Optimum Detection of a Randomly Frequency-Modulated Carrier.
Abstract
The logarithm of the likelihood ratio for detection of a frequency-modulated signal tone, received in the presence of white Gaussian noise, is derived and expressed in the form of an infinite Volterra series. The amplitude of the received signal tone and the received noise power density level are presumed known; the additive phase shift is uniformly distributed; and the frequency-modulating process is Gaussian, with a spectrum such that no carrier tone remains in the frequency-modulated signal spectrum. This is called a fully-random signal herein. When the time-bandwidth product (of observation time and signal bandwidth) is large enough, and there is at least a moderate amount of frequency modulation, the optimum processor is well-approximated by a filter followed by an energy detector; the filter passband is that of the spectrum of the received signal. The frequency modulation is termed moderate when the ratio of the RMS frequency deviation to the equivalent bandwidth of the frequency-modulating process is of the order of 2-3. Numerous approximations have been necessary to facilitate evaluation of some of the multiple integrals; to what degree the sufficient conditions cited above can be relaxed, without violating the conclusions, is unknown.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 02, 1979
- Accession Number
- ADA079795
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center