Glossary entry

NRZ (Non-Return-to-Zero)

A binary modulation format where the optical intensity holds at one of two levels (logical 0 or 1) for the entire symbol period. The simplest and historically dominant format in optical communications.

Fiber & telecomUpdated October 2026

NRZ (Non-Return-to-Zero) is the simplest optical modulation format: a binary intensity-modulation scheme where the laser output holds at one of two levels (corresponding to logical 0 or logical 1) for the entire bit period. NRZ-OOK (NRZ with On-Off Keying) has been the dominant format in optical communications from the 1980s through the 2010s and remains widely deployed.

Operating principle. A digital "0" maps to the low optical power level (ideally zero; in practice set by the extinction ratio); a digital "1" maps to the high level. Information is encoded entirely in the time-domain intensity sequence; no phase, frequency, or polarization information is used.

The format is called "Non-Return-to-Zero" because the signal does not return to zero between consecutive 1 bits, unlike RZ (Return-to-Zero) where the signal pulses high then returns to zero each bit.

Standard parameters.

Parameter	Definition	Typical value
Bit period $T_{b}$	Time per bit	100 ps for 10 G, 40 ps for 25 G, 9.4 ps for 106.25 G (NRZ-PAM2)
High level $P_{1}$	Optical power for logical 1	$0$ to $+ 10$ dBm typical
Low level $P_{0}$	Optical power for logical 0	$P_{1}$ minus the extinction ratio in dB
Extinction ratio	$P_{1} / P_{0}$ in dB	6 – 15 dB typical
Rise/fall time	20%-80% transition time	$\sim 0.3 T_{b}$ for typical implementations

Eye diagram. The NRZ eye diagram is the canonical "two-level eye":

Two horizontal rails representing the 0 and 1 levels
Transitions crossing through a central crossing point
"Eye opening" at the center of the bit period, where the decision threshold is set
Wider eye opening = lower BER

NRZ eye diagrams are easy to measure and interpret; "eye height", "eye width", and "eye mask" are standard quality metrics in 10G/25G systems.

Generation.

Method	Description
Direct modulation (DML)	Modulate laser injection current; cheap but adds chirp
External modulation, Mach-Zehnder (MZM)	Drive MZM with $V_{π}$ for full extinction; standard for $> 10 G$
External modulation, EAM	Electro-absorption modulator with reverse bias swing; integrated into EML

For long-haul applications, externally-modulated lasers (EMLs) or MZMs are preferred because direct modulation introduces frequency chirp that interacts with chromatic dispersion to limit reach.

Spectral characteristics. An NRZ signal at rate $R = 1 / T_{b}$ has main lobe width $R$ in frequency. For rectangular bits the main lobe ( $∣ f ∣ < R$ ) holds about 90% of the power, and the side lobes fall off as ${sinc}^{2}$ .

Bit rate	First null frequency
10 Gb/s	10 GHz
25 Gb/s	25 GHz
28 Gb/s	28 GHz
56 Gb/s	56 GHz
112 Gb/s	112 GHz

The high bandwidth of high-rate NRZ is the principal reason PAM4 has displaced NRZ at 50G and above. At 100 GBaud, NRZ needs at least the 50 GHz Nyquist bandwidth and in practice about 0.75 of the symbol rate, which strains available electronic components.

OSNR requirements. For NRZ-OOK with optimum decision threshold:

BER = \frac{1}{2} erfc ⁣ (\frac{Q}{\sqrt{2}}),

where $Q$ is the Q-factor (signal-to-noise quality):

Q = \frac{P_{1} - P_{0}}{σ_{1} + σ_{0}} .

For BER = $10^{- 12}$ : $Q \geq 7$ , requiring electrical SNR of $\geq 17$ dB ( $20 \log_{10} Q$ ).

In an amplified link the same Q requirement sets a minimum OSNR at the receiver, and forward error correction lowers it by accepting a higher pre-FEC BER.

Variants.

Variant	Description	Use
NRZ-OOK	Standard on-off keying	Most common; "NRZ" usually means this
NRZ-DPSK	Differential phase-shift keying with NRZ pulse shape	Submarine, before coherent
NRZ-DQPSK	Differential QPSK with NRZ	Submarine
CSRZ (carrier-suppressed RZ)	Phase alternates between bits	Improved chromatic dispersion tolerance
Duobinary	3-level field (−1, 0, +1) from filtered NRZ, detected as two intensity levels	Half bandwidth for same bit rate

Standards using NRZ.

Standard	Bit rate	Distance	Notes
OC-192 / STM-64	9.95 Gb/s	up to 80 km	SONET/SDH, mid-1990s onward
10GBASE-SR / -LR	10.3 Gb/s	26 – 300 m (OM1 – OM3) / 10 km	10 Gb Ethernet, multi-mode/single-mode
100GBASE-LR4 / -ER4	4× 25.78 Gb/s	10 km / 40 km	100G Ethernet over 4 WDM lanes; ER4 adds an SOA preamplifier
OTU4 client optics	4× 27.95 Gb/s	10 – 40 km	The same four-lane design at the OTN rate of 111.8 Gb/s

Limitations.

Spectral efficiency capped at 1 bit/symbol: Cannot exceed 1 bit/Hz without spectral filtering
High bandwidth at high rates: 100G NRZ requires roughly 50 – 75 GHz electronic bandwidth
Chromatic dispersion sensitivity: a 10G NRZ signal at 1550 nm tolerates only ~ 1000 ps/nm of cumulative dispersion; at 40G, only ~ 60 ps/nm
Mid-bit transitions invisible: no clock recovery from runs of all-1s or all-0s (mitigated by scrambling)
Poorer noise tolerance than coherent formats, which detect the optical field and can use soft-decision FEC

Why NRZ persists. Despite the limitations:

Receiver is simple: a photodiode + TIA + decision circuit. No DSP, no LO, no complex calibration.
TX is simple: a directly-modulated laser or single MZM
Cost: $5 transceivers for 10G; $25 transceivers for 25G
Mature ecosystem: every protocol, test instrument, and IT skillset knows NRZ
Power consumption: very low compared to coherent, which needs a DSP, a local oscillator and fast ADCs

For short-reach datacom (LAN, datacenter top-of-rack), NRZ remains competitive even as PAM4 enters at 50G+. For long-reach (>10 km at 100G+), coherent has displaced NRZ.

NRZ and PAM4 are compared within the full chain of an optical link in Bits to Light.

References: Agrawal, Fiber-Optic Communication Systems (4th ed., 2010), Ch. 8 (modulation formats and direct-detection systems); IEEE 802.3 specifications for Ethernet NRZ standards; ITU-T G.957/G.691 for SONET/SDH NRZ standards.