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Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication
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abstract
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. The filter taps can simply be read off from the response to a single Zak-OTFS point (impulse) pulsone waveform, and the I/O relation can be reconstructed for a sampled system that operates under finite duration and bandwidth constraints. Predictability opens up the possibility of a model-free mode of operation. The time-domain realization of a Zak-OTFS point pulsone is a pulse train modulated by a tone, hence the name, pulsone. The Peak-to-Average Power Ratio (PAPR) of a pulsone is about $15$ dB, and we describe a general method for constructing a spread pulsone for which the time-domain realization has a PAPR of about 6dB. We construct the spread pulsone by applying a type of discrete spreading filter to a Zak-OTFS point pulsone. The self-ambiguity function of the point pulsone is supported on the period lattice ${\Lambda}_{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${\Lambda^*}$. We show that if the channel satisfies the crystallization conditions with respect to ${\Lambda^*}$ then the effective DD domain filter taps can simply be read off from the cross-ambiguity between the channel response to the spread pulsone and the transmitted spread pulsone. If, in addition, the channel satisfies the crystallization conditions with respect to the period lattice ${\Lambda}_{p}$, then in an OTFS frame consisting of a spread pilot pulsone and point data pulsones, after cancelling the received signal corresponding to the spread pulsone, we can recover the channel response to any data pulsone.
Forward citations
Cited by 7 Pith papers
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ISAC with Affine Frequency Division Multiplexing: An FMCW-Based Signal Processing Perspective
With the parameter choice c1 = 1/(2Np), c2 = 0, AFDM subcarriers are mathematically identical to Nyquist-sampled FMCW chirps, so every DAFT index maps to a delay-Doppler coordinate, enabling FMCW-style single-symbol r...
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Low-Complexity Frequency Domain Equalization of Zak-OTFS in Doubly-Spread Channels
Equalizing Zak-OTFS in the frequency domain exploits the banded channel structure, cutting complexity from O(M^3 N^3) to O(M^2 N^2).
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Inter-frame Channel Prediction for Zak-OTFS
Effective DD-domain channel filters of Zak-OTFS frames evolve deterministically with known phase factors, enabling ESPRIT-style inter-frame prediction that removes pilots from future frames.
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Zak-OTFS based Multiuser Uplink in Doubly-Spread Channels
A delay-Doppler pulse-shaping phase ramp shifts each Zak-OTFS user's signal into its own time-frequency slot, and simulations show multiuser uplink performance matching single-user performance without guard bands.
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A Gaussian-Sinc Pulse Shaping Filter for Zak-OTFS
A Gaussian-sinc pulse shaping filter for Zak-OTFS combines sinc nulls with Gaussian sidelobe suppression and is reported to improve BER by 4 to 6 dB in simulations.
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Multiuser Zak-OTFS on the Uplink with Superimposed Spread-Pilots
TF-shift multiuser Zak-OTFS with heterogeneous frames and superimposed ZC spread-pilots yields near-single-user IOR estimation and filter-dependent spectral-efficiency gains over embedded pilots.
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Differential Communication in Channels with Mobility and Delay Spread using Zak-OTFS
In Zak-OTFS, the cross-ambiguity of received and transmitted random data is approximately the channel, so detected data can replace periodic pilots and enable pilot-free differential detection.
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