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.

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 (meaning 1 complete cycle every second)

This means the signal oscillates between +5 and −5, and it has a period of 1 second.

 

2. Pulse Position Modulation Concept

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

Let’s assume we sample the sinusoidal signal at regular time intervals (every Δt = 0.1 seconds). At each sample point, we adjust the position of the pulse based on the amplitude of the sine wave at that time.

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

If the amplitude is small (close to zero), the pulse will be closer to the reference time.

 

3. Calculating the Pulse Positions

Let’s compute the values of x(t) at several sample times and determine the pulse positions.

Time Sample 1: t = 0

x(0) = 5 sin(2π ⋅ 1 ⋅ 0) = 5 sin(0) = 0

Since the value is 0, the pulse will be positioned at the reference time, say at t = 0.

Time Sample 2: t = 0.1

x(0.1) = 5 sin(2π ⋅ 1 ⋅ 0.1) = 5 sin(0.2π) ≈ 5 × 0.5878 = 2.939

Since the amplitude is positive and non-zero, the pulse will be shifted forward in time. Let’s say it’s shifted by:

0.1 × x(0.1) = 0.1 × 2.939 = 0.294

So, the pulse will appear at:

t = 0.1 + 0.294 = 0.394 seconds

Time Sample 3: t = 0.2

x(0.2) = 5 sin(2π ⋅ 1 ⋅ 0.2) = 5 sin(0.4π) ≈ 5 × 0.9511 = 4.7555

Since the amplitude is relatively high, we shift the pulse even further. Let’s say the pulse is shifted by:

0.1 × x(0.2) = 0.1 × 4.7555 = 0.47555

So, the pulse will be at:

t = 0.2 + 0.47555 = 0.67555 seconds

Time Sample 4: t = 0.3

x(0.3) = 5 sin(2π ⋅ 1 ⋅ 0.3) = 5 sin(0.6π) ≈ 5 × 0.809 = 4.045

The pulse will be shifted by:

0.1 × x(0.3) = 0.1 × 4.045 = 0.4045

So, the pulse will be at:

t = 0.3 + 0.4045 = 0.7045 seconds

Time Sample 5: t = 0.4

x(0.4) = 5 sin(2π ⋅ 1 ⋅ 0.4) = 5 sin(0.8π) ≈ 5 × 0.9511 = 4.7555

The pulse will be shifted by:

0.1 × x(0.4) = 0.1 × 4.7555 = 0.47555

So, the pulse will be at:

t = 0.4 + 0.47555 = 0.87555 seconds

Time Sample 6: t = 0.5

x(0.5) = 5 sin(2π ⋅ 1 ⋅ 0.5) = 5 sin(π) = 0

At t = 0.5 seconds, the sine wave is at 0 again, so the pulse will be at the reference time t = 0.5.

 

4. Summary of Pulse Timing

Based on the sinusoidal signal, we have the following pulse positions (where the pulse is shifted according to the amplitude of the sine wave):

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 of such a system by falsifying the time at which the modulated pulses are judged to occur. Immunity to noise can be established by making the pulse build up too rapidly that the time interval during which noise can exert any perturbation is very short. Indeed, additive noise would have no effect on the pulse positions if the received pulses were perfectly rectangular, because the presence of noise introduces only vertical perturbations. However, the reception of perfectly rectangular pulses would require an infinite channel bandwidth, and the received pulses have a finite rise time, so the performance of the PPM receiver is affected by noise, which is to be expected.

As in a continuous wave (CW) modulation system, the noise performance of a PPM system may be described in terms of the output signal-to-noise ratio (SNR). Also, to find the noise improvement produced by PPM over baseband transmission of a message signal, we may use the figure of merit defined as the output signal-to-noise ratio of the PPM system divided by the channel signal-to-noise ratio. Assuming that the average power of the channel noise is small as compared to the peak pulse power, the figure of merit of the PPM system is proportional to the square of the transmission bandwidth of the (say, BT) normalized with respect to the message signal bandwidth (say, W). When, however, the input signal-to-noise ratio drops below a critical value, the system suffers a loss of the wanted message signal at the receiver output. That is a PPM system suffers from a threshold effect of its own.

 

Further Reading

1.  MATLAB Code for Pulse Width Modulation (PPM)