If you've ever pressed a button on a TV remote, used a garage door opener, or transferred data over fiber optic cable, you've used On-Off Keying (OOK). It is the simplest possible digital modulation scheme: transmit a carrier to send a '1', transmit nothing to send a '0'.

Despite this apparent simplicity—or perhaps because of it—OOK is ubiquitous. It powers the overwhelming majority of optical fiber communications, dominates the infrared device control market, and forms the foundation of countless low-power wireless sensor networks. Understanding OOK deeply reveals fundamental principles that apply to all digital modulation.

Let's establish OOK with mathematical rigor, going beyond the simple on/off description to understand its signal space representation.

Time-Domain Representation:

The OOK signal s(t) over a bit period T_b can be expressed as:

$$s(t) = \sum_{n=-\infty}^{\infty} b_n \cdot A \cdot p(t - nT_b) \cdot \cos(2\pi f_c t)$$

Where:

• b_n ∈ {0, 1} is the n-th bit
• A is the carrier amplitude
• p(t) is the pulse shaping function (typically rectangular for OOK)
• T_b is the bit period (1/bit rate)
• f_c is the carrier frequency

For a Single Bit:

$$s(t) = \begin{cases} A \cdot p(t) \cdot \cos(2\pi f_c t) & \text{for bit } = 1 \ 0 & \text{for bit } = 0 \end{cases} \quad 0 \leq t < T_b$$

Signal Space Representation:

In signal space analysis, we represent signals as vectors. For OOK with orthonormal basis function:

$$\phi(t) = \sqrt{\frac{2}{T_b}} \cos(2\pi f_c t), \quad 0 \leq t < T_b$$

The two OOK signals become:

• Signal for bit '1': $s_1 = \sqrt{E_b}$ (where E_b = energy per bit = A²T_b/2)
• Signal for bit '0': $s_0 = 0$

Key Parameters:

$$E_b = \int_0^{T_b} s_1^2(t) , dt = \frac{A^2 T_b}{2}$$

$$d = |s_1 - s_0| = \sqrt{E_b}$$

The distance d between constellation points determines noise immunity. For OOK, this distance is √E_b, which is suboptimal compared to antipodal signaling (like BPSK) where d = 2√E_b.

The receiver must determine whether a '0' or '1' was transmitted. Several detection strategies exist, trading complexity for performance.

1. Envelope Detection (Non-Coherent):

The simplest approach—extract the envelope and compare against a threshold.

Process:

1. Rectify the received signal (full-wave or half-wave)
2. Low-pass filter to remove carrier ripple
3. Sample at the bit center
4. Compare against threshold Vth

Decision Rule: $$\hat{b} = \begin{cases} 1 & \text{if } , V_{sample} > V_{th} \ 0 & \text{if } , V_{sample} \leq V_{th} \end{cases}$$

Optimal Threshold: $$V_{th} = \frac{V_{max}}{2}$$

When noise is present, the optimal threshold shifts depending on the noise distribution.

2. Coherent Detection:

Multiply the received signal by a synchronized carrier and low-pass filter:

$$y(t) = r(t) \cdot 2\cos(2\pi f_c t)$$

$$z(t) = \text{LPF}{y(t)}$$

For a '1' bit: z(t) ≈ A (the baseband amplitude) For a '0' bit: z(t) ≈ 0 (plus noise)

3. Matched Filter Detection:

The optimal receiver in AWGN passes the signal through a filter matched to the transmitted pulse:

$$h(t) = s_1(T_b - t)$$

The matched filter output is sampled at t = T_b, yielding maximum SNR. This is equivalent to correlating with the expected signal.

Matched Filter Output: $$y(T_b) = \int_0^{T_b} r(t) \cdot s_1(t) , dt = \begin{cases} E_b + n & \text{for bit } = 1 \ n & \text{for bit } = 0 \end{cases}$$

The probability of error is the fundamental metric of any digital communication system. Let's derive OOK's BER under different detection scenarios.

Assumptions:

• Additive White Gaussian Noise (AWGN) channel
• Optimal threshold setting
• Equal probability of '0' and '1' bits

Coherent Detection (Optimal):

The bit error probability is:

$$P_b = Q\left(\sqrt{\frac{E_b}{N_0}}\right)$$

Where Q(x) is the Gaussian Q-function:

$$Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^{\infty} e^{-t^2/2} , dt$$

Non-Coherent (Envelope) Detection:

With envelope detection, the analysis is more complex because the noise statistics differ for '0' and '1' bits:

• For '1': Received envelope follows Rician distribution
• For '0': Received envelope follows Rayleigh distribution

The BER (for high SNR approximation) is:

$$P_b \approx \frac{1}{2}e^{-\frac{E_b}{2N_0}}$$

Comparison with BPSK:

Key Insight: Coherent OOK and BPSK have similar BER expressions, but BPSK has 2× the argument inside Q(). This translates to BPSK being 3 dB more power-efficient than coherent OOK, and 6 dB more efficient than non-coherent OOK.

OOK is the dominant modulation scheme in optical fiber communications, from short-range data center interconnects to long-haul undersea cables. Understanding why reveals deep insights about matching modulation to physical channel characteristics.

Why OOK Dominates Optical:

1. Natural Match to Photodetection: Photodiodes respond to optical intensity (power), not field amplitude. Intensity is inherently non-negative—perfect for OOK's on/off nature.

2. Laser Simplicity: Turning a laser on/off or modulating its current between two levels is straightforward. Phase control (for PSK) requires expensive, complex modulators.

3. Receiver Simplicity: A photodiode + transimpedance amplifier + comparator forms a complete OOK receiver. No carrier recovery, no frequency locking.

4. Proven at Extreme Data Rates: OOK has been demonstrated at 100+ Gbps per wavelength—decades of optimization have pushed it to remarkable performance.

OOK Optical Transmitter:

Typical implementation:

1. Direct Modulation: Vary laser diode current between threshold (off) and operating point (on)

   • Simple, low cost
   • Limited bandwidth by laser dynamics
   • Some chirp (frequency variation) during transitions

2. External Modulation: Separate laser (always on) + electro-optic modulator (Mach-Zehnder interferometer)

   • Higher bandwidth
   • Better extinction ratio
   • Required for highest data rates

Key Optical Metrics:

• Extinction Ratio (ER): Ratio of 'on' to 'off' optical power $$ER = \frac{P_1}{P_0}$$

  Typical values: 10-15 dB for direct modulation, 20+ dB for external modulation.

• Power Penalty: Non-infinite ER reduces effective signal swing, requiring more power.

$$\text{Power Penalty (dB)} = 10\log_{10}\left(\frac{1 + ER^{-1}}{1 - ER^{-1}}\right)$$

Beyond optical, OOK finds extensive use in RF wireless applications where simplicity, low power, and low cost outweigh spectral efficiency concerns.

Infrared Communication:

IR remote controls universally use OOK modulated on a carrier (typically 36-40 kHz):

1. Data modulates the carrier using OOK
2. Carrier pulses modulate the IR LED intensity
3. Receiver includes IR photodiode + bandpass filter at carrier frequency
4. Envelope detection recovers data

Benefits:

• Carrier frequency filters out ambient light interference
• Simple, cheap components
• Sufficient for 1-20 kbps command rates
• Battery lasts years in transmitter

OOK's simplicity hides synchronization challenges. The receiver must know when to sample—bit timing must be recovered from the received signal itself.

The Synchronization Problem:

Consider transmitting '0000...': the receiver sees constant zero. Without transitions:

• No edges to detect
• Clock drifts relative to transmitter
• Sample point gradually shifts
• Eventually samples at wrong time → errors

Solutions:

1. Preamble Training: Begin each transmission with a known pattern (e.g., 10101010...)

• Provides regular transitions for clock recovery
• Receiver PLL locks to edge timing
• Typical preamble: 16-64 bits

Baseline Wander Problem:

Unequal numbers of '1's and '0's create a DC offset that shifts over time:

• AC-coupled receivers lose the average reference
• Threshold drifts from optimal
• Error rate increases

DC Balance Solutions:

Trend: Modern systems use minimal-overhead codings (64b/66b, 128b/130b) that provide framing, synchronization, and DC balance with <5% overhead.

Designing a practical OOK system requires balancing multiple interacting parameters. Here's a framework for system design.

Link Budget Analysis:

The fundamental equation:

$$P_{rx} = P_{tx} - L_{path} - L_{components} + G_{antenna}$$

Must satisfy:

$$P_{rx} \geq P_{sensitivity}$$

Where sensitivity depends on required BER and receiver noise.

Receiver Sensitivity (typical values):

Eye Diagram Analysis:

The eye diagram is the universal tool for evaluating OOK signal quality. Created by overlaying many bit periods:

What to measure:

1. Eye Height: Vertical opening at center. Larger = better noise margin.
2. Eye Width: Horizontal opening. Larger = better timing margin.
3. Jitter: Horizontal blurring at zero crossings. Less is better.
4. Noise: Vertical blurring of '0' and '1' levels. Less is better.
5. Rise/Fall Time: Slope of transitions. Faster = better (usually).
6. Extinction Ratio: Ratio of '1' level to '0' level.

Mask Testing:

Standards define 'keep-out' regions (masks) that the eye must not enter. Passing mask test guarantees interoperability.

We've conducted an exhaustive exploration of OOK—from mathematical foundations through practical system design. Let's consolidate the key insights:

What's Next:

Having mastered OOK, we'll now examine amplitude modulation's Achilles heel: noise sensitivity. We'll analyze how amplitude variations—whether from the intended signal or unwanted interference—affect AM/ASK performance, and understand why this limitation drives the development of angle modulation (FM/PM) and hybrid schemes.