4-weighted fractional Fourier transform over doubly selective channels and optimal order selecting algorithm

An optimal order selecting scheme for 4-weighted fractional Fourier transform (4-WFRFT) over doubly selective channels is developed. First, the expression for carrier-to-interference ratio (CIR) is deduced and then through maximising the CIR the optimal order factor is obtained. Through selecting the optimal order factor of 4-WFRFT, this system can match the doubly selective channel characteristics through switching between orthogonal frequency division multiplexing (OFDM) and single carrier (SC) systems according to obtained channel state information. The simulation results show that the optimal order 4-WFRFT scheme can improve the performance over doubly selective channels with respect to the traditional SC or OFDM.