In order for us to gain some insight into the ML relationship, let us assume the desired signal experiences
flat fading as well as the interfering signals. We then have the following representation of the
received signal given in vector notation (assuming D receive antennas).
(6.84)
This allows us to write down the received signal??™s covariance matrix as
(6.85)
With these above definitions we can write down the ML metric to be used in the MLE procedure and
this is given as
(6.86) M(k) Sr (k) h^
(k) # s(k)T* # R1
In(k) # Sr(k) h^
(k) # s(k)T
Rrr(k) s2s
# h(k) # h*(k) aM
m1
s2
m # hm(k) # h*
m(k) s2n
I
r(k) h(k) # s(k) aM
m1
hm(k) # sm(k) n(k)
r1(k) aJ1
j0
h1( j) # s(k j) aI1
i0 aM
m1
h1,m(i) # sm(k i) n1(k)
Cw1(k 1)
(
wM(k 1)S Cw1(k)
(
wM(k)S m # Cs2d
h1(k) r1(k) # d*(k)
(
s2d
hM(k) rM(k) # d*(k)S
w(t) Ss2s
# H ~
(t) # H ~
*(t) aC1
i0
s2i
# H ~
i(t) # H ~
*i
(t) s2n
IT1 # s2s
# H ~
(t) # OD
r ~rd(t) s2s
# H ~
(t) # OD
rr ~
d(t) E5r ~
(t) # d*(t D)6
314 CHAPTER SIX
We used to denote the estimate of the channel response. If we temporarily assume the interference
can be modeled as either white or is nonexistent then the interference plus noise covariance
matrix will be a diagonal and greatly simplify the metric calculation.
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