Optimum Memoryless Nonlinear Transformation for Weak Narrowband Signals in Noise
Abstract
The optimum memoryless nonlinear transformation for weak narrowband signals in narrowband noise is derived in terms of the joint probability density function of the noise amplitude and phase modulations. The optimization is in terms of maximizing the magnitude of the deflection of the complex envelope at the nonlinearity output, for small signal inputs of arbitrary characteristics. The optimum nonlinearity is complex, in general, meaning that a phase modulation is superposed, in addition to that present at the input to the nonlinearity. A problem with the behavior of the optimum nonlinearity is traced back to a shortcoming in the approximate analysis, and a method for circumventing the problem is presented. Two methods of treating the spurious weak signal component at the nonlinearity output are considered and compared quantitatively. Finally, the optimum nonlinearity for processing phase differences is derived for a particular model of noise statistics and shown to be closely related to an earlier processor. (jhd)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1989
- Accession Number
- ADA218423
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center