3.3 Radar Targets Scattering Matrix
31
each other, i.e., ˙
S 12 = ˙
S 21 or S 12 = S 21 u ψ 12 = ψ 21 . Consequently, a mount of
parameters, characterizing a target, decreases up to three complex or six real numbers.
Let us review a physical sense of these parameters. For this purpose, return to
(3.25) system. Let the horizontally polarized wave be radiated, i.e., E
ver
rad = 0, then
we have the following:
E
hor
rsv = S hh exp( j hh )E
hor
rad ,
E
ver
rsv = S vh exp( j vh )E
hor
rad ,
(3.29)
from which we obtain for S hh and S vh :
S hh =
E
hor
rsv
·
E
hor
rad
−1 ,
S vh =
E
ver
rsv
·
E
hor
rad
−1 ,
(3.30)
and for hh and vh phases:
hh = arg
E
hor
rsv
E
hor
rad
,
vh = arg
E
ver
rsv
E
hor
rad
.
(3.31)
Thereby, relation argument of horizontal component of received wave near
antenna to analog value of radiated wave near a target equals to hh phase and
module of this relation to S hh value. Relation argument of vertical component of
received wave near antenna to horizontal component of radiated wave near a target
(E
ver
rad = 0) equals to vh and module of this relation S vh value. The same meaning
for S vv and S hv , where a radiation case of vertically polarized wave (E
hor
rad = 0) should
be examined.
Scattering matrix elements S 11 and S 22 are called primary and S 12 —switched or
crossing elements.
Measurements of absolute values 11 , 12 , 22 present severe difficulties; therefore, as a rule, measurements are limited to its relative values 12 – 11 , 22 – 11 ,
i.e., equivalent to the case when 11 phase is admitted to be equal to zero. Severe
difficulties arise at measuring of S 11 , S 12 , S 22 absolute values, and therefore, relative
measurements are also conducted and relations S 12 /S 11 i S 22 /S 11 are checked, i.e.,
equivalent to a case when S 11 is assumed equal to one. At such an approach, a target
describes not by six, but by four parameters.
In real conditions of radar operation due to continuous change of relative position
of antenna and target, all scattering matrix elements in general case are changed
randomly, and hence, the most complete characteristic of a radar target will be
corresponding to multi-dimension distribution laws.
We will return to further analysis of scattering matrix properties latter, and now,
let us examine the most commonly encountered nowadays case when radar operates
only on one fixed polarization as both in transmission mode and in receiving mode.
31
each other, i.e., ˙
S 12 = ˙
S 21 or S 12 = S 21 u ψ 12 = ψ 21 . Consequently, a mount of
parameters, characterizing a target, decreases up to three complex or six real numbers.
Let us review a physical sense of these parameters. For this purpose, return to
(3.25) system. Let the horizontally polarized wave be radiated, i.e., E
ver
rad = 0, then
we have the following:
E
hor
rsv = S hh exp( j hh )E
hor
rad ,
E
ver
rsv = S vh exp( j vh )E
hor
rad ,
(3.29)
from which we obtain for S hh and S vh :
S hh =
E
hor
rsv
·
E
hor
rad
−1 ,
S vh =
E
ver
rsv
·
E
hor
rad
−1 ,
(3.30)
and for hh and vh phases:
hh = arg
E
hor
rsv
E
hor
rad
,
vh = arg
E
ver
rsv
E
hor
rad
.
(3.31)
Thereby, relation argument of horizontal component of received wave near
antenna to analog value of radiated wave near a target equals to hh phase and
module of this relation to S hh value. Relation argument of vertical component of
received wave near antenna to horizontal component of radiated wave near a target
(E
ver
rad = 0) equals to vh and module of this relation S vh value. The same meaning
for S vv and S hv , where a radiation case of vertically polarized wave (E
hor
rad = 0) should
be examined.
Scattering matrix elements S 11 and S 22 are called primary and S 12 —switched or
crossing elements.
Measurements of absolute values 11 , 12 , 22 present severe difficulties; therefore, as a rule, measurements are limited to its relative values 12 – 11 , 22 – 11 ,
i.e., equivalent to the case when 11 phase is admitted to be equal to zero. Severe
difficulties arise at measuring of S 11 , S 12 , S 22 absolute values, and therefore, relative
measurements are also conducted and relations S 12 /S 11 i S 22 /S 11 are checked, i.e.,
equivalent to a case when S 11 is assumed equal to one. At such an approach, a target
describes not by six, but by four parameters.
In real conditions of radar operation due to continuous change of relative position
of antenna and target, all scattering matrix elements in general case are changed
randomly, and hence, the most complete characteristic of a radar target will be
corresponding to multi-dimension distribution laws.
We will return to further analysis of scattering matrix properties latter, and now,
let us examine the most commonly encountered nowadays case when radar operates
only on one fixed polarization as both in transmission mode and in receiving mode.