  This study examines the coexistence of orthogonal time-frequency space (OTFS)
modulation with current fourth- and fifth-generation (4G/5G) wireless
communication systems that primarily use orthogonal frequency-division
multiplexing (OFDM) waveforms. We first derive the input-output-relation (IOR)
of OTFS when it coexists with an OFDM system while considering the impact of
unequal lengths of the cyclic prefixes (CPs) in the OTFS signal. We show
analytically that the inclusion of multiple CPs to the OTFS signal results in
the effective sampled delay-Doppler (DD) domain channel response to be less
sparse. We also show that the effective DD domain channel coefficients for OTFS
in coexisting systems are influenced by the unequal lengths of the CPs.
Subsequently, we propose an embedded pilot-aided channel estimation (CE)
technique for OTFS in coexisting systems that leverages the derived IOR for
accurate channel characterization. Using numerical results, we show that
ignoring the impact of unequal lengths of the CPs during signal detection can
degrade the bit error rate performance of OTFS in coexisting systems. We also
show that the proposed CE technique for OTFS in coexisting systems outperforms
the state-of-the-art threshold-based CE technique.
