  Orthogonal time frequency space (OTFS) is a promising technology for
high-mobility wireless communications. However, the equalization realization in
practical OTFS systems is a great challenge when the non-ideal rectangular
waveforms are adopted. In this paper, first of all, we theoretically prove that
the effective channel matrix under rectangular waveforms holds the
block-circulant property and the special Fourier transform structure with
time-domain channel. Then, by exploiting the proved property and structure, we
further propose the corresponding low-complexity algorithms for two mainstream
linear equalization methods, i.e., zero-forcing (ZF) and minimum mean square
error (MMSE). Compared with the existing direct-matrix-inversion-based
equalization, the complexities can be reduced by a few thousand times for ZF
and a few hundred times for MMSE without any performance loss, when the numbers
of symbols and subcarriers are both 32 in OTFS systems.
