Pulse Position Modulation (PPM)

Pulse Position Modulation (PPM) is a type of signal modulation in which M message bits are encoded by transmitting a single pulse within one of 2ᴹ possible time positions within a fixed time frame. This process is repeated every T seconds, resulting in a data rate of M/T bits per second.

Pulse Position Modulation Example

Bits per symbol: m = 3

Number of slots per symbol duration: M = 2^m = 2^3 = 8

Example symbol: 101 → decimal 5 → pulse sent in slot 5 (out of 0…7)

Symbol duration: T_s = 8 ms → each time slot: T_slot = T_s / M = 8 / 8 = 1 ms

Pulse for symbol 101 is transmitted between 5 ms and 6 ms.

Timeline representation of 3-bit PPM

Slot: 0   1   2   3   4   5   6   7
Time: 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 ms
Pulse →                           █
    

PPM is a form of analog modulation where the position of each pulse is varied according to the amplitude of the sampled modulating signal, while the amplitude and width of the pulses remain constant. This means only the timing (position) of the pulse carries the information.

PPM is commonly used in optical and wireless communications, especially where multipath interference is minimal or needs to be reduced. Because the information is carried in timing, it's more robust in some noisy environments compared to other modulation schemes.

Although PPM can be used for analog signal modulation, it is also used in digital communications where each pulse position represents a symbol or bit pattern. However, it is not ideal for transmitting complex data files, as it is generally used for simple or low-data-rate signaling.

Fig: PPM Waveforms

Demodulation of PPM Signal

The noise-corrupted PPM waveform is received by the PPM demodulator circuit. A pulse generator produces fixed-duration pulses from the incoming PPM signal and applies these pulses to the reset (R) input of an SR flip-flop.

Simultaneously, a reference pulse train of fixed frequency is extracted (or generated) from the PPM signal and applied to the set (S) input of the flip-flop.

As a result of these set and reset signals, the SR flip-flop generates a PWM (Pulse Width Modulated) waveform at its output. The width of each pulse corresponds to the time delay between the reference pulse and the received PPM pulse — effectively recovering the original signal information.

Pulse Position Modulation (PPM) of Sinusoidal Signal

We have a sinusoidal signal:

x(t) = A sin(2π f t)

And we want to modulate this signal using Pulse Position Modulation (PPM).

Step-by-Step Example

1. Sinusoidal Signal

Let’s define a sinusoidal signal as:

x(t) = 5 sin(2π ⋅ 1 ⋅ t)

This is a sine wave with:

• Amplitude: A = 5
• Frequency: f = 1 Hz

2. Pulse Position Modulation Concept

We’ll now encode information into the timing of pulses based on this sinusoidal signal.

If the amplitude is large (positive or negative), the pulse will be farther from a reference time (i.e., delayed). If it’s small, the pulse will be closer to the reference time.

3. Calculating the Pulse Positions

We compute the values of x(t) and the corresponding pulse positions:

Time Sample 1: t = 0

x(0) = 5 sin(0) = 0

Pulse at reference time t = 0.

Time Sample 2: t = 0.1

x(0.1) = 5 sin(0.2π) ≈ 2.939
Shift = 0.1 × 2.939 = 0.294
t = 0.1 + 0.294 = 0.394 seconds

Time Sample 3: t = 0.2

x(0.2) = 5 sin(0.4π) ≈ 4.7555
Shift = 0.1 × 4.7555 = 0.47555
t = 0.2 + 0.47555 = 0.67555 seconds

Time Sample 4: t = 0.3

x(0.3) = 5 sin(0.6π) ≈ 4.045
Shift = 0.1 × 4.045 = 0.4045
t = 0.3 + 0.4045 = 0.7045 seconds

Time Sample 5: t = 0.4

x(0.4) = 5 sin(0.8π) ≈ 4.7555
Shift = 0.1 × 4.7555 = 0.47555
t = 0.4 + 0.47555 = 0.87555 seconds

Time Sample 6: t = 0.5

x(0.5) = 5 sin(π) = 0
Pulse at reference time t = 0.5

4. Summary of Pulse Timing

Pulse positions based on sinusoidal amplitude:

Sample Time (t)	Amplitude x(t)	Pulse Position (tpulse)
0.0	0	0.0
0.1	2.939	0.394
0.2	4.7555	0.67555
0.3	4.045	0.7045
0.4	4.7555	0.87555
0.5	0	0.5

Effect of Noise on Pulse Position Modulation

Since in a PPM system the transmitted information is contained in the relative positions of the modulated pulses, the presence of additive noise affects the performance by falsifying the perceived pulse timing. Immunity to noise can be improved by making the pulse rise rapidly, reducing the time window for noise interference.

In theory, noise would have no effect if pulses were perfectly rectangular (requiring infinite bandwidth). In practice, finite rise times mean some degradation is inevitable. Similar to continuous-wave modulation, PPM performance can be evaluated using the output signal-to-noise ratio (SNR). The figure of merit compares output SNR to channel SNR, showing that performance improves with bandwidth but suffers a threshold effect when SNR drops too low.

Further Reading

1. MATLAB Code for Pulse Position Modulation (PPM)