Rethink Delay Doppler Channels and Time-Frequency Coding

In this paper, we rethink delay Doppler channels (also called doubly selective channels). We prove that no modulation schemes can compensate a non-trivial Doppler spread well. This means that the current active OTFS (that is the same as VOFDM) cannot compensate a non-trivial Doppler spread. We then discuss some of the existing methods to deal with time-varying channels, in particular time-frequency (TF) coding in an OFDM system. TF coding is equivalent to space-time coding in the math part. We also summarize state of the art on space-time coding that was an active research topic over 10 years ago.