Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication
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| Format: | Preprint |
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2024
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| _version_ | 1866908425818996736 |
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| author | Ubadah, Muhammad Mohammed, Saif Khan Hadani, Ronny Kons, Shachar Chockalingam, Ananthanarayanan Calderbank, Robert |
| author_facet | Ubadah, Muhammad Mohammed, Saif Khan Hadani, Ronny Kons, Shachar Chockalingam, Ananthanarayanan Calderbank, Robert |
| contents | 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 $Λ_{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${Λ^*}$. We show that if the channel satisfies the crystallization conditions with respect to ${Λ^*}$ 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 $Λ_{p}$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_04182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication Ubadah, Muhammad Mohammed, Saif Khan Hadani, Ronny Kons, Shachar Chockalingam, Ananthanarayanan Calderbank, Robert Signal Processing Information Theory 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 $Λ_{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${Λ^*}$. We show that if the channel satisfies the crystallization conditions with respect to ${Λ^*}$ 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 $Λ_{p}$, 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. |
| title | Zak-OTFS to Integrate Sensing the I/O Relation and Data Communication |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2404.04182 |