plotter
- Waterfall Effect: As $E_b/N_0$ increases, the BER curve drops rapidly. This steep degradation region is commonly referred to as the “waterfall region.”
- Modulation Efficiency vs. Noise Immunity: BPSK and QPSK deliver superior energy efficiency, requiring roughly $9.6\ \text{dB}$ of $E_b/N_0$ to achieve a target BER of $10^{-5}$. Higher-order modulations like 16-QAM and 64-QAM transmit more bits per second per Hertz but require higher $E_b/N_0$ ratios (~$13.4\ \text{dB}$ for 16-QAM and ~$17.8\ \text{dB}$ for 64-QAM at $10^{-5}$ BER) to achieve equivalent bit error integrity.