43)
Next we can write the optimum weight vector as
(6.44)
which can also be written as
(6.45)
Now if we assume the cross-correlation vector is in the signal subspace then we can ideally write the
optimum weights as
(6.46)
Here we have essentially cancelled the noise subspace.
6.2 SPACE-TIME EQUALIZATION (STE)
In the previous sections, we have assumed a single receive antenna was used with the equalization
methods presented. In this section, we perform a joint equalizer in both time and across antennas,
hence the name space-time equalization. Figure 6.10 presents a space-time equalizer block diagram
assuming M 2 antennas, with each antenna supporting a linear equalizer of length K taps. We have
chosen to show a fractionally spaced version for sake of discussion. The equalizer weights are jointly
derived from information from both antennas [9??“15]. We have assumed the square root raised cosine
wopt US # D1
S # U*S
# rxd
wopt U # D1 # U* # rxd
wopt aM
j1
1
lj
# v j # v*
j # rXd
R1
XX aM
i1
1
li
# vi # v*i
vi li
304 CHAPTER SIX
FIGURE 6.10 Fractionally spaced, space-time equalizer architecture with M 2 antennas and K taps on each antenna.
x(k)
y(k)
???RC . . . Z??“Tc/2 Z??“Tc/2 Z??“Tc/2
Z??“Tc/2 Z??“Tc/2 Z??“Tc/2 ???RC .
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