Proof of a simple formula for ICI caused by single frequency offset in wireless OFDM system

Exact Interchannel interference (ICI) expression caused by single frequency offset (SFO) is shown to be a function of normalized SFO (NSFO). Due to its high complexity, it is inconvenient for communication engineer to use this expression to calculate ICI value. Some upper bounds ICI, such as Moose and Feng, has been derived to reduce computational amount. But, they are still about 2dB difference from real ICI value. Fornuately, this real ICI is proved to equal a third of the square of NSFO from mathematics under the condition that NSFO is small and N large. Numerical simulation further indicates that this identity holds when |NSFO|⩽0.2.