TEL AVIV UNIVERSITY Gaddi Blumrosen

extended channel response. In SISO modeling where there was only one receive one
transmit antenna, the antenna array response could have been seen as one. With the
assumption that the steering vector is time independent, each element of H, can be
expressed as a function of its steering vector and its fading coefficients e.g. as in [4],
[5], [13]:
hi, j ( t, ) st, i ( ) i, j ( t, ) sr, j ( ) stl,
i ( l ) sl, i, j ( t, l ) srl,
j ( l
) (2.13)
Where 1... N , j 1...
N , l 1...
L and s ( ) s ( ) are transmit and receive
i t
r
steering vectors i'th element, respectively. Each elements, ( t,
)
, is a complex
random variables reflecting the channel statistics. Fig. 1 shows a diagram of a general
MIMO system. In our system model, flat fading, i.e. L=1, is assumed:
h ( t, ) s ( ) ( t, ) s ( )
(2.14)
i, j t, i s, i, j r, j
Correlated MIMO channel
l
t,
i
r,
i
For analyzing the correlated MIMO channel we define the correlation coefficients
between each element as follows:
i j E hi hj
(2.15)
where h is an vector formed by, the operator vec which is the span of H
*
,
N 1
r Nt
*
columns to one column and iE( hihi) 1. Following, the correlation matrix, Rhh
, is
defined as:
H
R [ ] E(
h h)
(2.16)
hh i, j
The additional input parameters to the MIMO model compared to the conventional
SISO models, are the antenna correlation matrices at transmit and receiving ends.
These correlation matrices might be selected to be different for each delay component
in the radio channel. We assume fixed correlation matrices, i.e. time-invariant, but the
model can be extended to support time-varying correlation matrices as in [13].
Another common assumption, as in [4]-[13], based on the fact that correlation is
caused by the nearby surrounding of the antenna array, is that the correlation between
the receive antenna elements are independent of the transmit antennas. Let us define
now, RT as the transmit correlation matrix as of size Nt Nt
, where the index of the
receive array is fixed on one element:
H
RT
E(
H H)
(2.17)
Similarly we define Nr Nr
receive correlation matrix, R , where the index of the
transmit array is fixed on one element
(2.18)
In the general case, of scatterers on the propagation path, we define the elements,
based on general scatterers‟ distribution, same as in [5], as:
(2.19)
R
H
RR E(
HH )
RR
r / 2 di
, j
i2
sin( )
e p(
)
d
i j
RR
i,
j
r / 2
1
i j
hi, j