TEL AVIV UNIVERSITY Gaddi Blumrosen

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where Uˆ U , Vˆ V
tr(
)
Later we will see that SVD enables, with appropriate pre and post coding, the transmit
and receive antennas to use independent data streams, called sub-channels.
Rice distribution
A common general MIMO channel distribution is Rice distribution which consists of
weighted summation of a Rayleigh distributed channel, and LOS channel, H ,
based on physical wave superposition:
H aHbH 2 2
Where a, and b are constants normalized to one, a b 1
.
It is common to describe HRician
also as:
H Rician
K
H LOS
K 1
1
H Ray
K 1
a
where K, the Rician constant (Cofactor), equals to, K
b
Channel matrix rank
1/ 2 1/ 2
R T
T
Rician LOS Ray
(2.25)
(2.26)
Let us denote by r, the rank of channel matrix H. If we define, as above, G to be
consisted of independent Gaussian variables, covariance of G is full rank (though the
H
instantaneous value of GG is not necessarily full rank, due to fading effect), and
thus the channel rank is explicitly determined by the minimum rank of RT and RR
.
Consequently, channel rank is determined by the matrix correlation at receive and
transmit ends and thus determines spatial selectivity.
A more realistic approach, in which G is not assumed to be full is analyzed at [5]. In
this approach wide scale reflectors causes keyhole effect for instance, and reduce the
channel rank. Still, different physical scenarios can lead to same channel
characteristics, so the above assumption is justified for analysis purpose.
2.3.5 Channel feedback quality
H Ray
LOS
Channel Side Information (CSI), is based on the channel estimates, the instantaneous
approximated channel value, h and on channel statistics, the estimated channel mean
value, , and the estimated channel covariance matrix, , and some times on
ˆ
R
m
h/ hˆ
hh/ hˆ
higher statistical moments.
A Lot of research was being held recently in the subject of channel feedback quality.
One of the most extensive works, which studied and tested the effects of noisy side
information and quantized side information on the expected SNR and mutual
information, was held by Narula in [8].
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