### Abstract

We consider the problem of binary hypothesis testing using binary decisions from independent and identically distributed (i.i.d). sensors. Identical likelihood-ratio quantizers with threshold λ are used at the sensors to obtain sensor decisions. Under this condition, the optimal fusion rule is known to be a κ-out-of-n rule with threshold κ. For the Bayesian detection problem, we show that given κ, the probability of error is a quasi-convex function of λ and has a single minimum that is achieved by the unique optimal λ _{opt}. Except for the trivial situation where one hypothesis is always decided, we obtain a sufficient and necessary condition on λ _{opt}, and show that λ _{opt} can be efficiently obtained via the SECANT algorithm. The overall optimal solution is obtained by optimizing every pair of (κ, λ). For the Neyman-Pearson detection problem, we show that the use of the Lagrange multiplier method is justified for a given fixed κ since the objective function is a quasi-convex function of λ. We further show that the receiver operating characteristic (ROC) for a fixed κ is concave downward.

Original language | English (US) |
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Pages (from-to) | 2105-2111 |

Number of pages | 7 |

Journal | IEEE Transactions on Information Theory |

Volume | 48 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2002 |

### Keywords

- Decision-making
- Multisensor systems
- Quantization
- Signal detection

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*48*(7), 2105-2111. https://doi.org/10.1109/TIT.2002.1013153