On-off keying (OOK)

On-off keying is the simplest optical modulation format: each bit sets the transmitted power to one of two levels, high for a 1 and low for a 0, and the receiver compares the photocurrent against a threshold. It is the original intensity-modulation, direct-detection (IM/DD) scheme, needs no phase reference, and was the format of almost every fiber link from the first 45 Mb/s systems to the 10 and 25 Gb/s Ethernet and SONET/SDH optics still deployed. In the vocabulary of multilevel formats it is PAM2, the two-level member of the family that includes PAM4, and it carries one bit per symbol, so its bit rate equals its symbol rate.

NRZ and RZ forms

In non-return-to-zero OOK the power holds its level for the whole bit period, and a run of 1s is a continuous high level; this is the form meant when a link is described simply as NRZ, and that entry covers its spectrum, generation and standards. In return-to-zero OOK each 1 is a pulse occupying part of the bit slot, typically half. RZ needs about twice the bandwidth but tolerates some nonlinear impairments better and was used in long-haul systems in the 2000s before coherent detection replaced them.

Levels and extinction ratio

The low level is never zero in practice. A directly modulated laser is held above threshold to keep it fast, and an external modulator has finite contrast, so the 0 level carries some power. The ratio $r = P_1/P_0$ is the extinction ratio, usually 6–15 dB for OOK transmitters. Referenced to average power, a finite $r$ costs a power penalty of

$$\text{PP} = 10\log_{10}\frac{r + 1}{r - 1},$$

which is 2.23 dB at 6 dB extinction ratio and 0.87 dB at 10 dB. Transmitter specifications therefore state a minimum extinction ratio alongside the average launch power, or specify the optical modulation amplitude $P_1 - P_0$ directly.

Q factor and bit error rate

With Gaussian noise on both levels and the threshold at its optimum, the bit error rate of OOK depends on a single number, the Q factor of the eye:

$$Q = \frac{P_1 - P_0}{\sigma_1 + \sigma_0}, \qquad \text{BER} = \tfrac{1}{2}\,\text{erfc}\!\left(\frac{Q}{\sqrt{2}}\right).$$

Here $\sigma_1$ and $\sigma_0$ are the noise standard deviations on the two levels, expressed in the same units as the levels. $Q = 6$ gives BER $= 9.9 \times 10^{-10}$ and $Q = 7$ gives $1.3 \times 10^{-12}$, the two classic targets for links without error correction. In dB, $20\log_{10}Q$ is 15.6 dB and 16.9 dB respectively. With forward error correction, the required pre-FEC BER rises to the 10⁻⁴–10⁻³ range and the required Q falls accordingly.

The eye diagram is how OOK signals are inspected in the lab: a sampling oscilloscope overlays many bit periods, the two rails give $P_1$ and $P_0$, their thickness gives $\sigma_1$ and $\sigma_0$, and the Q factor can be read from histograms at the center of the eye. Mask tests on the same display catch overshoot, ringing and jitter that a Q value alone does not reveal.

Sensitivity limits

The ideal limit for OOK with a perfect photon-counting receiver and no 0-level power is a BER of $\tfrac{1}{2}e^{-N_p}$, where $N_p$ is the photon number in a 1 bit. For $10^{-9}$ this requires 20 photons per 1 bit, 10 photons per bit on average. At 10 Gb/s and 1550 nm, with 0.80 eV per photon, that is 13 nW, or −48.9 dBm. Practical PIN photodiode receivers at 10 Gb/s are limited by the thermal noise of the amplifier and need about −18 to −20 dBm, roughly a thousand times more power; avalanche photodiodes and optical preamplifiers close part of the gap.

Comparison with PAM4

For a given bit rate, PAM4 halves the symbol rate and therefore the bandwidth, which is why it replaced OOK at 50 Gb/s per lane and above. The cost is in eye amplitude: at the same peak-to-peak swing, each of the three PAM4 eyes is one third the height of the single OOK eye. The ideal eye-amplitude penalty is $20\log_{10}3 = 9.54$ dB in electrical SNR, or $10\log_{10}3 = 4.77$ dB of optical power for a thermal-noise-limited receiver at equal average power. Real PAM4 links pay more, for level nonlinearity and the tighter timing of three eyes, and recover some of it with equalization and FEC.

Common questions

Is on-off keying the same as NRZ?

The terms overlap. OOK names the modulation (two intensity levels), and NRZ names the pulse shape (level held for the full bit). In optical communication "NRZ" is commonly used as shorthand for NRZ-OOK, which is the usual combination.

Why is the 0 level not set to zero power?

A directly modulated laser driven below threshold turns on slowly and with large chirp, so it is biased just above threshold. External modulators reach high extinction only with large drive voltages. A moderate extinction ratio is the practical balance between penalty and speed or drive power.

What Q factor is needed for a BER of 10⁻¹²?

About 7, which is 16.9 dB in $20\log_{10}Q$ terms. A BER of 10⁻⁹ needs about 6.

References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); P. J. Winzer and R.-J. Essiambre, "Advanced optical modulation formats," Proceedings of the IEEE 94, 952 (2006).