Method for beam formation by calculation, in particular adapted to the compensation of failures of active modules of a radar with electronic scanning
The invention relates to a method for beam formation by calculation. For each defective active module of rank ip, the missing samples of the microwave signal a(îp) are calculated by one or more non-adaptive interpolations using the samples coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules, the beam being formed as if the interpolated samples a(îp) were the real measurements. In particular, the invention is applicable to the compensation for the effects of failures of one or more active modules distributed over an antenna of a radar with electronic scanning. The method according to the invention can notably be implemented within an airborne weather radar.
1. A method of determining a radar beam based upon a scanning antenna having active modules wherein at least one of the active modules is defective, the method comprising:
orienting a main lobe of a microwave signal in a direction Uzf pointed to by a scanning antenna comprising active modules, the scanning being effected in one or more planes;
sampling and identifying the active modules by a rank i and by coordinates in a reference base forming a plane within which the active modules of the antenna are substantially included, wherein the active modules are distributed according to a non-constant distribution law over a surface of the antenna;
determining for each defective active module of rank ip, missing samples of the microwave signal a(îp) relating to the defective active module, by calculating one or more non-adaptive interpolations using the samples coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules, the beam being formed as if the interpolated samples a(îp) were the missing samples;
wherein the non-adaptive interpolation step comprises the steps of:
reducing the phase gradient equal to zero in the neighborhood of a particular direction Uz 1 of the samples of the microwave signal coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules;
non-adaptive linear interpolation of the missing samples of the microwave signal; and
rephasing of the missing samples obtained in the preceding step.
2. The method as claimed in claim 1 , wherein the method comprises the following steps:
forming the beam by excluding the missing samples of the microwave signal a(îp);
calculating using a non-adaptive linear interpolation of the estimations of the samples of the missing microwave signal a 1 (îp),. . ., a P (îp) starting from P assumptions of particular direction Uz 1 , Uz 2 , ..., Uzp;
calculating signals S 1 . . . S P according to the formula S 1 =S 0 +W(ip)×a 1 (îp), . . ., S P =S 0 +W(ip)×a P (îp) where W(ip) corresponds to the weighting coefficient of the sample from the defective module ip;
normalizing the signals S 1 . . . S P in such a manner that all the beams thus formed have the same gain in the directed orientation Uzf;
selecting the signal S 1 . . . S P whose measured power is the lowest amongst the full set of calculated signals.
3. The method as claimed in claim 2 , wherein the method of claim 2 is applied to a radar designed for the detection and localization of weather phenomena.
4. A method of determining a radar beam based upon a scanning antenna having active modules wherein at least one of the active modules is defective, the method comprising:
orienting a main lobe of a microwave signal in a direction Uzf pointed to by a scanning antenna comprising active modules, the scanning being effected in one or more planes;
sampling and identifying the active modules by a rank i and by coordinates in a reference base forming a plane within which the active modules of the antenna are substantially included, wherein the active modules are distributed according to a non-constant distribution law over a surface of the antenna;
determining for each defective active module of rank ip, missing samples of the microwave signal a(îp) relating to the defective active module, by calculating one or more non-adaptive interpolations using the samples coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules, the beam being formed as if the interpolated samples a(îp) were the missing samples;
wherein the active modules of a scanning antenna in a plane are arranged in rows and have as coordinates a position along an axis perpendicular to the rows of active modules of the antenna, the method includes the active modules delivering, after sampling, samples a(i), the samples of the missing microwave signal a(îp) are defined, for a particular direction Uz 1 , according to the following formula:
a
(
ip
)
^
=
(
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
)
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
-
1
)
×
a
(
ⅈ
p
-
1
)
+
z
(
ⅈ
p
)
-
z
(
ⅈ
p
-
1
)
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
-
1
)
×
a
(
ⅈ
p
+
1
)
)
×
exp
(
+
j2π
Uz
-
Uz
1
λ
z
(
ⅈ
p
)
)
being the rank of a defective active module.
5. The method of claim 4 , comprising the following steps:
forming the beam by excluding the missing samples of the microwave signal a(îp);
calculating, by a non-adaptive linear interpolation of the estimations of the samples of the missing microwave signal a 1 (îp),. . .,a P (îp) starting from P assumptions of particular direction Uz 1 , Uz 2 , . . ., Uzp;
calculating signals S 1 . . . S P according to the formula S 1 =S 0 +W(ip)×a 1 (îp), . . ., S P =S 0 +W(ip)×a P (îp) where W(ip) corresponds to the weighting coefficient of the sample from the defective module ip;
normalizing signals S 1 . . . S P in such a manner that all the beams thus formed have the same gain in the directed orientation Uzf;
selecting the signal S 1 . . . S P whose measured power is the lowest amongst the full set of calculated signals.
6. The method as claimed in claim 5 , wherein a number of particular directions of the radar signal is a function of the number of defective active modules.
7. The method as claimed in claim 5 , wherein it is applied to a radar designed for the detection and localization of weather phenomena.
8. A method of determining a radar beam based upon a scanning antenna having active modules wherein at least one of the active modules is defective, the method comprising:
orienting a main lobe of a microwave signal in a direction Uzf pointed to by a scanning antenna comprising active modules, the scanning being effected in one or more planes;
sampling and identifying the active modules by a rank i and by coordinates in a reference base forming a plane within which the active modules of the antenna are substantially included, wherein the active modules are distributed according to a non-constant distribution law over a surface of the antenna;
determining for each defective active module of rank ip, missing samples of the microwave signal a(îp) relating to the defective active module, by calculating one or more non-adaptive interpolations using the samples coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules, the beam being formed as if the interpolated samples a(îp) were the missing samples;
arranging the active modules of a scanning antenna in a plane area in rows and having as coordinates, a position along an axis perpendicular to the rows of active modules of the antenna;
the active modules delivering, after sampling, samples a(i), the samples of the missing microwave signals a(îp) are defined according to the following formula:
a
(
ip
)
^
=
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
)
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
-
1
)
×
a
(
ⅈ
p
-
1
)
+
z
(
ⅈ
p
)
-
z
(
ⅈ
p
-
1
)
z
(
ⅈ
p
+
1
)
-
z
(
ⅈ
p
-
1
)
×
a
(
ⅈ
p
+
1
)
.
wherein ip is the rank of a defective active module.
9. A method of determining a radar beam based upon a scanning antenna having active modules wherein at least one of the active modules is defective, the method comprising:
orienting a main lobe of a microwave signal in a direction Uzf pointed to by a scanning antenna comprising active modules, the scanning being effected in one or more planes;
sampling and identifying the active modules by a rank i and by coordinates in a reference base forming a plane within which the active modules of the antenna are substantially included;
determining for each defective active module of rank ip, missing samples of the microwave signal a(îp) relating to the defective active module, by calculating one or more non-adaptive interpolations using the samples coming from the active modules in nominal operating mode situated in the neighborhood of the defective active modules, the beam being formed as if the interpolated samples a(îp) were the real measurements and, wherein the active modules of a scanning antenna in a plane area are arranged in rows and have as coordinates a position along an axis perpendicular to the rows of active modules of the antenna, said active modules delivering, after sampling, samples a(i), the samples of the missing microwave signals a(îp) are defined according to the following formula:
a
(
i
^
p
)
=
z
(
ip
+
1
)
-
z
(
ip
)
z
(
ip
+
1
)
-
z
(
ip
-
1
)
×
a
(
ip
-
1
)
+
z
(
ip
)
-
z
(
ip
-
1
)
z
(
ip
+
1
)
-
z
(
ip
-
1
)
×
a
(
ip
+
1
)
ip being the rank of a defective active module.