DQPSK inserts the information into phase differences of the signal to be transmitted. In the
Cartesian coordinate system, this is represented as (where k denotes the symbol time index)
(2.20)
And in the Polar coordinate system this is represented as (given ) and called phase differential
encoding.
(2.21)
where is the present phase to be transmitted, is the previously transmitted phase, and
is the present phase change to be used to transmit the information signal. Let us present an alternative
approach and discuss the polar coordinate implementation.
Figure 2.36 depicts the DQPSK modulator.
The LUT is essentially performing the operation of a phase state
table. An example of such a phase state table or mapping is provided
in Table 2.3.
This table has the corresponding signal constellation diagram in
Fig. 2.37.
Sometimes, this is referred to as /2-DQPSK because the four
allowable phase changes are multiples of /2. These phase changes
are controlled by the phase state table and implemented with the
phase differential encoding equation given earlier. In the receiver,
we wish to determine the phase change amount on the signal. Since we have a single equation with a
single unknown, the answer is trivial and is mathematically represented as
(2.
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