Statistical distributions of OFDM signals on multi-path fading channel

Bit error rate (BER) performance of the OFDM system has been widely studied on multi-path fading channel with the channel gain being modeled as various distributions. But the statistical distribution of the OFDM signal on the receiver side has neither been well studied, nor given the close- formed expression. In order to design the optimum detection criteria, especially for the hypothesis test of the OFDM symbol, the probability density function (pdf) of the received OFDM signal on the multi-path channel is presented in this paper. At first, the pdf of the frequency domain impulse response of the channel is derived through the characteristic function method. Secondly, we can show that the joint pdf of the complex channel frequency response and the complex additive white Gaussian noise leads to the pdf of the received OFDM symbol under the condition of given transmitted symbol on a given subcarrier. Lastly, the theoretical analysis is verified by the simulations, and the theoretical and simulation results agree with each other perfectly.