Z87200 View Datasheet(PDF) - Zilog
Part Name
Description
MFG CO.
'Z87200' PDF : 54 Pages View PDF
Zilog
Z87200
Spread-Spectrum Transceiver
Differential Demodulation
The fixed phase rotation ωfixed has been introduced to later
As noted in the preceding text, computation of the “Dot”
and “Cross” products is fundamental to operation of the
DPSK Demodulator and Frequency Discriminator. Let Ik
and Qk represent the I and Q channel inputs, respectively,
simplify the decision criteria. The ability to express real and
imaginary parts of the complex conjugate product between
consecutive symbols with the Dot and Cross products is
the key to their use in DPSK demodulation.
4
for the kth symbol after downconversion and despreading. DBPSK Demodulation
The Dot and Cross products can then be defined as:
In DPSK, the phase difference between successive sam-
Dot(k) = Ik Ik-1 + Qk Qk-1; and,
Cross(k) = Qk Ik-1 - Ik Qk-1
ples is due to the data modulation phase differences,
Ưmod, plus any induced phase rotation between sym-
bols, Ưrot, resulting from, for example, a frequency offset
In the complex domain, these products can be seen to
have been defined to form the complex conjugate product
between two input samples, one symbol apart. Let the kth
input sample, sin(k), be defined as:
between the received signal’s I.F. and that provided by the
Downconverter. For DBPSK, the data modulation differ-
ences ∆Ømod can take only the values of 0° or 180°. Ex-
pressing the complex phase difference [Ø(k)-Ø(k-1)] in
terms of these components, the decision can be seen to be
sin(k) = I(k) + j Q(k),
based on:
where I(k) and Q(k) are the 8-bit peak power PN Matched
Sout(k)=A(k) A(k-1) ejØ(k)*e-jØ(k-1)
Filter I and Q channel outputs directed to the DPSK De-
modulator. In polar form, sin(k) may be conveniently de-
fined as:
= A(k)*A(k1)*ej[Ưmod(k)+Ưrot(k)]
For DBPSK, only the real part of sout(k), Dot(k), is needed
sin(k) = A(k)e jØ(k)
to determine the modulated phase transition:
with
Dot(k)= A(k)*A(k-1)*cos(Ưmod(k)+Ưrot(k))
A(k)
= ±A(k)*A(k-1)*cos(∆Ørot(k))
Ø(k) = arctan
where the sign is determined by the transmitted data since
cos[∆Ømod(k)] = ±1* As a result,
Dot(k)≈ ±A2(k)
Simple substitution then shows that the complex conjugate
product between consecutive symbols (with an arbitrary
phase shift introduced to the previous symbol value) may
be expressed as:
sout(k)= sin(k) [sin(k–1) . ωfixed]*
if the amplitude of the signal is constant for consecutive
symbols and if the phase rotation Ưrot(k) between sym-
bols is small. The Z87200 DPSK Demodulator can thus
use the sign of the Dot product in order to make DBPSK
symbol decisions without the introduction of any fixed
phase rotation.
= Dot(k) + j Cross(k)
where
ωfixed = arbitrary fixed phase rotation;
Dot(k)= Re[sout(k)]; and,
Cross(k)= Im[sout(k)]*
DS96WRL0400
4-47
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