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Waveform for Next Generation Communication Systems: Comparing Zak-OTFS with OFDM

T0 review · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Zak-OTFS outperforms CP-OFDM in effective spectral efficiency for doubly-spread channels, with the largest gains (more than 2x) in high mobility plus large cell scenarios.

arxiv 2505.13966 v1 pith:LGWTP5XK submitted 2025-05-20 eess.SP cs.ITmath.IT

Imran Ali Khan , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank , Anton Monk , Shachar Kons , Shlomo Rakib
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Yoav Hebron
This is my paper · ORCID
classification eess.SPcs.ITmath.IT
keywords zak-otfschoiceofdmarchitecturallargeperformancerelationacquisition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

OFDM, the workhorse of 4G and 5G, sends data on many narrow sub-carriers. When a user moves fast, the channel changes quickly and the sub-carriers leak into each other, creating inter-carrier interference (ICI). The standard fix is to space sub-carriers further apart, but that raises overhead and still requires extra pilot symbols to track a rapidly changing channel.

Zak-OTFS takes a different route. It places data on pulses spread across a delay-Doppler grid, where the channel response is more predictable. The price is that the pulses interfere with each other, so the receiver must equalize them jointly, which costs computation. The paper argues that in difficult channels, this trade is worth it.

The authors simulate a standardized Veh-A channel over a grid of delay spreads (0 to 4.7 microseconds) and Doppler spreads (0 to 2 kHz). Both waveforms are optimized over 3GPP modulation and coding schemes, pilot placements, and power ratios. At a fixed 12 dB signal-to-noise ratio, Zak-OTFS's effective spectral efficiency, the number of information bits delivered per second per hertz after overhead, is reported to be about 20% higher in most high-mobility cases and more than double in high-mobility, large-cell cases. In easy low-mobility, small-cell cases the two are close. The paper is short, does not release code, and says a full paper with a system-level view is coming, so the numbers are best read as an interim result.

Extended reading notes

Core claim

The load-bearing claim is that in doubly-spread channels, Zak-OTFS's predictable delay-Doppler I/O relation enables complete acquisition and joint equalization, yielding materially higher effective spectral efficiency than CP-OFDM. The abstract states: 'Zak-OTFS exhibits superior performance in doubly-spread 6G use cases with high delay/Doppler channel spreads (i.e., high mobility and/or large cells).' In Section III, the authors report that in the high-mobility/large-cell quadrant (e.g., NTN and aircraft-to-ground), the effective SE of Zak-OTFS is more than double that of CP-OFDM.

Load-bearing premise

The paper assumes the crystallization condition from cited prior work: if the Zak-OTFS delay period τp exceeds channel delay spread and Doppler period νp exceeds Doppler spread, then the DD-domain I/O relation is predictable and fully acquirable from a single pilot. This condition is not re-derived or stress-tested here. The point-pilot overhead model in Section II-D (guard strips with width tied to the channel spread, yielding overheads like 2.5% versus 28.4% for OFDM) is also a modeling choice. If real channels violate the period bounds or the guard strips are too optimistic, the claimed 2x advantage shrinks or disappears.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on the crystallization-condition theory inherited from prior work, a point-pilot overhead model, a single channel model and SNR, and design parameters swept during optimization. No new physical entities are introduced, but the chosen simulation envelope (12 dB, Veh-A, guard-strip widths) carries much of the weight of the conclusion.

free parameters (4)
  • Zak-OTFS Doppler period νp search set = 1, 2, 4, 6, 8, 12, 14, 24 kHz
    Optimization parameter swept to maximize effective SE; not fitted to external data, but the chosen set shapes the achievable overhead in Section III.
  • Pilot-to-data power ratio PDR = -15 to 15 dB in 5 dB steps
    Swept for Zak-OTFS frame design in Section III; affects channel estimation quality and data power, and therefore the reported SE.
  • Total transmit power to noise ratio = 12 dB
    A single operating point for all simulations; the conclusion may not hold at other SNRs, and this is a chosen scenario parameter, not a fitted constant.
  • Point-pilot overhead factor = 2 (guard strips on both sides of pilot)
    The overhead formula in Section II-D assumes symmetric guard regions with width equal to channel delay spread or Doppler spread. This assumption directly sets the Zak-OTFS overhead and thus the SE comparison.
assumptions (5)
  • domain assumption Crystallization condition: if τp ≥ channel delay spread and νp ≥ channel Doppler spread, the Zak-OTFS I/O relation is predictable and fully acquirable from a single pilot pulsone.
    Taken from refs [2], [3], not re-derived here. It is the theoretical basis for the claimed acquisition advantage and for the overhead model in Section II-D.
  • domain assumption CP-OFDM I/O relation cannot be completely acquired in a doubly-spread channel, making full joint equalization impossible.
    Asserted in Section II-B with an informal pilot-tracking argument; no formal proof, bound, or citation to prior channel-estimation results is provided.
  • domain assumption The 3GPP Veh-A channel model with the listed delay/Doppler spread pairs represents 6G propagation environments across cell sizes.
    Section III uses a single channel model and a sparse grid of spreads to stand in for 'the full range of 6G propagation environments' claimed in the abstract.
  • domain assumption BLER < 0.1 as defined in 3GPP is the reliability threshold for computing effective SE.
    The paper adopts this threshold and even questions it in Section III-A, noting that a lower BLER might change the comparison.
  • domain assumption Gauss-Sinc pulse shaping filters provide an appropriate baseline Zak-OTFS waveform.
    Reference [13] is under review and not independently verified here; the pulse shape affects out-of-band leakage and equalization performance.

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Cite this review

Pith. "Pith review of Waveform for Next Generation Communication Systems: Comparing Zak-OTFS with OFDM." pith.science (2026). https://pith.science/paper/LGWTP5XK

@misc{pith2026250513966,
  author       = {Pith},
  title        = {Pith review of: Waveform for Next Generation Communication Systems: Comparing Zak-OTFS with OFDM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LGWTP5XK}},
  note         = {Machine review of arXiv:2505.13966}
}
read the original abstract

Across the world, there is growing interest in new waveforms, Zak-OTFS in particular, and over-the-air implementations are starting to appear. The choice between OFDM and Zak-OTFS is not so much a choice between waveforms as it is an architectural choice between preventing inter-carrier interference (ICI) and embracing ICI. In OFDM, once the Input-Output (I/O) relation is known, equalization is relatively simple, at least when there is no ICI. However, in the presence of ICI the I/O relation is non-predictable and its acquisition is non-trivial. In contrast, equalization is more involved in Zak-OTFS due to inter-symbol-interference (ISI), however the I/O relation is predictable and its acquisition is simple. {Zak-OTFS exhibits superior performance in doubly-spread 6G use cases with high delay/Doppler channel spreads (i.e., high mobility and/or large cells), but architectural choice is governed by the typical use case, today and in the future. What is typical depends to some degree on geography, since large delay spread is a characteristic of large cells which are the rule rather than the exception in many important wireless markets.} This paper provides a comprehensive performance comparison of cyclic prefix OFDM (CP-OFDM) and Zak-OTFS across the full range of 6G propagation environments. The performance results provide insights into the fundamental architectural choice.

Figures

Figures reproduced from arXiv: 2505.13966 by the authors.

Figure 1
Figure 1. Orthogonal allocation of TF resources [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Zak-OTFS (Embracing ICI) vs. CP-OFDM (avoiding ICI). [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. (a) Effect of channel Doppler spread on overhead in CP-OFDM. (b) Effect of channel delay spread on [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: A typical Zak-OTFS frame with pilot, guard and data regions. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Ratio of effective SE achieved by Zak-OTFS to that achieved by CP-OFDM. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Three different Zak-OTFS frame structures for pilot-data allocation. Each frame is [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Industrial Viewpoints on RAN Technologies for 6G

    cs.NI 2025-08 conditional novelty 3.0 of 10

    An industry-authored survey predicts 6G radio access will center on mid-band spectrum, evolved massive MIMO, AI/ML integration, OFDM-compatible waveforms, and native satellite support, explicitly labeled as speculation.

Reference graph

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