Estimation of channel state information in doubly selective channels (DSC) is a demanding task. In addition, the bandwidth expended in pilot signals may considerably impact the system throughput. Furthermore, the computational resources required for estimation and equalization of the DSC may limit the implementation of practical communication systems. In this correspondence paper, a differential system with incoherent reception on DSCs is presented. The proposed approach uses a virtual trajectory representation of the received signals by means of the basis expansion modeling of the channel. This allows the receiver to convert the Doppler dispersion in virtual antennas and mitigate intercarrier interference while preserving frequency correlation. The proposed approach achieves incoherent reception of multicarrier signals with O(Nlog₂N) complexity avoiding channel estimation in a simple autocorrelation differential phase shift keying detector.