An analytical method for linear combining with application to FFH NCFSK receivers

A method for obtaining the probability density function (PDF) and the cumulative density function (CDF) of sum-independent random variables is presented. The method is capable of determining the PDF and CDF of this sum for an input consisting of any combination of a signal tone, white Gaussian noise, and multiple interfering tones. It is based upon circularly symmetric function theory, Fourier-Bessel series, and Fourier series. To illustrate this method, applications are presented for a fast frequency-hopped noncoherent frequency-shift-keyed communications system. From the PDF and CDF of the received signal, performance values such as the error probability for demodulation, the probability of detection and false alarm for coarse-time synchronization and the mean and variance of timing-error estimates for fine-time synchronization are obtained