### Abstract

Due to errors in the phase and amplitude of element excitations in an antenna array, the array radiation pattern gets distorted. In order to derive statistical results on this distortion, specifically on determining the probability of exceeding a certain sidelobe level (SLL), it is often assumed that the magnitude of the array amplitude pattern follows a Rician distribution. It is shown that the Rician distribution implies two assumptions, and therefore, a more general Beckmann distribution is proposed to describe the distribution of the magnitude of the array amplitude pattern. Using Monte Carlo simulations, it is shown that the use of a Beckmann distribution outperforms the Rician distribution. Also, the seemingly counterintuitive result that the maximum probability of exceeding a certain SLL, in general, does not have to be at the angle where the highest sidelobe in the error-free case is located, is obtained. Due to this result, the importance of using an angular probability plot is emphasized. Furthermore, a physical explanation for the observed seemingly counterintuitive behavior is given.

Original language | English |
---|---|

Pages (from-to) | 2309-2317 |

Number of pages | 9 |

Journal | IEEE Transactions on Antennas and Propagation |

Volume | 66 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 2018 |

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### Keywords

- Antenna radiation patterns
- error analysis
- phased arrays
- probability
- random noise

### Cite this

*IEEE Transactions on Antennas and Propagation*,

*66*(5), 2309-2317. https://doi.org/10.1109/TAP.2018.2800519

}

*IEEE Transactions on Antennas and Propagation*, vol. 66, no. 5, pp. 2309-2317. https://doi.org/10.1109/TAP.2018.2800519

**Improved statistical model on the effect of random errors in the phase and amplitude of element excitations on the array radiation pattern.** / van den Biggelaar, A.J.; Johannsen, U.; Mattheijssen, P.; Smolders, A.B.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Improved statistical model on the effect of random errors in the phase and amplitude of element excitations on the array radiation pattern

AU - van den Biggelaar, A.J.

AU - Johannsen, U.

AU - Mattheijssen, P.

AU - Smolders, A.B.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Due to errors in the phase and amplitude of element excitations in an antenna array, the array radiation pattern gets distorted. In order to derive statistical results on this distortion, specifically on determining the probability of exceeding a certain sidelobe level (SLL), it is often assumed that the magnitude of the array amplitude pattern follows a Rician distribution. It is shown that the Rician distribution implies two assumptions, and therefore, a more general Beckmann distribution is proposed to describe the distribution of the magnitude of the array amplitude pattern. Using Monte Carlo simulations, it is shown that the use of a Beckmann distribution outperforms the Rician distribution. Also, the seemingly counterintuitive result that the maximum probability of exceeding a certain SLL, in general, does not have to be at the angle where the highest sidelobe in the error-free case is located, is obtained. Due to this result, the importance of using an angular probability plot is emphasized. Furthermore, a physical explanation for the observed seemingly counterintuitive behavior is given.

AB - Due to errors in the phase and amplitude of element excitations in an antenna array, the array radiation pattern gets distorted. In order to derive statistical results on this distortion, specifically on determining the probability of exceeding a certain sidelobe level (SLL), it is often assumed that the magnitude of the array amplitude pattern follows a Rician distribution. It is shown that the Rician distribution implies two assumptions, and therefore, a more general Beckmann distribution is proposed to describe the distribution of the magnitude of the array amplitude pattern. Using Monte Carlo simulations, it is shown that the use of a Beckmann distribution outperforms the Rician distribution. Also, the seemingly counterintuitive result that the maximum probability of exceeding a certain SLL, in general, does not have to be at the angle where the highest sidelobe in the error-free case is located, is obtained. Due to this result, the importance of using an angular probability plot is emphasized. Furthermore, a physical explanation for the observed seemingly counterintuitive behavior is given.

KW - Antenna radiation patterns

KW - error analysis

KW - phased arrays

KW - probability

KW - random noise

UR - http://www.scopus.com/inward/record.url?scp=85041384600&partnerID=8YFLogxK

U2 - 10.1109/TAP.2018.2800519

DO - 10.1109/TAP.2018.2800519

M3 - Article

AN - SCOPUS:85041384600

VL - 66

SP - 2309

EP - 2317

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 5

ER -