Mellin-Transform-Based Performance Analysis of FFH $M$ -ary FSK Using Product Combining for Combatting Partial-Band Noise Jamming

We employ the Mellin transform to facilitate the bit error ratio (BER) analysis of a fast frequency hopping (FFH)-assisted, $M$-ary frequency-shift keying (MFSK) using product combining (PC) when the transmitted signal is subjected to both Rayleigh fading and partial-band noise jamming. Exploiting the fact that the Mellin transform of the product of independent random variables is the product of their Mellin transforms, we derive the probability density function (PDF) of the PC's output. The derivation of the PDF then allows the computation of the system's BER. It is shown that the Mellin transform substantially simplifies the analysis of the PC receiver and hence facilitates, for the first time, the analysis of the FFH-MFSK PC receiver for modulation orders of $M ≫ 2$.