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Extremum-Based Joint Compression and Detection for Distributed Sensing

Amir Weiss, Alejandro Lancho

Abstract

We study joint compression and detection in distributed sensing systems motivated by emerging applications such as IoT-based localization. Two spatially separated sensors observe noisy signals and can exchange only a $k$-bit message over a reliable one-way low-rate link. One sensor compresses its observation into a $k$-bit description to help the other decide whether their observations share a common underlying signal or are statistically independent. We propose a simple extremum-based strategy, in which the encoder sends the index of its largest sample and the decoder performs a scalar threshold test. We derive exact nonasymptotic false-alarm and misdetection probabilities and validate the analysis with representative simulations.

Extremum-Based Joint Compression and Detection for Distributed Sensing

Abstract

We study joint compression and detection in distributed sensing systems motivated by emerging applications such as IoT-based localization. Two spatially separated sensors observe noisy signals and can exchange only a -bit message over a reliable one-way low-rate link. One sensor compresses its observation into a -bit description to help the other decide whether their observations share a common underlying signal or are statistically independent. We propose a simple extremum-based strategy, in which the encoder sends the index of its largest sample and the decoder performs a scalar threshold test. We derive exact nonasymptotic false-alarm and misdetection probabilities and validate the analysis with representative simulations.

Paper Structure

This paper contains 8 sections, 2 theorems, 34 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Main Results
  4. Proposed Joint Compression and Detection Scheme
  5. The GLRT in a Constraint-Free Communication Setting and Its Relation to the Proposed Scheme
  6. Nonasymptotic Performance Analysis
  7. Simulation Results
  8. Concluding Remarks

Key Result

Proposition 1

For the decision rule eq:miedecisionrule, the FA probability $P_{\text{\tiny FA}}(\tau) \triangleq \mathbb{P}\mathopen{}\left({ \delta(\bm{\mathsf{m}}\xspace, \mathcal{Y}\xspace_N) = \mathcal{H}\xspace_1 \mid \mathcal{H}\xspace_0}\right)$ is given by where $Q(x)\triangleq \frac{1}{\sqrt{2\pi}}\int_{x}^{\infty}e^{-\frac{t^2}{2}}{\rm d}t$ is the standard $Q$-function.

Figures (3)

  • Figure 1: ROC curve for $k=8$ and $d_m=50$.
  • Figure 2: ROC curve for $k=12$ and $d_m=150$.
  • Figure 3: Probability of detection $P_{\mathrm{D}}$ as a function of the SNR in $\mathrm{dB}$ for fixed $P_{\mathrm{FA}}$, $\sigma_1=\sigma_2=1$, $k=8$ and $d_m=50$.

Theorems & Definitions (2)

  • Proposition 1: FA probability
  • Proposition 2: MD probability