TEL AVIV UNIVERSITY Gaddi Blumrosen

w is the complex antenna weight vector which describes antenna excitation
gain
s( ) is the steering vector describing the electrical field in the direction of
each single antenna element and has the form of (assuming antenna gain of 1):
2
2
jm1
d sin
j
Nt1
d sin
s(
)
1,...
e ,... e
(2.2)
2.3 Spatial channel modeling
2.3.1 Introduction
Spatial wireless channel modeling is essential for efficient ST processing. Appropriate
ST modeling is essential for determining the best ST processing technique, designing
STC, and getting statistics and measurement for capacity and performance evaluation
as well as for improving the overall performance by better adaptation to channel
conditions. Spatial physical channel models result in a channel response which varies
in space [3, p 43-91]. We will try as much as we can, for simplicity, to eliminate the
use of the spatial dimension as part of the spatial channel modeling, with certain
assumptions. But in most of the cases, it is straightforward to expand the model to
include the spatial dimension.
We start by describing a general spatial physical wireless channel suitable for one
transmit antenna and one receive antenna, later to be called Single-Input-Single-
Output (SISO). The terms Path Loss, fading and multi-path will be explained in the
space, frequency and time dimensions.
Later, we expand the description to a Multiple-Input-Multiple-Output (MIMO)
channel model ([4]-[7]) ,which is the general case for receive diversity Multiple-
Output-Single-Input (SIMO) and transmit diversity Multiple - Input - Single - Output
(MISO), with antenna correlation matrices at the transmit (Tx) and receiving (Rx)
ends.
Next we introduce the term channel feedback quality as was first explored in [8].
We will introduce a new channel parametric model, called virtual channel model, as
was introduced in [9], which is an example for new interesting ST channel model.
In the end of this chapter, we will develop statistical models versus CSI quality for
Gaussian channel assuming flat fading as a function of the correlation between the
real channel and the estimated one and CSI parameters.