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

R. Patchava, Yi Hong, Emanuele Viterbo, Ezio Biglieri

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254 Citations (Scopus)


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 languageEnglish
Pages (from-to)957-961
Number of pages5
JournalIEEE Transactions on Vehicular Technology
Issue number1
Publication statusPublished - Jan 2019


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

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