COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
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It cannot be duplicated or distributed without expressed written consent.
3.3.6.3.5. Constellation Mapper for 4D-8PSK-TCM
The constellation mapper principles is given for the 2 bits/channel-symbol modulation as an example. The
mapper is slightly different for each rate. These mappers implement the straightforward logical mapping
described in the equations below. The correspondence between the signals Z(i) at the input of the modular and
the 8PSK phase states of the constellations follows a natural mapping (i.e., 0, 1, 2 …, 7).
If Z(i) represents the signals (three lines) at the input of the modulator with Z(0) being the signal set of the first
constellation and Z(3) being the signal set of the fourth constellation, the signal set Z(i) is 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 π/4 and will be differentially
encoded.
Equation for 2 bits/channel symbol efficiency:
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