### 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 |
---|---|

Pages (from-to) | 957-961 |

Number of pages | 5 |

Journal | IEEE Transactions on Vehicular Technology |

Volume | 68 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2019 |

### Keywords

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

### Cite this

*IEEE Transactions on Vehicular Technology*,

*68*(1), 957-961. https://doi.org/10.1109/TVT.2018.2878891

}

*IEEE Transactions on Vehicular Technology*, vol. 68, no. 1, pp. 957-961. https://doi.org/10.1109/TVT.2018.2878891

**Practical pulse-shaping waveforms for reduced-cyclic-prefix OTFS.** / Patchava, R.; Hong, Yi; Viterbo, Emanuele; Biglieri, Ezio.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

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

Y1 - 2019/1

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.

KW - circulant matrices

KW - delay-Doppler domain

KW - Delays

KW - Doppler shift

KW - Matrix decomposition

KW - OFDM

KW - OTFS

KW - Receivers

KW - Sparse matrices

KW - Time-frequency analysis

UR - http://www.scopus.com/inward/record.url?scp=85055879953&partnerID=8YFLogxK

U2 - 10.1109/TVT.2018.2878891

DO - 10.1109/TVT.2018.2878891

M3 - Article

VL - 68

SP - 957

EP - 961

JO - IEEE Transactions on Vehicular Technology

JF - IEEE Transactions on Vehicular Technology

SN - 0018-9545

IS - 1

ER -