The received signals are represented
as rj where j 1 to M.
318 CHAPTER SIX
X DFT
w1
r1
+ I-DFT Demodulate
X DFT
wM
rM
.
.
.
.
.
.
Frequency Domain Equalizer
FIGURE 6.22 Single-carrier frequency domain equalizer receiver.
When determining the size of the DFT, one should consider the size to be enough to represent the
inverse of the channel response in the time domain.
The well-known weights used to perform the combining are defined below assuming the MMSE
cost function.
( j 1, 2, . . . , M) (6.92)
Above 2
d is the desired signal??™s power, 2j
is the noise power present on the jth antenna. Allow us
to assume M 2 in order to provide some insight into the above general equation. We then have the
following two FDE weights [24].
(6.93)
(6.94)
One can further assume the noise power is the same for all receive antennas, then the denominator
becomes the same for both weights and can be applied after the summing operation shown in Fig. 6.22.
In either case we can see the denominator contains a term inversely proportional to the SNR.
w2(k)
H*
2 (k) as2
s1b2
# ZH1(k) Z2 ZH2(k) Z2 as2
sdb2
w1(k)
H*
1 (k)
ZH1(k) Z2 as1
s2b2
# ZH2(k) Z2 as1
sdb2
wj (k) asd
sj b2
# H*
j (k)
aM
i1 asd
si b2
# ZHi(k) Z2 1
One last point to make here is that this type of equalization was applied to High Speed Downlink
Packet Access (HSDPA) in [23] and shown to produce better performance than the conventional
RAKE receiver.
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