A Robust and Low-Complexity Walsh-Hadamard Modulation for Doubly-Dispersive Channels

In this letter, we present a generic modulation framework for robust wireless communications over doubly dispersive channels. This robustness is achieved by spreading the symbols over time and frequency such that they experience the same channel gain. Interestingly, we show that our modulation framework is a generalization of the recently proposed orthogonal time frequency space modulation (OTFS). By exploiting an additional degree of freedom enabled by the generic framework, we propose in this letter a low-complex waveform based on the sparse Walsh-Hadamard transform (WHT). We show that the proposed sparse WHT modulation exhibits the same frame error rate performance as OTFS, while significantly reducing the implementation complexity due to the multiplication-free small-size WHT compared with the discrete Fourier transform used by symplectic finite Fourier transform (SFFT) of OTFS.