TEL AVIV UNIVERSITY Gaddi Blumrosen

Jake‟s model describes sum of discrete multi-path model each one has time-selective
fading distribution (e.g., Rayleigh fading distribution).
Coherence bandwidth, f c , is the frequency separation for which frequency-space
correlation function of channel impulse response (see [3, p 52.] for graph of
correlation versus DOA and frequency) at two frequencies is sufficiently correlated
(exceeding predetermined threshold). The Coherence frequency is inversely
1
proportional to Delay spread, i.e., Fc
. When coherence bandwidth is several
d s
times larger than the inverse of Symbol time, the channel is called frequency nonselective
fading channel, or flat fading channel, if not the fading is called, frequency
selective fading.
Space-selective fading
Space-selective fading, the variations of signal in space, is caused by different
receiver departure angles of the multi-paths due to reflection, scattering and
diffraction from scatterers (include obstacles such as buildings) in the propagation
path. In LOS conditions, there is low space selectivity. Space selectivity is determined
by antenna spacing, scatterers‟ distribution (mainly angle spread) and wave length.
Different scatterers‟ distribution models are well summarized in [3, p 63-91]. A
popular assumption (not realistic in correlated fading) is uniform distribution over
[ 0,
2
) or over the Angle Spread.
Coherence distance, c , is the angle or space separation for which channel response
at two antennas is sufficiently correlated (exceeding determined threshold). The
1
Coherence distance is inversely proportional to angle spread, i.e., c
. If
as
coherence distance (proportional to angle spread) is several times larger than the
antenna spacing, the channel is space non-selective fading cahnnel. If not, the fading
is called, space selective fading. Table 1 below (taken from [23]), summarize the
relations between channel parameters.
Spatial Noise
The noise in space time models is sometimes referred to as spatial noise with spatial
statistics which is related to scatterers‟ distribution. For instance, in a multi-user
environment, transmission from different users in different locations, are spatial
sources contributing to noise distribution. Spatial distribution of the scatterers (other
users) which depends on spatial location is referred to as "colored noise". For
simplicity, we will assume from now on, unless mentioned otherwise, that the noise is
independent of the space dimension, and it is a stationary white Gaussian process
(AWGN). We will denote this noise as n
t .