SNR Calculator for Modulation & Coding
Compute common SNR-related quantities used in coded modulation. Enter modulation order, code rate, and either $E_b/N_0$ or $E_s/N_0$ (dB). The tool derives the rest, including noise variance and the pre-decoder $BER_{in}$ using the Gaussian $Q$-function.
Useful Equations
Assumptions
- $E_s = 1$ (normalized constellation).
- $k$ is message length, $n$ is the code length.
- $M$ is the number of symbols.
- $N_0 = 2\,\sigma^2$.
Key Equations
- $E_b =\frac{ E_s}{ \log_2(M) \times \dfrac{k}{n}}$
- $\sigma^2 = \frac{1}{ 2\times \log_2(M) \times \frac{k}{n} \times \frac{E_b}{N_0}}$
dB conversions: $10\log_{10}$.
QPSK vs BPSK
- BPSK: symbols $\pm1$ (unit energy per symbol).
- QPSK (Gray, normalized): symbols $\pm\tfrac{1}{\sqrt{2}} \pm j\tfrac{1}{\sqrt{2}}$.
Calculator
Allowed: BPSK (2), QPSK (4)
0 < $R_c$ ≤ 1
Enter either Eb/N0 or Es/N0
Leave Eb/N0 empty when using this
Outputs: Eb/N0, Es/N0, bits/symbol, noise variance/std, BER
Results
Quick QPSK results from BPSK
Leave QPSK symbols at $\pm1$ (I) and $\pm1$ (Q) in simulation, set
$\sigma = \sqrt{\dfrac{1}{10^{\frac{E_s/N_0\,(\text{dB})}{10}} \times \color{red}1.0}}$
This injects the required noise for a target $E_s/N_0$ without changing symbol amplitudes.
Enjoy Reading This Article?
Here are some more articles you might like to read next: