Z87200 datasheet(47/54 Pages) ZILOG

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Z87200

Zilog

Spread-Spectrum Transceiver

DS96WRL0400

4-47

Differential Demodulation

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,

for the kth symbol after downconversion and despreading.

The Dot and Cross products can then be defined as:

Dot(k) = Ik Ik-1 + Qk Qk-1; and,

Cross(k) = Qk Ik-1 - Ik Qk-1

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:

sin(k) = I(k) + j Q(k),

where I(k) and Q(k) are the 8-bit peak power PN Matched

Filter I and Q channel outputs directed to the DPSK De-

modulator. In polar form, sin(k) may be conveniently de-

fined as:

sin(k) = A(k)e

jØ(k)

with

A(k)

Ø(k) = arctan

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]*

= Dot(k) + j Cross(k)

where

fixed = arbitrary fixed phase rotation;

Dot(k)= Re[sout(k)]; and,

Cross(k)= Im[sout(k)]*

The fixed phase rotation

fixed has been introduced to later

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.

DBPSK Demodulation

In DPSK, the phase difference between successive sam-

ples is due to the data modulation phase differences,

∆Ømod, plus any induced phase rotation between sym-

bols,

∆Ørot, resulting from, for example, a frequency offset

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

based on:

Sout(k)=A(k) A(k-1) ejØ(k)*e-jØ(k-1)

A(k)*A(k1)*e

∆Ø

mod

(k)+

∆Ø

rot(k)]

For DBPSK, only the real part of sout(k), Dot(k), is needed

to determine the modulated phase transition:

Dot(k)= A(k)*A(k-1)*cos(∆Ømod(k)+∆Ørot(k))

±A(k)

*A(k-1)*cos(∆Ørot(k))

where the sign is determined by the transmitted data since

cos[

∆Ø

mod(k)] = ±1* As a result,

Dot(k)

≈ ±A2(k)

if the amplitude of the signal is constant for consecutive

symbols and if the phase rotation

∆Ø

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.

Z87200 Datasheet(PDF) 47 Page - Zilog, Inc.

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