98)
In Eqs. (7.97) and (7.98), we used h1 and h2 to represent the channel response of the first and second
arriving rays. Ci is the ith chip of the complex-valued PN sequence, and dk is the QPSK symbol
at the time instance k. We have assumed that the channel impulse is not changing during the symbol
time, so the channel behaves time invariant during the despreading operation. Also we initially
assumed the delay spread is within the SF of the QPSK symbol. Note that depending on the channel
model of interest (i.e., outdoors and indoors), this may or may not be a valid assumption.
Then we can write the RAKE output signal as follows:
(7.99) h1 # h*2
# dk1 # C1 # C*
SF 2 # dk # Re eh2 # h*1
# a SF1
i1
Ci # C*i1 f y 5Zh1 Z2 Zh2 Z26# dk # aSF
i1
Ci # C*i
h2 # h*1
# dk1 # CSF # C*1
x2 h2 # dk # aSF
i1
Ci # C*i
h1 # dk1 # C1 # C*
SF h1 # dk # a SF1
i1
Ci1 # C*i
x1 h1 # dk # aSF
i1
Ci # C*i h2 # dk1 # CSF # C*1
h2 # dk a SF1
i1
Ci # C*i1
r^
xd R^
xx
wMMSE R^
1
xx # r^
xd
wMRC(t) h(t)
y(t) w*(t) # x(t)
3G WIDEBAND CDMA 403
The RAKE output consists of four components:
1. First is the desired signal output.
2. Second is the interference from the past symbol.
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