mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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90 LINEAR EQUALIZATION<br />
where emj(n) can be interpreted as a chip estimate during symbol period m»<br />
for transmitter i () . We can stack these estimates into an N c x 1 vector β^" =<br />
[e ( m,}(0) ... e {^{N c - l)] r , which is obtained by<br />
where<br />
e = W H v, (4.122)<br />
W = C" 1^"' (4.123)<br />
F(¿„) = [f(¿n)( 0 ) ... f( ¿ ")(iV c -l)l . (4.124)<br />
We can interpret the operation in (4.122) as a matrix equalizer (matrix multiply),<br />
in which the nth column of W is a weight vector used to obtain an estimate of the<br />
nth chip transmitted from transmitter ¿ ( > during symbol period mo.<br />
While the elements of F**"' do not depend on fco or mo, the elements of C„ do.<br />
As a result, the entries in W will be code-specific , a function of the spreading codes<br />
used during symbol period mo.<br />
We can trade performance for reduced complexity by approximating C„ with<br />
its average, averaged over the possible spreading codes. Then W would be the<br />
same for each symbol period, requiring fewer weight computations. However, even<br />
with code-averaging, we would still need a separate weight vector for each chip<br />
period. We can reduce complexity further by constraining the equalizer to use a<br />
sliding window of receive samples when computing different chip estimates. Such a<br />
form of equalization is called transversal equalization. Specifically, when forming<br />
em„ (no), we use<br />
v(m 0 7' + n„T c + djT s ), j = 0, ...,J-1, (4.125)<br />
where dj is a relative processing delay, relative to both the symbol period and the<br />
chip period within the symbol. Complexity is reduced because with code averaging,<br />
the weight vector is the same for each chip period no and each symbol period mo.<br />
Before performing code averaging, let's look at the code-specific transversal solution.<br />
To obtain the weight vector for forming eS„(no), we can use the analysis<br />
above, assume<br />
Aj = n t) T c + d/F a , (4.126)<br />
and examine the noth column of W in (4.123) (denoted w). From (4.123),<br />
C v (m 0 )w = ¥*\n 0 T c ). (4.127)<br />
where C„(mo) is a JN r x JN r matrix of the form given in (4.111) and (4.113) and<br />
f (i ">(n7' c ) is defined in (4.120). From (4.120) and (4.126), we see that f' io >(n 0 ï' c )<br />
is really independent of no and can be denoted f**"'.<br />
The elements of f' 1 "' are code-independent, but the elements of C„(mo) are not.<br />
To obtain a code-averaged solution, we average C„(mo) over the spreading codes<br />
and use the result in (4.127) to solve for the weights. Thus,<br />
C„w = f (i,l) , (4.128)