16 STE eigenvalue CDF plot (shown in terms of percentages).
The desired signal??™s channel matrix (of size M L) can be written as (we have dropped the index
over time for simplicity). The interfering signal??™s channel matrix can be similarly written.
(6.70)
And the desired signal vector (of size L 1) is given as
(6.71)
Let us collect K 1 consecutive samples so we can write the received signal vector (of size
M*(K 1) 1).
(6.72)
Then the overall channel matrix (of size M*(K 1) (L K)) can be written in a very nicely compacted
form.
(6.73)
And the overall desired signal vector of size (L K) 1 can be written as
(6.74)
Using the above new definitions we can write the received signal as
(6.75)
The MMSE-based STE weights are created with the estimate of the covariance matrix and correlation
vectors provided below.
(6.76)
(6.77)
Now if we are allowed to invoke a very popular assumption that the received signal is only correlated
with itself and that the interfering signals all have the same property then the signal covariance
matrices can be approximated by diagonal matrices thus simplifying the result as follows.
(6.78) R~r
~ r (t) s2s
# H ~
(t) # H ~
*(t) aC1
i0
s2i
# H ~
i (t) # H ~
*
i (t) s2n
I
R~r
~ r (t) H ~
(t) # R~d
~
d (t) # H ~
*(t) aC1
i0
H ~
i (t) # R~di
~
di
(t) # H ~
*
i (t) s2n
I
R~r
~r
(t) EUr ~
(t) # r ~
*(t)V
r
~
(t) H
~
(t) # d
~
(t) aC1
i0
H
~
i(t) # di
~
(t) n
~
(t)
d
~
(t) [d(t) d(t 1) cd(t L K 1]T
H ~
Dh0
0
(
0
h1
h0
c
c
h1
h0
hL1
c
f
h1
0
hL1
c
0
c
(
hL1T
r ~
(t) [rT(t) rT(t 1) c rT(t K)]T
d(t) D d(t)
d(t 1)
(
d(t L 1)T
H [h0 h1chL1]
H Ch1, 0 h1, 1
c
h1, L1
( (
hM, 0 hM, 1
c
hM, L1
S
RECEIVER DIGITAL SIGNAL PROCESSING 313
Similarly, the correlation vector can be written as
(6.
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