Z87200 Datasheet, PDF (47/54 Pages) Zilog, Inc. – Spread-Spectrum Transceiver

Zilog
Z87200
Spread-Spectrum Transceiver
Differential Demodulation
The fixed phase rotation ω_fixed 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 I_k
and Q_k 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.
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for the k^th 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) = I_k I_k-1 + Q_k Q_k-1; and,
Cross(k) = Q_k I_k-1 - I_k Q_k-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 k_th
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
s_in(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) e^jØ(k)*e^-jØ(k-1)
Filter I and Q channel outputs directed to the DPSK De-
modulator. In polar form, s_in(k) may be conveniently de-
fined as:
= A(k)_*A(k1)_*e^{j[Ưmod(k)+Ưrot}(k)]
For DBPSK, only the real part of sout(k), Dot(k), is needed
s_in(k) = A(k)e ^jØ(k)
to determine the modulated phase transition:
with
Dot(k)= A(k)_*A(k-1)_*cos(Ư_mod(k)+Ưrot(k))
A(k)
= ±A(k)_*A(k-1)_*cos(∆Ø_rot(k))
Ø(k) = arctan
where the sign is determined by the transmitted data since
cos[∆Ø_mod(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:
s_out(k)= s_in(k) [s_in(k–1) . ω_fixed]_*
if the amplitude of the signal is constant for consecutive
symbols and if the phase rotation Ư_rot(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
ω_fixed = arbitrary fixed phase rotation;
Dot(k)= Re[s_out(k)]; and,
Cross(k)= Im[s_out(k)]_*
DS96WRL0400
4-47