0195136047.pdf

742 COMMUNICATION SYSTEMS

whereSˆi/Niis the ratio of the power in the signal

peak amplitude (at the integrator output at the

sample time) to the average noise power at the

same point. For(Sˆi/Ni)PCM=32 at the sampler,

findPefor a unipolar and a polar system. In which

system will the bit errors occur more frequently?

15.3.15For a Manchester PCM system, expressions forEb
andPeare given in Problems 15.3.13 and 15.3.14.
Determine:

(a) The minimum value of(Sˆi/Ni)PCMthat is

needed to realizePe= 10 −^4.

(b) The minimum input-pulse amplitudeAre-

quired ifPe= 10 −^4 ,N 0 = 8 × 10 −^7 V^2 /Hz,

andTb= 0. 4 μs.

15.3.16For polar or Manchester PCM, Equation (15.3.13)
is sometimes expressed as
(
S 0
N 0

)

PCM

=

S 0 /Nq

1 + 22 Nb+^1 erfc





√√

√√ 1

2

(

Sˆi

Ni

)

PCM





whereSˆi/Niis the ratio of the power in the signal

peak amplitude (at the integrator output at the

sample time) to the average noise power at the

same point, andNbis the number of bits in a

natural binary code. In a polar PCM system, with

Nb=8 and(Sˆi/Ni)PCM=20, find(S 0 /N 0 )PCM

for the message if its crest factor is 3. Assume that

all levels span the variations of the analog mes-

sage. Comment on whether the system is operating

above threshold.

*15.3.17The expression given in Problem 15.3.16 for

(S 0 /N 0 )PCMis plotted for a sinusoidal message in

Figure P15.3.17 to show the performance curves

for a PCM system using a polar waveform.

(a) Comment on the threshold effect.

(b) For the polar system of Problem 15.3.14, with

Nb=8 and(Sˆi/Ni)PCM = 32, determine

whether the system noise has significant effect

on performance.

15.3.18Four voice messages, each with 3-kHz bandwidth,

are to be sampled at Nyquist rate, and time-

multiplexed with samples taken at twice the

Nyquist rate from six analog monitoring signals,

each with 0.5-kHz bandwidth. Determine the du-

ration of the frame and suggest a sampling scheme

indicating the timing of samples.

70

614

Si

NiPCM, dB

S^0

PCM

, dB

N^0

10 18 22 26

Nb = 10

9 8 7 6 5 4 3 2

60

50

40

30

20

()

()

10

0

^

Figure P15.3.17