Optimal simultaneous detection and signal and noise power estimation

Abstract

Abstract-Simultaneous detection and estimation is important in many engineering applications. In particular, there are many applications where it is important to perform signal detection and Signal-to-Noise-Ratio (SNR) estimation jointly. Application of existing frameworks in the literature that handle simultaneous detection and estimation is not straightforward for this class of application. This paper therefore aims at bridging the gap between an existing framework, specifically the work by Middleton et al., and the mentioned application class by presenting a jointly optimal detector and signal and noise power estimators. The detector and estimators are given for the Gaussian observation model with appropriate conjugate priors on the signal and noise power. Simulation results affirm the superior performance of the optimal solution compared to the separate detection and estimation approaches.

Sequential joint signal detection and signal-to-noise ratio estimation

“…The procedure is stopped for the first time when Gm 0 ,m 1 = Rm 0 ,m 1 . The min term in (20) signifies the detection cost if the decision rule (17) is employed, while the last two terms correspond to the estimation cost, i.e., the deviation of the estimatorθ * from the true SNR. At first glance, the optimal decision rule as well as the optimal estimator seem equivalent to Bayesian solutions because of the following reason: The term E can be interpreted as the conditional moments of the posterior distribution of ρ (or, θ) with prior µ, and the optimal estimatorθ * as the posterior expected value of θ − 2.…”

“…In [19], it was shown that a scheduling scheme performed detection in an energy-efficient manner by jointly estimating the SNR. However, [20] reported that the techniques developed in some of the papers mentioned above were not readily applicable to the problem of joint detection and signal and noise power estimation. For a Bayesian formulation, it was shown [20, Sec.…”

“…III] that knowledge of the priors Pr(H0) and Pr(H1) or of the distribution of the unknown parameters was not amenable for problems addressed in [17] - [19]. Instead, an optimal solution for Gaussian observation models was presented using conjugate priors on the signal and noise powers [20,Sec. IV].…”