Partial order generalized Marcum Q-function contour integral representation

ABSTRACT

A new contour integral representation of generalized Marcum Q-function is presented. The obtained expression is valid for an arbitrary positive order of the function and for a specific case of integer order yields a well known result. As an example of practical application the problem of energy base signal detection in presence of fading is considered. A novel closed form analytic expression for an average probability of detection for various channel models is obtained.

KEYWORDS:

• Generalized Marcum Q-function
• contour integral
• Laplace transform
• energy detection
• probability of detection
• Rayleigh fading

AMS CLASSIFICATION:

• 30E20
• 33C65
• 44A10
• 94A05
• 94A13

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

A. S. Gvozdarev http://orcid.org/0000-0001-9308-4386