Near-Optimal Angle of Transform in FrFT-OFDM Systems Based on ICI Analysis

In this paper, we establish an analytical framework to derive a closed form for a close approximation of the optimal angle of transform in fractional-Fourier-transform orthogonal-frequency-division-multiplexing (FrFT-OFDM) systems. In this framework, we derive a tight upper bound for the intercarrier interference (ICI) power and use this bound instead of the exact ICI power to obtain the near-optimal angle of transform. We also analyze the sensitivity of the FrFT-OFDM systems to the angle of transform. In other words, we derive the increase in the ICI power when we exploit a nonoptimal angle of transform due to channel estimation errors. We show that once the error in the channel state information (CSI) is reasonable, the ICI power increase is tolerable. For instance, for a two-path channel, if the error in estimating the slope of the channel spread function in the delay-Doppler plane is less than 20%, the ICI power increase is smaller than 0.1 dB.