Communications Blockset

Gray Coded M-PSK Modulation

The M-PSK Modulator Baseband block:

• Accepts binary-valued inputs that represent integers between 0 and M-1
• Maps binary representations to constellation points using a Gray-coded ordering
• Produces unit-magnitude complex phasor outputs, with evenly spaced phases between 0 and 2(M-1)/M

The table indicates which binary representations in the input correspond to which phasors in the output. The second column of the table is an intermediate representation that the block uses in its computations.

Modulator Input	Gray-Coded Ordering	Modulator Output
000	0
001	1
010	3
011	2
100	7
101	6
110	4
111	5

The table below sorts the first two columns of the table above, according to the output values. This sorting makes it clearer that the overall effect of this subsystem is a Gray code mapping as shown in the figure below. Notice that the numbers in the second column of the table below appear in counterclockwise order in the figure.

Modulator Output	Modulator Input
	000
	001
	011
	010
	110
	111
	101
	100

Integer-to-Bit Conversion

AWGN Channel