0195136047.pdf

15.3 DIGITAL COMMUNICATION SYSTEMS 729

Pe

Eb

N 0

100

ASK (noncoherent)

FSK (noncoherent)

ASK (coherent)

FSK (coherent)

PCM (unipolar)

PCM (polar)

PCM (Manchester)

PSK

DPSK

0168 12

10 log (dB)

4

10 −^1

10 −^2

10 −^3

10 −^4

10 −^5

10 −^6

10 −^7

Figure 15.3.20Plots ofPeversus [Eb/N 0 ]dBfor various

digital communication systems.

EXAMPLE 15.3.3

Let both coherent ASK and coherent PSK systems transmit the same average energy per bit interval
and operate on the same channel such thatEb/N 0 =18. Determine the bit-error probabilityPe
for the two systems.

Solution

From Equation (15.3.24) it follows for coherent ASK,

Pe=

1

2

erfc

√

Eb

2 N 0

=

1

2

erfc

√

18

2

=

1

2

erfc( 3 )

∼=^1

2

e−^9

3

√

π

[from Equation (15.3.26)]

∼= 1. 16 × 10 −^5

and for coherent PSK,

Pe=

1

2

erfc

√

Eb

No

=

1

2

erfc

√

18 =

1

2

erfc( 4. 243 )