Optimal beamforming for Rayleigh-faded time-frequency varying channels using fractional Fourier transform

A method of optimal beamforming for Rayleigh-faded time-frequency selective channels using fractional Fourier transform (FRFT) is considered in this paper. The conventional minimum mean squared error (MMSE) beamforming in the frequency domain or spatial domain becomes a special case of optimal beamforming with FRFT. The method is especially useful in moving source problems, where Doppler effect produces frequency shift when the sinusoidal source is moving in wireless communication where the user produces frequency shift while moving. With the advent of FRFT and its related concept, it is seen that the properties and applications of the ordinary Fourier transform are special cases of those of the FRFT. It is not only richer in theory and more flexible in application but is also not costly in implementation. The advantage of the proposed optimum FRFT domain beamformer is the practical consideration that the synthesis or analysis of the FRFT can be implemented with the same complexity as the conventional fast Fourier transform (FFT).