In PIM, the modulating signal is represented by a stream of pulses where the information is encoded in the time between two successive pulses. Unlike PPM no synchronisation of reference frame positions between modulator and demodulator is required. Demodulation is simply carried out by generating a sawtooth waveform, triggered by the received PIM signal, followed by a low pass filter to recover the original signal. Therefore, PIM offers the attractive features of PPM together with a less complex circuitry. Figure 3.1 shows PIM modulator and demodulator block diagrams and waveforms.
Uetio et al introduced PIM as modified PPM for transmission of a colour TV signal or 600 telephone channels [Uenol%\. He showed that low repetition rate of the modulating signal is also immune from the pattern effect due to the turn on delay of the laser in optical systems.
In Fig. 3.1, the modulating signal is compared with a linear ramp signal. The comparator generates an output signal (a pulse) every time the ramp signal exceeds the modulating signal. The pulse density of the PIM signal is high when the modulating signal amplitude level is low and vice versa. The PIM characteristic is exactly opposite to that of PFM. Okazaki investigated PIM for narrow-band transmission in industrial television systems \Okazakil%\. He showed that PIM is highly suitable for this type of application due to the reduction of the transmission time, low cost and reduced circuit complexity [Okazakil9].
PIM output D C shift Ramp Pulse generator Com parator PIM signal Modulating signal PIM signal (a) Sawtooth generator LPF (b) (c) Signal output Ramp signal Time
Fig. 3.1 PIM system block diagram: (a) modulator, (b) demodulator and (c) waveforms.
Nishida et al showed that PIM noise characteristics are similar to that of analogue FM and it can be further improved by employing pre-emphasis techniques [Nishida], Fyath
et al analysed the PIM spectral profile and showed that just like PWM and PFM it too
contains a baseband component. The spectral profile is expressed as [Fyath].
(3.1) 1+ ^ 2Z>* cos kcoj k=1 00 CO CO 1+2Z n I X M O0055 (ncoj+Lkk(Dj) n=l k=\ £*=—00 where
/.
= f c l + f t :1 - b - b = l - ( l V ) ^ P k = —r r s- ’ 2 b k f mt = tp_Pl2TaV.
f a - Average PIM sampling frequency,f c - PIM unmodulated sampling frequency
tp.p - Peak-to-peak pulse deviation
Ta - Average sampling time
A - Modulating signal peak amplitude.
V0 - PIM pulse amplitude,
f m - Modulating signal frequency
In Eqn. 3.1, the first square bracket contains the modulating signal and its harmonics, whereas the second square bracket shows the sampling frequency, its harmonics and a set of side tones displaced by the modulating signal frequency around them, see Fig. 3.2. V. < : 2/m 3/ 2'fm 2/* 3 / f a Frequency 2fa
Fig. 3.2 PIM spectra.
Spectral results were confirmed by Tripathi [TripathiSO], From Eqn. 3.1, the baseband component and its harmonics can be given by,
*.(*) = 2 K L i - O -rzy
v r
(3.2)
where xm(k) represents the k01 harmonic component.
From Eqn. 3.2, the harmonics of the modulating signal frequency are modulation index dependant and the results for second and the third harmonic distortion are presented in Fig. 3.3.
-10 Second harm onic Third harm onic -50 -60 0.2 0.4 0.6 Modulation index 0.8
Fig. 3.3 PIM harmonic distortion.
From Fig. 3.3, it can be seen that second and the third harmonic level increases with the modulation index. At low modulation indices (<20 %), where harmonic distortion levels are small, a low order low pass filter may be used to recover the information signal. At higher modulation indices, spectral overlap may take place in the base band region, and a higher order low pass filter is required.
The required bandwidth (B) for PIM depends on the pulse width r such that,
r
Both the channel and the receiver must provide adequate bandwidth in order to propagate and regenerate the PIM pulse train. The sampling interval must also be large enough so that the minimum interval between two pulses is large enough in order to avoid inter pulse interference. Ueno et al investigated PIM for frequency division multiplexed (FDM) telephone signals transmission over optical fibre [UenolS]. The
SNR expression developed for FDM signals can be modified for a single base band signal by assuming that the system transmission bandwidth is B, sampling ratio is 2,
average sampling frequency is twice the unmodulated PIM frequency and pulse rise time Tr - 2/7LB [Black]. This is given by,
Tripahy has reported that PIM demonstrate a threshold effect at CNR of about 18 dB at corresponding to the output SNR of 17 dB and it gives SNR/CNR gradient of 1 dB for any further increase in CNR [Tripathy$3]. Ueno also showed that when applied in optical transmission of colour TV signal, PIM can achieve an output SNR of 52 dB for - 20 dB of peak optical power [Uenol5].
The predominant source of non-linear distortion of the demodulated signal in the PIM signal is the non-linearity of the ramp waveforms. This can be reduced by proper circuit design as it does not require absolute linearity of the ramp signal but there must be identical slopes at the modulator and demodulator. It has also been reported that there exists self-imposed non-linear distortion as the PIM signal also has a component of pulse density modulation because of the modulation principal [ UenolZ]. The source of this distortion is inherent in the ramp signal and the reset operation to the reference level after each sample of the input signal. The deviation in reset time translates itself into density modulation. At the demodulator, by converting PIM pulse train into a ramp waveform this effect can be reduced. Ghassemlooy has shown that, this distortion can be kept to a minimum provided the ramp waveform is reset within a PIM pulse duration, no matter what the amplitude of the modulating signal is. Therefore, PIM pulse become less dependant on the reset time [Ghassemlooy91].
Ghassemlooy et al proposed digital means of generating PIM, namely digital pulse interval modulation (DPIM) to over come the non-linearity problems caused by the mismatches of the ramp waveforms [Ghassemlooy95/l],