### Abstract

Exact finite sum expressions for the probability density function (PDF) and cumulative distribution function (CDF) for the magnitude response of the SCB MVDR beamformer are derived. Exact expressions for the mean and variance of this beam pattern are given which generalize and extend the classical results of Ruze (1952) as well as those of Gilbert and Morgan (1955) to this MVDR processor. These tools allow the exact prediction of the likelihood of interference in a given direction obtaining a specified level of sidelobe or mainlobe suppression by the adaptive beamformer. Sample support and degrees of freedom can be chosen to meet specifications with a certain level of probability. These useful calculations are facilitated by judicious exploitation of Sehlafli's contour integral representation for the modified Bessel function.

Original language | English (US) |
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Title of host publication | Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000 |

Publisher | IEEE Computer Society |

Pages | 73-76 |

Number of pages | 4 |

Volume | 2000-January |

ISBN (Electronic) | 0780363396 |

DOIs | |

State | Published - Jan 1 2000 |

Externally published | Yes |

Event | IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000 - Cambridge, United States Duration: Mar 16 2000 → Mar 17 2000 |

### Other

Other | IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000 |
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Country | United States |

City | Cambridge |

Period | 3/16/00 → 3/17/00 |

### Fingerprint

### Keywords

- Adaptive arrays
- Adaptive filters
- Apertures
- Distribution functions
- Interference suppression
- Laboratories
- Least squares approximation
- Probability density function
- Signal to noise ratio
- Stochastic processes

### ASJC Scopus subject areas

- Signal Processing
- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000*(Vol. 2000-January, pp. 73-76). [877971] IEEE Computer Society. https://doi.org/10.1109/SAM.2000.877971

**MVDR adaptive sidelobes : Extending Ruze's formula and providing an exact calculation of the probability of sidelobe suppression.** / Richmond, Christ.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000.*vol. 2000-January, 877971, IEEE Computer Society, pp. 73-76, IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000, Cambridge, United States, 3/16/00. https://doi.org/10.1109/SAM.2000.877971

}

TY - GEN

T1 - MVDR adaptive sidelobes

T2 - Extending Ruze's formula and providing an exact calculation of the probability of sidelobe suppression

AU - Richmond, Christ

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Exact finite sum expressions for the probability density function (PDF) and cumulative distribution function (CDF) for the magnitude response of the SCB MVDR beamformer are derived. Exact expressions for the mean and variance of this beam pattern are given which generalize and extend the classical results of Ruze (1952) as well as those of Gilbert and Morgan (1955) to this MVDR processor. These tools allow the exact prediction of the likelihood of interference in a given direction obtaining a specified level of sidelobe or mainlobe suppression by the adaptive beamformer. Sample support and degrees of freedom can be chosen to meet specifications with a certain level of probability. These useful calculations are facilitated by judicious exploitation of Sehlafli's contour integral representation for the modified Bessel function.

AB - Exact finite sum expressions for the probability density function (PDF) and cumulative distribution function (CDF) for the magnitude response of the SCB MVDR beamformer are derived. Exact expressions for the mean and variance of this beam pattern are given which generalize and extend the classical results of Ruze (1952) as well as those of Gilbert and Morgan (1955) to this MVDR processor. These tools allow the exact prediction of the likelihood of interference in a given direction obtaining a specified level of sidelobe or mainlobe suppression by the adaptive beamformer. Sample support and degrees of freedom can be chosen to meet specifications with a certain level of probability. These useful calculations are facilitated by judicious exploitation of Sehlafli's contour integral representation for the modified Bessel function.

KW - Adaptive arrays

KW - Adaptive filters

KW - Apertures

KW - Distribution functions

KW - Interference suppression

KW - Laboratories

KW - Least squares approximation

KW - Probability density function

KW - Signal to noise ratio

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=0038100982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038100982&partnerID=8YFLogxK

U2 - 10.1109/SAM.2000.877971

DO - 10.1109/SAM.2000.877971

M3 - Conference contribution

AN - SCOPUS:0038100982

VL - 2000-January

SP - 73

EP - 76

BT - Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2000

PB - IEEE Computer Society

ER -