Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and Properties

TL;DR

This paper derives a closed-form expression for the error exponent in Neyman-Pearson detection of Gauss-Markov signals in noise, revealing how correlation and SNR influence detection performance.

Contribution

It provides a novel closed-form formula for the error exponent and explores its properties, linking detection performance to the Kalman filter and signal correlation.

Findings

Error exponent decreases with correlation at high SNR (>1)

Optimal correlation maximizes error exponent at low SNR (<1)

Established connection between detection and Kalman filtering

Abstract

The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) >1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR <1 there is an optimal correlation that maximizes the error exponent for a given SNR.