On explicit expressions of transfer function of OFDM systems in time-dispersive multipath channels

For orthogonal frequency-division multiplexing (OFDM) systems, the OFDM signals are typically designed such that the guard interval is long enough compared to the channel delay spread. In this case, the transfer function for each subcarrier is a Fourier transform of the channel impulse response. However, if the guard interval is shorter than the maximum channel delay, it is not true any more, and intersymbol and interchannel interferences from adjacent OFDM symbols and subchannels must be taken into account. In this paper, we re-visit the transfer function of two equivalent implementations of OFDM systems operating in multipath channels with a generalized guard interval, which could be shorter or longer than the maximum channel delay, and evaluate the impact of interferences on the link performance in terms of signal-to-interference-plus-noise-ratio.