Modulation Bandwidth & Eb/N0
Turns a data rate and a modulation scheme into the numbers you plan a link with: the symbol rate, the occupied bandwidth after raised-cosine (RRC) filtering, and the spectral efficiency in bits/s/Hz. Enter an Eb/N0 to also get the per-symbol Es/N0 and the SNR measured in the occupied bandwidth — the three ways the same link margin gets quoted.
Equations & Parameters ▸
\(R_s=\dfrac{R_b}{\log_2 M} \qquad BW=R_s(1+\alpha) \qquad \eta=\dfrac{R_b}{BW}=\dfrac{\log_2 M}{1+\alpha}\)
\(\dfrac{E_s}{N_0}=\dfrac{E_b}{N_0}\log_2 M \qquad \text{SNR}=\dfrac{E_b}{N_0}\cdot\dfrac{\log_2 M}{1+\alpha}\)
\(\dfrac{E_s}{N_0}=\dfrac{E_b}{N_0}\log_2 M \qquad \text{SNR}=\dfrac{E_b}{N_0}\cdot\dfrac{\log_2 M}{1+\alpha}\)
| Rb | Information bit rate (Mbps). |
| M | Modulation order (points in the constellation). log₂M bits per symbol. |
| α | Raised-cosine roll-off factor (0–1). Occupied BW = Rs(1+α). |
| Eb/N0 | Energy per bit to noise density (dB), optional. |
| η | Spectral efficiency (bits/s/Hz). |
Reference: J. G. Proakis & M. Salehi, Digital Communications, 5th ed., McGraw-Hill, 2008.
Inputs
Mbps
Data rateConstellation order
0 – 1
dB
For SNRResults
Bandwidth
Bits per symbol—
Symbol rate Rs—
Occupied bandwidth—
Spectral efficiency η—
Link (from Eb/N0)
Es/N0—
SNR in occupied BW—
Diagram