Digital Pulse Position Modulation (DPPM)

DPPM can be used to transmit an analogue signal or a block of symbols. In the former case, input to the DPPM modulator is M bit symbols generated by an ADC. The DPPM frame time is made equivalent to the sampling time of the analogue signal. In the later case, the frame time is equivalent to the M bit symbol time. Figure 2.11 shows the

(2.9)

parameters used to describe a DPPM frame. An M bit symbol is encoded as a single pulse of one time slot duration placed in a frame of L time slots (TJ), where L = 2M

accommodating all the M bit symbol permutations. A guard space is introduced in each frame to avoid inter frame interference due to dispersion in narrow band channels. Thus, an actual frame is a combination of a guard space and an effective frame. The ratio of effective frame to actual frame is given in terms of compression index (c), which is also known as modulation index in most of the literature on DPPM. The number of time slots in the guard band is given by (l-c )lo g2 Z,/c. The compression

index determines the effective frame, hence the slot width. The higher the compression index the longer the effective frame and vice versa.

A DPPM time slot Td can be represented by, clogj^,

i L b

where Tb is the source bit period.

(2.11)

The slot frequency (fd) can be determined by,

LB

/ , = clog2i (2.12)

where B is the source bit rate.

M bit symbols

Frame. T,_'-*1r~r-r- L-DPPM

Fig. 2.11 A typical DPPM frame.

i rn ii 11 in n—h i rn 111 n n i cT, slots

/

0 ' C)T f time

The pulse stream shown in Fig. 2.11 can be represented by,

* W = ( 2 1 3 )

k= -< X )

where Sk represents the random symbol sequence coded into DPIM process.

This scheme was initially proposed in the late 1960s as a suitable modulation scheme for deep space communications [Karp]. It was shown that information capacity can be increased by selecting a higher symbol level. But the drawback is as the symbol level increases the slot width or the pulse width reduces, demanding higher transmission bandwidth. Garrett proposed DPPM for optical fibre communications, where bandwidth is not a bottleneck. In this work he showed that receiver sensitivity is optimum for coding level of M = 5 and a matched filter followed by a proportional- derivative and delay network can be used to improve the detection process

[Garrett%3/\,2]. Calvert reported receiver sensitivity improvement upto 4.2 dB

[Calvert], whereas Garrett reported a further 3.5 dB more compared to equivalent PCM [GarrettS9]. Further improvement is possible when using APDs over long haul communication links [Pires], Matin investigated DPPM over local area networks and concluded that it is feasible to deploy DPPM which provide pulses with higher peak power than that of PCM [Matin$9,92], This is ideal for applications where laser or LED is used as an optical source. Furthermore, high peak narrow optical pulses aid detection under noisy environment [Prati].

Figure 2.12 shows block diagram representation of the modulator and demodulator for transmission of an analogue signal or a block of symbols. System modulator and demodulator are shown in Fig. 2.12 and can be simply described as follows. The input to the modulator is either a serial bit stream of B bps or M bit symbols from an ADC at

symbol rate of ff= HTf. In the former case, serial to parallel conversion has taken place while in the latter the ADC converts the modulating signal to M bit symbols. In both cases, symbols are stored into the data latch in a controlled manner defined by an enable signal. This signal allows a sufficient time for the comparator to identify the symbols in the latch before comparison takes place. The counter is clocked at the slot rate and is reset by the source symbol rate. The slot frequency is chosen to be an integer multiple of the symbol frequency and the two signals are in phase with each other.

From Eqn. 2.12,

L _ = L (2.13)

/ / c

To include a guard space in an each frame, the counter resolution (Mc) should be selected to be higher than the symbol resolution. When the counter output is equivalent to the source symbols the comparator gives a pulse of one slot duration. This is in fact the DPPM signal. Enable / M, / ,H z DPPM M bit symbols B bps

Serial bit stream u =?

Comparator Reset

latch ADC

SIPO _shaperPulse

Counter

SIPO - serial input parallel output

Encoder (a)

M , /-H z

___

M bit symbols _{B bps}

Serial bit stream

Reset

DAC

PISO

Counter Latch

PISO - parallel input serial output Decoder

(b)

Fig. 2.12 (b) DPPM block diagram: Demodulator for an analogue or a digital link. A pulse transform circuit is applied at the comparator output if a different form of pulse

is required. The guard band is chosen by selecting c according to Eqn. 2.12 and the

counter is selected with resolution of M z such that M c > L/c.

At the receiver the incoming DPPM signal is used to extract slot frequency and frame

phase [Elmirghani94/\,3], [Davidson89], [Sun9Qi\. The recovered slot clock is used as

the clock for the counter and the frame clock resets the counter at regular frame intervals. The counter output is latched on occurrence of a pulse in the incoming signal.

In the case of analogue signal transmission the latched symbols are sent through a DAC and the original signal is reconstructed, whereas for discrete information source the latched symbols are sent through a parallel to serial converter. DPPM spectral profile has been presented by Elmirghani for pulse shape of g(t) as [Elmirghan94! 1,95],

to II A. -jrfl 2' G ( / ) 2 > 1 e t J > V ' U I II o

where Ln is the number of DPPM frames used in the spectral realisation and G(j) is the

pulse shape transform G( f ) A 3{g(/)}. Figure 2.13 shows the spectra corresponding

to rectangular half slot width pulses. Spectra have been shown to exhibit a distinct component at odd harmonics of the slot frequency. The power of the slot frequency

component is sensitive to the pulse width. It is optimum for pulse width of half a time

slot. For dispersed pulses i.e. Gaussian shaped pulses, the spectra become flattened and the slot component remains distinct along with its harmonics. The slot frequency and the correct phase can be extracted by simply using a phase lock loop (PLL) .

At high speed and high coding levels slot and frame synchronisation becomes a complex and tedious task. To ease this, line coding [Yichad\\ transition sequence detection

[Elmirghani93], block synchronisation [Sugiyama93] or sequence detection

[Gagliadi&l] have been suggested.

Slot frequency component

1 2 3 4

Normalised frequency

Fig. 2.13 DPPM spectral profile for half slot width pulses.

Receiver sensitivity performance is said to be limited by the effect of three error sources in noisy conditions, namely: erasure, false alarm and wrong slot errors. Erasure is when the pulse goes undetected due to noise forcing the actual pulse below the receiver threshold. The reverse effect causes the false alarm error. That is, noise crossing the threshold and falsely indicating a presence of a pulse. A wrong slot error occurs when

adjacent slots, corresponding to a correct pulse are wrongly detected. This is due to noise corrupting the pulse edges. Receiver sensitivity of the system is determined by the above three error sources.