An optimum Laguerre expansion for the envelope PDF of two sine waves in Gaussian noise

Abstract

The sum of two randomly-phased sine waves and Gaussian noise arises in various fields of communications. A Laguerre series and also a power series are introduced, for the envelope PDF of this random process. Moreover, tight upper bounds are derived for the truncation error of these two infinite series. Comparison of these two upper bounds show that the Laguerre series is superior to the power series; because for a fixed number of terms, it yields minimum truncation error.