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Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication
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Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication
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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 8 Pith papers
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Inter-frame Channel Prediction for Zak-OTFS
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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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Zak-OTFS: A Predictable Physical Layer for Communications and Sensing
Zak-OTFS carriers, realized as pulsone waveforms, yield predictable non-selective I/O relations under bounded channel spreads due to their structure as common eigenvectors of the discrete Heisenberg-Weyl group, with s...
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DD-domain sensing with overlaid Zadoff-Chu pilot on CP-OFDM yields the frequency-domain I/O relation, enabling pilot cancellation and joint ICI equalization that improves spectral efficiency over standard CP-OFDM in h...
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Delay-Doppler Channel Estimation using Arbitrarily Modulated Data Transmissions
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