Optical signal-to-noise ratio (OSNR)

The optical signal-to-noise ratio in decibels is

$$\text{OSNR}=10{\log }_{10}\text{\hspace{0.17em}⁣}\left(\frac{P_{\text{signal}}}{P_{\text{noise}}}\right),$$

both measured in a specified reference optical bandwidth. The reporting convention for telecom is a 0.1 nm reference bandwidth, which corresponds to approximately 12.5 GHz at 1550 nm.

OSNR scales with bandwidth. A wider measurement bandwidth captures more noise but the same signal. Conversion between reference bandwidths:

$${\text{OSNR}}_{\text{dB}}(B^{\mathrm{\prime }})={\text{OSNR}}_{\text{dB}}(B)+10{\log }_{10}(B\mathrm{/}{B}^{\mathrm{\prime }})\mathrm{.}$$

For an amplified link, OSNR degrades through the cascade of amplifiers. The accumulated noise from $N$ amplifiers with noise factors $F_i$ produces:

$$\frac{1}{{\text{OSNR}}_{\text{out}}}\approx \sum _{i=1}^N\frac{F_i}{P_i\mathrm{/}(h\nu B_{\text{ref}})},$$

where $P_i$ is the per-channel input power to amplifier $i$ and $B_{\text{ref}}$ is the reference bandwidth. For identical-loss spans with identical EDFAs and per-channel input power $P_{\text{in}}$:

$$\text{OSNR}\approx \frac{P_{\text{in}}}{N\cdot h\nu \cdot B_{\text{ref}}\cdot F},$$

where $F$ is the linear noise figure.

Typical required OSNR at 0.1 nm reference bandwidth, measured back to back, without the impairments of a transmission link:

The direct-detection rows (OOK and DPSK) are for a bit error rate of ${10}^{-12}$ without forward error correction (FEC). The coherent rows are for the pre-FEC threshold, the error rate of roughly ${10}^{-3}$ to ${10}^{-2}$ that the transceiver's FEC reduces to a negligible output error rate. Without FEC the coherent formats would need far more: an ideal receiver limited only by amplifier noise needs 12.0 dB for DP-QPSK at 28 GBd to reach an error rate of $3.8\times {10}^{-3}$, and 20.4 dB to reach ${10}^{-12}$.

Higher-order modulation formats require higher OSNR to maintain the same bit error rate.

Measurement (the full procedure is in How to Measure OSNR): OSA scan with the per-channel signal power read at the channel peak when the channel is narrower than the 0.1 nm resolution bandwidth, or integrated across the channel when it is wider, as coherent channels are, and the noise level interpolated between channels. Where ROADM filtering makes simple interpolation fail, polarization-nulling techniques (subtracting orthogonal polarization measurements) give an in-band OSNR measurement for single-polarization signals; they do not work for polarization-multiplexed signals, which need other in-band methods.

The OSNR and Noise Figure Calculator evaluates the cascade formula above for a chain of identical spans, using the exact amplifier noise $(FG-1)h\nu B$ in place of the approximation, and finds the longest chain that meets a required OSNR.