Orthogonal time chirp space modulation based upon fractional Fourier transform

•OTCS-FrFT is a general form of OTFS modulation and works on delay-fractional Doppler coordinate system.•The free parameter in OTCS-FrFT enables OTCS-FrFT to flexible to different types of time-varying channels.•Computational complexity of OTCS-FrFT is the same as that of the OTFS using sampling-type DFrFT algorithm. Linear chirps play a significant role in communications because of their ability to spread spectrum and provide secure and robust communication. Orthogonal time frequency space (OTFS) modulation is suitable for high-mobility transmissions over a stationary delay-Doppler channel. The advantages of linear chirps and OTFS modulation are combined in this study. Specifically, orthogonal time chirp space modulation based on fractional Fourier transform (OTCS-FrFT) is proposed, which is obtained by replacing the two-dimensional (2D) sinusoidal carriers of OTFS modulation with 2D linear chirps. As the Fourier transform is the kernel of OTFS modulation, FrFT underlies the proposed OTCS-FrFT system for its complete and orthogonal linear chirp bases and its fast computation algorithms. The information symbols are originally placed on the delay-fractional Doppler plane, which is a rotation of the delay-Doppler plane, where the rotation angle is a free parameter that enables the OTCS-FrFT to adapt to different time-varying Doppler scenarios. It is proven that the OTCS-FrFT is robust to time-varying channels with linear delay/Doppler spreading functions. For other time-varying channels, simulations are performed to validate the superior performance of the OCTS-FrFT over other FrFT-based OTFS modulation methods, where the bit error rate is reduced by approximately 1 dB for both high-speed and high-acceleration terminals.