Computational and Statistical Foundations of Radar Signal Processing in the Low False Alarm Regime
Abstract
This project has addressed two foundational problems in statistical signal processing in the context of multi-channel radar: (1) Signal detection in the low false alarm regime of operation and (2) Estimation and tracking of signal subspaces. Prior to this project, work of the PI and others established that optimal multi-channel detection statistics take the form of functions of the eigen spectrum of a Gram matrix formed from data collected at the multiple receivers. This project focused on the most important special case for radar applications, where the signal has rank one and the key detection statistic is the largest eigenvalue of the Gram matrix. Setting detection thresholds that yield desired probabilities of false alarm requires explicit calculation of values of the conditional probability distribution of this statistic under the null hypothesis that the channels are statistically independent and contain only zero-mean white gaussian noise, in which case the Gram matrix is has a central Wishart distribution. Prior to the outset of this project, it had been observed that the probability distributions of the largest eigenvalue of such a matrix, although known analytically, were not amenable to direct numerical evaluation - particularly for values of the statistic corresponding to low false-alarm probabilities necessary in practical radar signal detection scenarios and for realistic signal vector dimensionality and numbers of receiver channels. This project developed a suitable transformation of the distribution of the largest eigenvalue of a central Wishart distribution that circumvents the key obstructions to direct numerical calculations when the data dimensionality is large and the number of channels is in a realistic range.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 10, 2022
- Accession Number
- AD1230287
Entities
People
- Douglas Cochran
Organizations
- Arizona State University