NRZ (Non-Return-to-Zero)

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 (typically near zero); 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	$-10$ to $-30$ dBm
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 $V_\pi$ for full extinction; standard for $> 10G$
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. The full bandwidth (typically the 99% energy width) is $\sim 1.2 R$. Side lobes fall off as $\text{sinc}^2$.

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 requires 100+ GHz of analog bandwidth, which is at the edge of available electronic components.

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

$$\text{BER} \;=\; \frac{1}{2} \text{erfc}\!\left( \frac{Q}{\sqrt{2}} \right),$$

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

$$Q \;=\; \frac{P_1 - P_0}{\sigma_1 + \sigma_0}.$$

For BER = $10^{-12}$: $Q \geq 7$, requiring electrical SNR of $\geq 17$ dB or OSNR $\geq 14 + 10 \log_{10}(R)$ dB/0.1nm.

For 10G NRZ at 1550 nm: typical OSNR threshold is 17 dB/0.1nm pre-FEC; with FEC, OSNR threshold lowers to 12 – 14 dB/0.1nm depending on FEC overhead.

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 signal (0, 1, 0) from filtered NRZ	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
10G-SR / 10G-LR	10.3 Gb/s	26 m / 10 km	10 Gb Ethernet, multi-mode/single-mode
100GBASE-LR4	4× 25.78 Gb/s	10 km	100G Ethernet using 4 WDM lanes
28 GBaud NRZ	28 Gb/s	up to 80 km	OTU3
OTU4 NRZ × 4	4× 28 Gb/s	up to 80 km	112G coherent has displaced this

Limitations.

• Spectral efficiency capped at 1 bit/symbol: Cannot exceed 1 bit/Hz without spectral filtering
• High bandwidth at high rates: 100G NRZ requires ~ 90 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)
• Poor noise immunity vs coherent: 3 – 5 dB worse OSNR than DP-QPSK at same rate

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 efficiency: very low compared to coherent

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.

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.