• With 8-PSK, three bits are encoded, forming tribitsand producing eight different output phases. With 8-PSK, n=3,M=8, and there are eight possible output phases. To encode eight different phases, the incoming bits are encoded in groups of three, called tribits (2^3 = 8).

2-to-4-levelconverter

2-to-4-levelconverter

Reference oscillator

Productmodulator

+90°

Productmodulator

Bandpassfilter

Linear summer

Bandpassfilter

Q I CInput data fb

I Channelfb/3

fb/3

fb/3

C

C’PAM

Sin ωct

Cos ωct

Q Channel

Bandpassfilter 8-PSKoutput

Fig. 23 : 8-PSK modulator

I C Output0 0 -0.5410 1 -1.3071 0 +0.5411 1 +1.307

I C’ Output0 0 -1.3070 1 -0.5411 0 +1.3071 1 +0.541

I- and Q-channel 2-to-4-level converters: (a) I-channel truth table; (b) Q-channel truth table (c) PAM levels

+1.307 V

+0.514 V- 0.514 V

-1.307 V

0 V

(a) (b) (c)

For a tribit input of Q 0, I= 0, and C 0 (000), determine the output phase for the 8-PSK modulator shown in Figure 23

8-PSK modulator: truth table

Q I C0 0 0 -112.5°0 0 1 -157.5°0 1 0 -67.5°0 1 1 -22.5°1 0 0 +112.5°1 0 1 +157.5°1 1 0 +67.5°1 1 1 +22.5°

Binary Input 8-PSK output phase

c c Sin ωct- Sin ωct

Cos ωct

- Cos ωct

-0.541 sin ωct + 1.307 cos ωct

-1.3071 sin ωct + 0.541 cos ωct

+0.541 sin ωct + 1.307 cos ωct

+1.3071 sin ωct + 0.541 cos ωct

+1.3071 sin ωct - 0.541 cos ωct

+0.541 sin ωct - 1.307 cos ωct

-1.3071 sin ωct - 0.541 cos ωct

-0.541 sin ωct - 1.307 cos ωct

Phasor Diagram

c c Sin ωct- Sin ωct

Cos ωct

- Cos ωct

100

101

001

000

110

111

011

010

Constellation Diagram

It should also be noted that the tribit code between any two adjacent phases changes by only one bit. This type of code is called the Gray code or, sometimes, the maximum distance code. This code is used to reduce the number of transmission errors. If a signal were to undergo a phase shift during transmission, it would most likely be shifted to an adjacent phasor. Using the Gray code results in only a single bit being received in error.