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

## TL;DR

This paper presents a new sequential method for joint signal detection and SNR estimation in Gaussian models, reducing complexity and improving efficiency for applications with strict data and computation constraints.

## Contribution

It introduces a transformation-based approach that simplifies the joint detection and estimation problem into a Bernoulli sequence, enabling more efficient computation.

## Key findings

- Reduced sample size for desired error and MSE levels.
- Simpler sufficient statistic compared to traditional methods.
- Demonstrated effectiveness in resource-constrained scenarios.

## Abstract

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.