We can therefore approximate the p/4-DQPSK as a 4-level frequency shift keyed (FSK) modulation
scheme [14]. We will make use of this representation in the following mathematical coherent
analysis. Modeling p/4-DQPSK as 4-Level FSK we can write the above equations as
(4.23)
where a(t) are the symbols to be transmitted and given as .
The idealized transmit spectrum can be shown as in Fig. 4.6, assuming each phase change generates
a single spectral tone. In reality there will be many additional frequency components, but for
illustrative purposes let us assume they create a single spectral tone.
a(t) 5
1,
36 s(t) A(t) # cos[vct a(t) # 2p # fd1]
Rs /8,
3Rs /8
fd2
3
8Ts
3fd1
2pfd 2Ts
3p
4
u2 v2Ts
3p
4
fd1
1
8Ts
2pfd1Ts
p
4
u1 v1Ts
p
4
178 CHAPTER FOUR
fc + 3fd1 fc ??“ 3fd1 fc + fd1 fc ??“ fd1 fc
S( f )
f [Hz]
Rs
8
fd1 = ?±
FIGURE 4.6 Ideal 4-level FSK transmit spectrum.
The approach is to generate a local frequency such that when mixed with the received signal will
generate a spectral line (or tone) that can be used to estimate the received signal phase offset. A block
diagram of one such technique is given in Fig. 4.7, the performance results for GMSK are given in
[15] where this technique was called the open loop coherent detector.
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