0195136047.pdf

15.3 DIGITAL COMMUNICATION SYSTEMS 719

where the numeratorS 0 /Nqis given by Equation (15.3.5), or by Equation (15.3.9) when Equation
(15.3.6) applies. Ifε^2 n(t) << ε^2 q(t), noise has no effect on performance; otherwise it has a
significant effect. Thus,εn(t)gives rise to athreshold effectin PCM.

Signal Multiplexing

Frequency-division multiplexing (FDM) and time-division multiplexing (TDM) systems were
introduced in Section 14.2. When data from many sources in time are interlaced, the interlacing
of data is calledtime multiplexing, in which case a single link can handle all sources. Figure
15.3.9(a) illustrates time multiplexing soon after sampling forNsimilar messages. With proper
interleaving of sampling pulses [see Figures 15.3.9(b) and (c) for individual message signal
waveforms], the train of samples can be added for the signal at pointAin Figure 15.3.9(a), as
shown in Figure 15.3.9(d). If we considerNsimilar messages of spectral extentWfrad/s, the
sampling intervalTsmust satisfy

Ts≤

π

Wf

(15.3.14)

based on the sampling theorem (see Section 14.2). Atime slotis the time per sampling interval
that is allowed per message. It is equal to the sum of the sampling-pulse durationτand separation
τg, called theguard time. Thus, we have

τ+τg=

Ts

N

≤

π

NWf

(15.3.15)

The time that is required to gather at least one sample of each message is known as aframe,
which isTs, as shown in Figure 15.3.9(d). Now, with a single composite source of the waveform
shown in Figure 15.3.9(d) at pointAof Figure 15.3.9(a), the time multiplexer of Figure 15.3.9(a)
operates beyondA. ForNb-bit encoding, each time slot in the output PCM signal will haveNbbits
of duration,

Tb=

Ts

NNb

(15.3.16)

It is assumed that all sample trains are derived from the same timing source, called aclock, and
hence have the same frequency. Instead of using up all frame time for messages, some time is
usually allocated for synchronization so that the receiver will know the start times of frames. The
American Telephone and Telegraph Company (AT & T) employs a device known as aD3 channel
bank, which is a synchronous multiplexer, whose characteristics are as follows:

• It multiplexes 24 telephone messages, each having an 8-kHz sampling rate so thatTs=
  1 /( 8 × 103 )= 125 μs. The digital structure of each input message is determined by a single
  master clock.


• Each sample uses 8-bit encoding, so that there are 8× 24 =192 message bits; one extra
  bit, known as aframing bit, of less than one time slot is allowed for frame synchronization.
  Thus, a total of 193 bits per frame, with a total bit rate of 193× 8000 = 1 .544 megabits
  per second (Mbit/s), is available.


• The frame structure is illustrated in Figure 15.3.10.


• Bit robbingorbit stealing,which is the occasional borrowing of a message bit for purposes
  other than message information, is done for signaling, which refers to conveying information
  concerning telephone number dialed, dial tone, busy signal, ringing, and so on.