Process compensating for array antenna radiating element positioning errors

US 7,453,398 B2
Filed: 03/17/2007
Issued: 11/18/2008
Est. Priority Date: 03/17/2006
Status: Expired due to Fees

First Claim

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1. A process of compensating for the effects of the errors of location of the radiating elements of an array antenna on the radiation pattern of said antenna, said process comprising the following steps:

measuring the positioning error for each radiating element n and compiling an imperfection vector I, whose components are values of the positioning error function δ

(n);

computing a spectral decomposition of the positioning error function δ

(n), in the spatial domain, in the form of the sum of spectral sinusoidal components dd(i) calculated by application of a Fourier transform to the imperfections vector I, and applying an inverse Fourier transform to vector dd obtained in this way, each component of vector I being then expressed as a sum of sinusoidal errors;

calculating correcting functions Δ

_a(n), Δ

_φ(n), from the sinusoidal spectral components dd(i) of the error function δ

(n), said correcting functions being defined as sums of sinusoidal spectral components A_n(i) and Φ

_n(i);

elaborating a correction function Δ

(n) from Δ

_a(n) and Δ

₁₀₀(n) to apply to the radiation pattern F(θ

) of the antenna, as a function of the aiming angle θ

₀of the antenna, said correction Δ

(n) being applied to the radiation patterns of the sources forming the radiation pattern F(θ

) of the antenna, to correct the error of location of the considered source.

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Abstract

The invention refers to array antennas consisting of a set of individual sources set out over the surface of the antenna and whose mechanical positioning is determined in such a way as to obtain the desired radiation pattern. The process according to the invention is designed to compensate for the positioning errors of radiating elements occurring when such an antenna is constructed. These positioning errors follow a law that is in theory random and whose result is known by determining the imperfection vector I whose components of real positioning errors measured for each feed of the antenna obtained comprising components forming values of an error function δ(n) where n represents the index attributed to the radiating element in question. The process according to the invention consists in first measuring the positioning errors. It then consists in determining the spatial spectral components making up error function δ(n). It finally consists in applying to each component an amplitude or phase modulation correction in order to compensate for the degradation of the error function δ(n) on the obtained antenna radiation pattern F(θ). The process according to the invention applies more particularly to antennas comprising radiating beams.

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15 Claims

1. A process of compensating for the effects of the errors of location of the radiating elements of an array antenna on the radiation pattern of said antenna, said process comprising the following steps:
- measuring the positioning error for each radiating element n and compiling an imperfection vector I, whose components are values of the positioning error function δ
  
  (n);
  
  computing a spectral decomposition of the positioning error function δ
  
  (n), in the spatial domain, in the form of the sum of spectral sinusoidal components dd(i) calculated by application of a Fourier transform to the imperfections vector I, and applying an inverse Fourier transform to vector dd obtained in this way, each component of vector I being then expressed as a sum of sinusoidal errors;
  
  calculating correcting functions Δ
  
  _a(n), Δ
  
  _φ(n), from the sinusoidal spectral components dd(i) of the error function δ
  
  (n), said correcting functions being defined as sums of sinusoidal spectral components A_n(i) and Φ
  
  _n(i);
  
  elaborating a correction function Δ
  
  (n) from Δ
  
  _a(n) and Δ
  
  ₁₀₀(n) to apply to the radiation pattern F(θ
  
  ) of the antenna, as a function of the aiming angle θ
  
  ₀of the antenna, said correction Δ
  
  (n) being applied to the radiation patterns of the sources forming the radiation pattern F(θ
  
  ) of the antenna, to correct the error of location of the considered source.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
- - 2. The process according to claim 1, wherein Δ
    - _a(n) is defined by the following relation;
      
      $Δ_{a} (n) = \frac{- 2}{λ \cdot N} \cdot \sum_{i = 1}^{N^{'}} \langle {dd}_{i} \rangle \cdot \sin (\frac{2 \cdot Π \cdot (n - 1) \cdot (i - 1)}{N} + \arg ({dd}_{i}))$ Where nε
      
      [1, N], N′
      
      being equal to the integer part of the number (N/2+1).
  - 3. Process according to claim 1, wherein Δ
    - _φ(n) is defined by the following relation;
      
      $Δ_{φ} (n) = \frac{1}{P \cdot N} \cdot \sum_{i = 1}^{N^{'}} \cdot \langle {dd}_{i} \rangle \cdot \cos (\frac{2 \cdot Π \cdot (n - 1) \cdot (i - 1)}{N} + \arg ({dd}_{i}))$ Where nε
      
      [1, N], N′
      
      being equal to the integer part of the number (N/2+1).
  - 4. The process according to claim 1, wherein the perturbed radiation pattern being expressed as:
    - $F_{perturbed} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)}$ the corrected radiation pattern is expressed as;
      
      $F_{corrected} (θ) = \sum_{n = 1}^{N} [a_{n} + Δ_{a} (n)] \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)} .$
  - 5. The process according to claim 2, wherein the perturbed radiation pattern being expressed as:
    - $F_{perturbed} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)}$ the corrected radiation pattern is expressed as;
      
      $F_{corrected} (θ) = \sum_{n = 1}^{N} [a_{n} + Δ_{a} (n)] \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)} .$
  - 6. The process according to claim 1, wherein the perturbed radiation pattern being expressed as:
    - $F_{perturbed} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)}$ the diagram of corrected brilliance(radiation) has for expression;
      
      $F_{corrected} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)} \cdot ⅇ^{{jΔ}_{φ} (n)} .$
  - 7. The process according to claim 3, wherein the perturbed radiation pattern being expressed as:
    - $F_{perturbed} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)}$ the diagram of corrected brilliance(radiation) has for expression;
      
      $F_{corrected} (θ) = \sum_{n = 1}^{N} a_{n} \cdot ⅇ^{- j \cdot k \cdot n \cdot P \cdot \sin θ_{0}} ⅇ^{(j \cdot k \cdot (n \cdot P + δ_{n}) \sin θ)} \cdot ⅇ^{{jΔ}_{φ} (n)} .$
  - 8. The process according to claim 1, wherein the correction Δ
    - (n) is expressed as;
      
      $Δ (n) = \sum_{i} γ (i) \cdot A_{n} (i) + (1 - γ (i)) \cdot Φ_{n} (i)$ the terms A_n(i) and Φ
      
      _n(i) representing respectively the components of Δ
      
      _a(n) and Δ
      
      _φ(n) and y(l) representing a function equal to 1 or 0.
  - 9. The process according to claim 6, wherein y(l) is defined as a function of a threshold calculated from the aiming angle θ
    - ₀.
  - 10. The process according to claim 1, further comprising a complementary spectral components weighting step for functions Δ
    - _a(n) and Δ
      
      _φ(n) while the overall correction function Δ
      
      (n) is then expressed as;
      
      $Δ (n) = \sum_{i} f (i) \cdot γ (i) \cdot A_{n} (i) + f (i) \cdot (1 - γ (i)) \cdot Φ_{n} (i)$ the terms A_n(i) and φ
      
      _n(i) representing respectively the components of Δ
      
      _a(n) and Δ
      
      _φ(n) and y(l) representing a function equal to 1 or 0;
      
      f(i) being a weighting factor.
  - 11. The process according to claim 8, further comprising a complementary spectral components weighting step for functions Δ
    - _a(n) and Δ
      
      _φ(n) while the overall correction function Δ
      
      (n) is then expressed as;
      
      $Δ (n) = \sum_{i} f (i) \cdot γ (i) \cdot A_{n} (i) + f (i) \cdot (1 - γ (i)) \cdot Φ_{n} (i);$ f(i) being a weighting factor.
  - 12. The process according to claim 10, wherein weighting f(i) follows an increasing linear law according to i.
  - 13. The process according to claim 11, wherein weighting f(i) follows an increasing linear law according to i.
  - 14. The process according to claim 10, wherein weighting f(i) follows an increasing logarithmic law according to i.
  - 15. The process according to claim 11, wherein weighting f(i) follows an increasing logarithmic law according to i.

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Current Assignee
Thales SA
Original Assignee
Thales SA
Inventors
Chekroun, Claude, Lienhart, Marc-Yves, Rouzeaud, Benjamin
Primary Examiner(s)
PHAN, DAO LINDA

Application Number

US11/687,638
Publication Number

US 20080030412A1
Time in Patent Office

612 Days
Field of Search

342/174, 342/196, 342/368, 342/420, 342/442, 342/451
US Class Current

342/368
CPC Class Codes

G01S 2013/0245   Radar with phased array ant...

G01S 7/2813   Means providing a modificat...

G01S 7/4004   of parts of a radar system

H01Q 3/267   Phased-array testing or che...

Process compensating for array antenna radiating element positioning errors

First Claim

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Process compensating for array antenna radiating element positioning errors

First Claim

1 Assignment

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0 Petitions

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Accused Products

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Abstract

8 Citations

15 Claims

Specification

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Use Cases

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Others