As
time and technology progressed more accurate signal processing algorithms were invented and
applied in the baseband, complex envelope domain (digital section) [9??“11].
4.2.1 Costas Loop
This first coherent detection technique builds upon the Costas loop receiver shown below [12]. The
received signal is directly converted to ZIF by the quadrature demodulator operation. The locally
generated carrier signal is adjusted by low pass filtering the product of the baseband I- and Q-signals
(see Fig. 4.4).
The received signal is represented as follows, where u(t) is the modulation signal and f(t) is the
phase offset.
(4.2) r(t) A(t)cos[2pfct u(t) f(t)]
CR
r(t) = Re{ej[2pfct+q (t)+f]}
LPF
cos(2pfct + f)
d(t) = Re{ej[2p??†ft+q (t)+f??“f]} ?†
?† ?† ?†
??†f = fc ??“ fc
FIGURE 4.2 Coherent detection principle.
The corresponding baseband signals are, where is the locally generated phase offset.
(4.3)
(4.4)
The output of the mixer/multiplier is given as
(4.5)
Next we apply the low pass filter (LPF) to remove the modulation signal to produce
(4.6)
where K gain constant (overall). Hence the signal that controls the Voltage Control Oscillator
(VCO) is dependent on the phase difference between the received signal and the locally generated signal.
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