A Novel Approach for the Wigner Distribution Formulation of the Optimum Detection Problem for a Discrete-Time Chirp Signal

Abstract

The Wigner distribution is a signal transformation which has its origin in quantum mechanics. It possesses some important properties which make it very attractive for time-frequency signal analysis. The Wigner distribution was originally defined for continuous-time signals. A discrete-time version of it was proposed recently. Unfortunately, this discrete-time Wigner distribution suffers from aliasing effects, which prevent several of the properties of the continuous-time Wigner distribution from carrying over straightforwardly. In this report, a discrete-time Wigner distribution which does not suffer from aliasing is introduced. It is essentially an augmentation of the previous version, incorporating new information about the signal not contained in the previous version. A variety of methods have been proposed for the detection of a signal, with unknown signal parameters, in a noisy environment. In this report, the noise statistics are incorporated to reveal that certain processing of the Wigner distribution signal representation can lead to an optimal, and often easy to compute, detection scheme. For the special case of discrete-time chirp signals in complex white Gaussian noise, it is shown that the optimal detector is equivalent to integrating the Wigner distribution along the line of instantaneous frequency. If the position and sweep rate of the linear chirp are unknown, then a Generalized Likelihood Ratio Test (GLRT) leads one to integrate the Wigner distribution along all possible lines in the time-frequency plane and choose the largest integrated value for comparison to a threshold. Simulation examples of the Wigner distribution scheme are given to demonstrate the utility concerning the detection of the proposed method.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2001
Accession Number
ADA403432

Entities

People

  • Ambighairajah Yasotharan
  • Thayananthan Thayaparan

Organizations

  • Defence Research and Development Canada

Tags

Communities of Interest

  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Classification
  • Data Analysis
  • Detection
  • Detectors
  • Doppler Radar
  • Frequency
  • Gaussian Noise
  • Multiple Targets
  • National Security
  • Noise
  • Periodic Functions
  • Radial Velocity
  • Security
  • Signal Detection
  • Simulations
  • Statistics
  • Time Signals

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Statistical inference.

Technology Areas

  • Quantum Computing