Pulse Position Modulation (PPM)

The principle of PPM: information in timing

Pulse Position Modulation (PPM) is a digital technique in which information is represented by the time or position of a pulse within a defined symbol interval. The position is measured from the start of a frame or another synchronized reference. The receiver identifies the slot index containing the pulse and uses that index to recover the symbol.

In conventional PPM, pulses have a constant amplitude and duration $\tau$ , so the position carries the data relative to the synchronized reference. This parameter distinguishes PPM from ASK, which varies amplitude, and PWM, which varies pulse duration. With a normalized load, the energy of a rectangular pulse scales as $E_p \propto A^2\tau$ , and the average power in a frame of duration $T$ is $P_{\mathrm{avg}}=E_p/T$ .

How PPM works: symbols and time slots

PPM encoding divides time into frames and slots with known boundaries:

Time frame (T): Time is divided into frames of a fixed duration. Each frame carries one .
Time slots: Each frame is divided into smaller slots of equal duration. Their number depends on the number of bits assigned to a symbol, and the spacing must accommodate the pulse duration and any guard interval.
Encoding: To encode a group of $M$ bits, the system transmits a single pulse in one of the $2^M$ possible slots. Each bit combination is assigned one pulse position.

Example and raw bit rate

For 2 bits per symbol ( $M=2$ ), there are $2^2 = 4$ combinations ('00', '01', '10', '11'). The frame $T$ is divided into 4 slots. One possible assignment is:

'00' → Pulse in slot 1
'01' → Pulse in slot 2
'10' → Pulse in slot 3
'11' → Pulse in slot 4

With a frame duration of $T$ seconds and no coding overhead, $M$ bits per frame give a raw bit rate $R_b$ of $R_b = \frac{M}{T}$ bits per second.

Advantages and limitations of PPM

Advantages

Energy concentrated in a pulse: The transmitter emits one pulse with a defined energy in each frame, with the remaining frame interval left idle. In optical links with direct detection, this distribution can reduce the required average power for a target error performance. The result depends on the PPM order, pulse duration, and detector.
Position separated from amplitude: The information is the slot index, and the receiver can compare energy integrated in successive slots. Slow amplitude scaling can be compensated in the detection path. Thermal noise, interference, and timing jitter can still cause a missed pulse or a decision for the wrong slot.

Disadvantages and challenges

Requires precise : The receiver must know the frame start and the slot boundaries. Clock offset or jitter reduces the energy collected in the correct slot and increases the probability of a wrong decision.
Sensitivity to and echoes: In a wireless channel, a delayed copy of a pulse can enter a later slot and cause intersymbol interference. In fiber, modal or chromatic dispersion can produce a similar timing spread, so pulse duration and slot spacing must match the link response.
Bandwidth requirement: A short pulse has a wide spectrum. For pulse duration $\tau$ , the characteristic bandwidth scales approximately as $B \sim 1/\tau$ . The exact occupied bandwidth depends on pulse shape and filtering.

Applications and an advanced variant

Typical applications

PPM is used where pulse timing can be measured accurately and the power budget or detector architecture favors a pulse-based format:

Optical communication: Infrared systems, fiber links, and free-space optical links can generate precise pulses. Infrared remotes use time or position coding depending on the protocol.
Radio systems: Selected short-range systems, RFID, and Ultra-Wideband (UWB) links use pulse timing. The IEEE 802.15.4 HRP PHY uses burst position modulation (BPM) together with binary phase-shift keying.

Advanced variant: differential PPM (DPPM)

Differential PPM (DPPM), also called truncated PPM, starts the next symbol immediately after the slot containing the pulse. The remaining slots of the current symbol are flushed, so the pulse position also determines the symbol length and its relative position in the stream.

A variable symbol length can shorten the average transmission time and raise throughput. It also makes synchronization harder, and a missed pulse can shift the boundary of the next symbol. The receiver or decoder can then experience error propagation.