Let us provide the mathematical representation for a particular MIMO equalizer architecture
where a linear equalizer is used on each receive antenna. Assuming a single transmit and receive
antenna then one can write the received signal as
(9.30)
where N is the number of transmit antennas, M is the number of receive antennas, P is the oversampling
factor, L is the delay spread of the channel, and E is the equalizer duration. We can rewrite the
above equation in the following vector notation:
(9.31)
where _y(k) is the received signal vector of size PE 1,H(k) is the channel matrix of size PE (EL ??“ 1),
is the transmitted signal vector of size (E L ??“ 1) 1, and is the noise vector of size PE 1.
Now if we consider N transmit and M receive antennas then we have the following:
(9.32)
Which is rewritten as
(9.33)
Now the received signal vector is of size PEM 1, the channel matrix is of size PEM
N(E L ??“ 1), the transmitted signal vector is of size N(E L ??“ 1) 1, and the noise vector is of size
y ~
(k) H ~
(k) # x ~
(k) n ~
(k)
Cy1(k)
(
yM(k)S CH1,1 cH1, N
( f (
HM,1 cHM,NS# Cx1(k)
(
xN(k)S Cn1(k)
(
nM(k)S n(k) x(k)
y(k) H(k) # x(k) n(k)
G y(k)
(
yp(k)
(
y(k E 1)
(
yp(k E 1)W Gh(0)
(
hp(0)
(
0
c
c
c
h(L 1)
(
hp(L 1)
f
h(0)
(
hp(0)
c
c
c
0
h(L 1)
(
hp(L 1)W# G x(k)
x(k 1)
(
x(k E L 2)W G n(k)
(
np(k E 1)W
lj
H # H* l1, l2,c, lK
C4 aK
j1
log2 c1
SNR
N
# lj d
3G AND BEYOND DISCUSSION 503
PEM 1.
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