Capacity limits of bandlimited Gaussian channels in fractional Fourier domain

The well-known Shannon channel capacity theorem plays a fundamental role in modern wireless communications. However, this theorem, derived from the Fourier transform (FT) viewpoint, only holds for Fourier bandlimited Gaussian channels. It has already been shown that a signal can not be both Fourier bandlimited and fractional bandlimited with a certain angle α≠π/2. Hence, it is desirable to generalize the Shannon channel capacity theorem from Fourier bandlimited channels to fractional bandlimited ones. In this paper, we propose a formula to calculate the capacity limits of bandlimited Gaussian channels in the fractional Fourier domain. This formula is an extension of the Shannon channel capacity theorem for fractional bandlimited channels. The achieved results may be useful for designing communication systems in the fractional Fourier domain.