Constellation Mapper For 4D-8Psk-Tcm; Figure 22: Constellation Mapper For 2 Bits/Channel-Symbol - Safran CORTEX Series User Manual

3.3.7.2.3

Constellation Mapper for 4D-8PSK-TCM

The constellation mapper principles are given in next figures for the four possible efficiencies of this
modulation (i.e., 2 bits/channel-symbol, 2.25 bits/channel-symbol, 2.5 bits/channel-symbol and 2.75
bits/channel-symbol). These mappers implement the straightforward logical mapping described in the
equations below. The correspondence between the signals Z
8PSK phase states of the constellations follows a natural mapping (i.e., 0, 1, 2 ..., 7).
(i)
If Z represents the signals (three lines) at the input of the modulator with Z
the first constellation and Z
represented by the following equation. This representation shows that the bits which are common to
each vector set (shown in the first part of right-hand side of each equation) are sensitive to a phase

rotation of /4 and will be differentially encoded.
(i) Equation for 2 bits/channel symbol efficiency:

 
( ) 0
Z

 
( ) 1
 Z   


 
( ) 2
Z
  
  
( ) 3
 

Z
x0
x1
x2
x3
x4
x5
x6
x7
x8
(0)
Z
Z
2
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(3)
being the signal set of the fourth constellation, the signal set Z
 
1
 
 
1

 
4 x 2 x x
 
8 5 1
1
 
 
 
1
2 1 0 2 1 0
+
2 1 0
(0) (0)
(1) (1)
(1)
Z
Z Z
Z
1 0
0
2 1

Figure 22: Constellation Mapper for 2 bits/channel-symbol

Ref.
Is.Rev
Date:
(i)
at the input of the modular and the
 
0
 
 
x
 
7
4
 
x
 
6
 
 
 
x x x
7 6 4
0
0
2 1 0
2 1 0
+
2 1 0
(2) (2) (2)
Z Z
Z
2 1 0
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(0)
being the signal set of
(i)

 
0
 

 
x

3
2 mod
 

x
 
2 
 
 

 
x x x

3 2 0
0
2 1 0
(1) (1) (1)
2 1 0
Z Z
Z
0
2 1
+
2 1 0
2 1 0 2 1 0
+
2 1 0
(3) (3) (3)
Z Z
Z
2 1 0
.
is
8
0
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