On Commonalities in Signal Design for Non-Gaussian Channels

Abstract

We derive for additive non-Gaussian white noise channels signal waveforms that are simultaneously optimal with respect to the minimum probability of error, the mini-max, and the Neyman-Pearson criteria. We show that for a large class of non-Gaussian statistics, there exist only two asymptotically optimal signal waveforms; one impulsive while the other is constant in amplitude. The impulsive waveform is optimal when the tails of the noise density fall off faster than the tails of the Gaussian density. We show that under each of the three optimality criteria the asymptotic performance for small signals is essentially determined by the signal energy, while for large signals the performance is determined by a non-Euclidean metric that varies with respect to the tails of the noise density function. To support these results, we offer simulations for a variety of non-Gaussian channels. In each case, the asymptotic theory holds strikingly well even for decidedly nonasymptotic regimes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 26, 1994
Accession Number
ADA285385

Entities

People

  • Geoffrey C. Orsak
  • Nhi-anh Chu
  • Nirmal Warke

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Amplitude
  • Background Noise
  • Computational Science
  • Detection
  • Detectors
  • Engineering
  • False Alarms
  • Gaussian Channels
  • Gaussian Noise
  • Information Theory
  • Noise
  • Probability
  • Simulations
  • Statistics
  • Warning Systems
  • Waveforms

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Mathematical Modeling and Probability Theory.