MIMO Systems: Principles, Iterative Techniques, and Advanced Polarization - Adaptive Signal Processing in Wireless Communications - page 114

Table 4.2 Patterns of Different Electric Dipoles

E x E y E z E ϕ E θ

E θ (θ, ϕ) -cosθcosϕ -cosθcosϕ -sinθ 0 1

E ϕ (θ, ϕ) sinϕ -cosϕ 0 1 0

in terms of channel capacity. Moreover, different array configurations produce differ-
ent correlation effects. In this part, we will analyze five types of antennas [75], x -, y -,
and z -oriented dipole antennas, azimuth, and elevation isotropic antennas, applied to a
uniform linear array.
The radiating patterns of the antennas are considered in the far-field case, and are
also simplified by neglecting path loss and distance phase. Hence, these radiating pat-
terns are simply dependent on the azimuth and elevation angle direction as shown in
Table 4.2. A general expression of radiation patterns is given by [75]

 

= ( ) + ( )

EE θφθ θφφ , E , , (4.24)

θ φ

where E θ (θ,ϕ) and E ϕ (θ,ϕ) are the amplitudes of polarization vector at the θ → - and
ϕ → -directions, and x , y , and z are the antenna orientations. As different types of antennas
are employed in this chapter, it is necessary to normalize the radiation pattern when
comparing all channel performances. Thus, all radiation patterns of an antenna are nor-
malized by that of an isotropic antenna, and they can be written as

∫∫ sin

θθφ dd





( )

( ) + ( )

G =

∆∆
2

φθ ,

E θφθ θφφ , E ,

(4.25)

θ φ


 


 

∫∫

( ) + ( )

2

E θφ , E θφ , sin θθθφ dd

θ φ

∆∆ φθ ,

where G is the antenna gain that is used for the computation of the channel matrix.

4.5.2 Cross-Polarization Discrimination
In wireless communications, due to the interactions of environment, such as diffractions,
reflection, and refraction, the transmitted signals are generally not only attenuated but
also depolarized. Depolarization is the change of the original state of the polarization of
the electromagnetic wave propagated from the Tx.
Cross-polarization discrimination (XPD) is defined as the power ratio of the co-
polarization and cross-polarization components of the mean incident wave. The higher
the XPD, the less energy that is coupled in the cross-polarized channel. Therefore, there
are two transmission cases, azimuth transmission (χ θ ) and elevation transmission (χ ϕ ),
as follows: