
356 MIMO System Technology for Wireless Communications
which correspond to receiver antenna diversity. We note that the diversity
gain becomes M
R
and the expected array gain is also M
R
. For the MISO
configuration, multiple transmit antennas are deployed with a single receive
antenna. This corresponds to transmit diversity when the transmitter is
ignorant of the channel and to transmit beamforming if the transmitter
knows the channel, respectively. The limits in this table assume that the
receiver always knows the channel. We note that the gains are not just limited
by the numbers of antennas in a cellular network configuration, but also by
the availability of channel state information at the transmit side. For further
details, we refer to [3].
A key problem of network planning for MIMO systems is a lack of avail-
able MIMO propagation models, which can be used for predicting the signal
field strength jointly with the number of available dimensions in the signal
space for specific sites. In contrast, propagation models for single antenna
transmission and reception can be considered mature. In modern radio net-
work planning tools, the propagation model consists of a basic pathloss
model, line-of-sight checking, and corrections for topography, morphogra-
phy, and street orientation [4, chap. 3]. Propagation models for MIMO trans-
mission are much less understood, but the recently developed model within
COST 273 carries great promise [6].
For MIMO systems in which the transmitter does not have channel state
knowledge, the instantaneous capacity can be calculated from
where I
M
R
denotes the identity matrix of order M
R
and H is the MIMO channel
matrix, W is the mean receive SNR, and X
H
is the Hermitian transpose of X.
If the distribution of H were known, the distribution of C could be deter-
mined. Sadly, the distribution of H parameterized by receiver location, base
station antenna array height, and configuration in real environments is little
understood. Most current MIMO literature treats the matrix elements of H
as (more or less) independent identically distributed, which leads to opti-
mistic values of capacity. It would mean that adjacent receive antenna ele-
ments carry fully decorrelated signals, e.g., as a consequence of random
multipath from all directions in a non-line-of-sight (NLOS) environment. In
[7], it was shown that MIMO capacity can have a large local variation in an
indoor scenario, depending on the position of the antenna arrays and on the
environment. The only solution currently at hand is to carry out detailed
MIMO channel measurements to link topology and morphography with
MIMO channel statistics.
Finally, we point out that the gains summarized in Table 12.1 affect the
signal to interference plus noise ratio (SINR) of individual links. These gains
affect the link quality statistics directly. In interference-limited situations,
C
M
M
T
R
=+
©
«
ª
¹
»
º
log det
H
I
W
HH
4190_book.fm Page 356 Tuesday, February 21, 2006 9:14 AM