# Practical pulse-shaping waveforms for reduced-cyclic-prefix OTFS

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

In this paper we model <formula><tex>$M \times N$</tex></formula> orthogonal time frequency space modulation (OTFS) over a <formula><tex>$P$</tex></formula>-path doubly-dispersive channel with delays less than <formula><tex>$\tau_{\max}$</tex></formula> and Doppler shifts in the range <formula><tex>$(\nu_{\min},\nu_{\max})$</tex></formula>. We first derive in a simple matrix form the input--output relation in the delay--Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input--output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input--output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix (CP) is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.

Original language English 957-961 5 IEEE Transactions on Vehicular Technology 68 1 https://doi.org/10.1109/TVT.2018.2878891 Published - Jan 2019

### Keywords

• circulant matrices
• delay-Doppler domain
• Delays
• Doppler shift
• Matrix decomposition
• OFDM
• OTFS
• Sparse matrices
• Time-frequency analysis

### Cite this

@article{0d794c5d78cb4e43b4b266caa4305fe9,
title = "Practical pulse-shaping waveforms for reduced-cyclic-prefix OTFS",
abstract = "In this paper we model $M \times N$ orthogonal time frequency space modulation (OTFS) over a $P$-path doubly-dispersive channel with delays less than $\tau_{\max}$ and Doppler shifts in the range $(\nu_{\min},\nu_{\max})$. We first derive in a simple matrix form the input--output relation in the delay--Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input--output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input--output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix (CP) is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.",
keywords = "circulant matrices, delay-Doppler domain, Delays, Doppler shift, Matrix decomposition, OFDM, OTFS, Receivers, Sparse matrices, Time-frequency analysis",
author = "R. Patchava and Yi Hong and Emanuele Viterbo and Ezio Biglieri",
year = "2019",
month = "1",
doi = "10.1109/TVT.2018.2878891",
language = "English",
volume = "68",
pages = "957--961",
journal = "IEEE Transactions on Vehicular Technology",
issn = "0018-9545",
publisher = "IEEE, Institute of Electrical and Electronics Engineers",
number = "1",

}

In: IEEE Transactions on Vehicular Technology, Vol. 68, No. 1, 01.2019, p. 957-961.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - Practical pulse-shaping waveforms for reduced-cyclic-prefix OTFS

AU - Patchava, R.

AU - Hong, Yi

AU - Viterbo, Emanuele

AU - Biglieri, Ezio

PY - 2019/1

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N2 - In this paper we model $M \times N$ orthogonal time frequency space modulation (OTFS) over a $P$-path doubly-dispersive channel with delays less than $\tau_{\max}$ and Doppler shifts in the range $(\nu_{\min},\nu_{\max})$. We first derive in a simple matrix form the input--output relation in the delay--Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input--output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input--output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix (CP) is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.

AB - In this paper we model $M \times N$ orthogonal time frequency space modulation (OTFS) over a $P$-path doubly-dispersive channel with delays less than $\tau_{\max}$ and Doppler shifts in the range $(\nu_{\min},\nu_{\max})$. We first derive in a simple matrix form the input--output relation in the delay--Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input--output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input--output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix (CP) is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.

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KW - delay-Doppler domain

KW - Delays

KW - Doppler shift

KW - Matrix decomposition

KW - OFDM

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KW - Sparse matrices

KW - Time-frequency analysis

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