Zak-OTFS: Pulse Shaping and the Tradeoff between Time/Bandwidth Expansion and Predictability
arxiv(2024)
摘要
The Zak-OTFS input/output (I/O) relation is predictable and non-fading when
the delay and Doppler periods are greater than the effective channel delay and
Doppler spreads, a condition which we refer to as the crystallization
condition. When the crystallization condition is satisfied, we describe how to
integrate sensing and communication within a single Zak-OTFS subframe by
transmitting a pilot in the center of the subframe and surrounding the pilot
with a pilot region and guard band to mitigate interference between data
symbols and pilot. At the receiver we first read off the effective channel taps
within the pilot region, and then use the estimated channel taps to recover the
data from the symbols received outside the pilot region. We introduce a
framework for filter design in the delay-Doppler (DD) domain where the
symplectic Fourier transform connects aliasing in the DD domain (predictability
of the I/O relation) with time/bandwidth expansion. The choice of pulse shaping
filter determines the fraction of pilot energy that lies outside the pilot
region and the degradation in BER performance that results from the
interference to data symbols. We demonstrate that Gaussian filters in the DD
domain provide significant improvements in BER performance over the sinc and
root raised cosine filters considered in previous work. We also demonstrate
that, by limiting DD domain aliasing, Gaussian filters extend the region where
the crystallization condition is satisfied. The Gaussian filters considered in
this paper are a particular case of factorizable pulse shaping filters in the
DD domain, and this family of filters may be of independent interest.
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