Performance Analysis of OFDM with M-ary Modulation in Sum of Frequency-Selective Arbitrary Nakagami-m Fading Channels

Error rates of orthogonal frequency-division multiplexing (OFDM) signals using M-ary modulation in multipath slow fading Nakagami-m fading channel are considered. The exact probability density function of a sum of Nakagami-m random phase vector is used to derive a closed-form expression for the error rates of OFDM signals with arbitrary fading index m. This is done using the well-known moment generating function (MGF) analysis approach and in terms of the confluent hypergeometric function. For two-tap channel with finite value of Nakagami-m fading parameter, our analysis and numerical results show that error-rate performance of OFDM signal is similar to that of single carrier signal transmitted over a Rayleigh fading channel. Furthermore, our analysis shows that in a frequency-selective channel, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.