Page 278 - Antennas for Base Stations in Wireless Communications

Antennas for WLAN (WiFi) Applications 251

bandwidth and/or delay spread, the channel becomes frequency depen-
dent. The correlation properties in the frequency domain are a func-
tion of the power delay profile. The coherence bandwidth, which is
inversely proportional to the delay spread of the channel, is defined as
the minimum bandwidth separation in order to achieve decorrelation.
Furthermore, due to the motion of scatterers or the transmitter and/or
receiver, the channel realizations also vary with time. The coherence
time, which is inversely proportional to the Doppler spread, is defined
as the minimum time separation that is required for the decorrelation
of the time-varying channel. In the real world, due to antenna spac-
ing and scattering, H may differ significantly from H w . Also, the pres-
ence of a line-of-sight (LOS) component will result in Ricean fading.
The MIMO channel can then be modeled as the sum of a fixed and
fading component:

H = K H + 1 H (7.6)
1 + K 1 + K w

1
where 1+ K K H is the LOS component and 1+K H is the uncorrelated
w
fading component. K (≥0) is the Ricean factor of the channel and is
defined as the ratio of the power in the LOS component to the power
of the fading component. K = 0 corresponds to a Rayleigh channel and
K = ∞ corresponds to a nonfading channel.
7.2.2.2 MIMO System Capacity Capacity (bits/s/Hz) of a communication
system can be defined as the maximum rate at which reliable commu-
nication is possible, which can be characterized in terms of the mutual
information between the input and the output of the channel. For a time-
invariant additive white Gaussian noise (AWGN) channel with bandwidth
B and received SNR g, the Shannon’s channel capacity can be given as 9

γ
C = Blog (1 + ) (7.7)
2
In the case where there are N channels and the transmit power is
equally divided among them, the capacity becomes

N  γ   γ 
C = ∑ log 2  1 +  = N log 2  1 +  (7.8)
n=1  N  N
For deterministic MIMO channels, the channel gain matrix H is fixed.
It is assumed that the transmitter does not have any channel state infor-
mation (CSI) and hence cannot optimize the power allocation among the
antennas. The input vectors are independent complex Gaussian-distributed