Improving Doppler Resilience of OFDM through Delay-Doppler Sensing

Danish Nisar; Muhammad Ubadah; Robert Calderbank; Ronny Hadani; Saif Khan Mohammed

arxiv: 2606.21850 · v1 · pith:UWX7TRTVnew · submitted 2026-06-20 · 📡 eess.SP · cs.IT· math.IT

Improving Doppler Resilience of OFDM through Delay-Doppler Sensing

Danish Nisar , Saif Khan Mohammed , Muhammad Ubadah , Ronny Hadani , Robert Calderbank This is my paper

Pith reviewed 2026-06-26 11:57 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT

keywords CP-OFDMDelay-Doppler sensingInter-carrier interferenceZadoff-Chu pilotHigh mobilitySpectral efficiency3GPP TDL-C channel

0 comments

The pith

Overlaying a Zadoff-Chu pilot on CP-OFDM data carriers lets delay-Doppler sensing recover the full frequency-domain input-output relation and equalize inter-carrier interference.

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

The paper shows that traditional CP-OFDM loses performance in doubly spread channels because inter-carrier interference becomes hard to characterize with ordinary time-frequency processing. By placing a Zadoff-Chu pilot on top of the data subcarriers and processing the received waveform in the delay-Doppler domain, the method acquires an effective channel filter that stays stationary in that domain. From this single estimate the complete frequency-domain mapping between every pair of OFDM carriers is derived exactly. The pilot contribution is then subtracted and all data carriers are detected jointly, removing the ICI term. Simulations on the 3GPP TDL-C channel confirm that the resulting spectral efficiency stays high even at elevated Doppler spreads where standard CP-OFDM degrades sharply.

Core claim

Transmitting an overlaid Zadoff-Chu pilot with CP-OFDM data and performing delay-Doppler domain sensing yields an accurate estimate of the stationary effective DD-domain channel filter; this estimate directly supplies the full frequency-domain input-output relation among CP-OFDM carriers, which is then used to cancel the pilot and jointly equalize all data carriers.

What carries the argument

The stationary effective delay-Doppler domain channel filter acquired from the overlaid Zadoff-Chu pilot, from which the complete frequency-domain input-output relation is derived.

If this is right

The frequency-domain input-output relation among all CP-OFDM carriers becomes known once the DD-domain filter is estimated.
The received pilot component can be reconstructed and subtracted, leaving a data-only signal.
Joint detection across all carriers then removes the inter-carrier interference term.
Spectral efficiency improves markedly over conventional CP-OFDM in high-mobility 3GPP TDL-C channels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same pilot-overlay idea could be tested on other multicarrier formats that suffer from Doppler-induced leakage.
If the DD filter stationarity holds only approximately, an adaptive tracking loop inside the DD domain might still keep the frequency-domain map accurate enough for detection.
Hardware experiments with moving terminals and the standardized TDL-C profile would directly check whether the simulated spectral-efficiency gain appears in practice.

Load-bearing premise

The effective channel response remains stationary inside the delay-Doppler domain over the observation interval, so that one Zadoff-Chu pilot measurement suffices to reconstruct the entire frequency-domain carrier mapping.

What would settle it

A measurement or simulation in which the delay-Doppler channel filter changes appreciably inside one OFDM symbol interval, so that the single Zadoff-Chu estimate no longer reproduces the observed frequency-domain input-output relation.

Figures

Figures reproduced from arXiv: 2606.21850 by Danish Nisar, Muhammad Ubadah, Robert Calderbank, Ronny Hadani, Saif Khan Mohammed.

**Figure 2.** Figure 2: Zak-OTFS de-modulation implemented as CP-OFDM de-modulator followed by DFZT (see top chain). [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Block diagram of the ZC Spread Pilot CP-OFDM Transmitter. The DD domain ZC sequence is transformed via the IDFZT and superimposed on [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Block diagram of the DD domain sensing based CP-OFDM Receiver. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Auto-ambiguity function AXu,Xu [k, l] of the ZC sequence with M = 289, N = 5 and u = 7. The auto-ambiguity is strictly supported on the line l = −uk mod MN. In (34), hdd[k, l] ∗σ AXu,Xu [k, l] is the useful term for channel estimation. Expanding this term we get hdd[k, l] ∗σ AXu,Xu [k, l] = MN hdd[k, l] + X (k ′ ,l′ )̸=(0,0) l ′=−uk′ modMN AXu,Xu [k ′ , l′ ] hdd[k − k ′ , l − l ′ ] e j2π k ′(l−l ′) MN ,(36… view at source ↗

**Figure 6.** Figure 6: Heatmap of hdd[k, l] ∗σ AXu,Xu [k, l] with M = 289, N = 5 and u = 7. AXu,Xu [k, l] for the 3GPP TDL-C channel model (non lineof-sight) [17] where hphy(τ, ν) = P 24 i=1 hiδ(τ − τi)δ(ν − νi). Here hi , τi , νi is the complex gain, delay and Doppler shift of the i-th channel path. We model νi = νmax cos(θi), i = 1, 2, · · · , 24 where νmax is the maximum possible Doppler shift of any path and θi , i = 1, 2, … view at source ↗

**Figure 7.** Figure 7: NMSE vs PDR for a fixed total transmitted power (both pilot and [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 9.** Figure 9: Effective Spectral Efficiency (SE) versus TPNR. [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

The performance of traditional CP-OFDM degrades severely in doubly-spread wireless channels due to inter-carrier interference (ICI). In this paper, we propose DD domain sensing based CP-OFDM where we transmit a Zadoff-Chu (ZC) pilot signal overlaid on CP-OFDM data carriers. At the receiver, DD domain signal processing is used to acquire the effective DD domain channel filter which is stationary in the DD domain. From this DD domain estimate, we derive the complete frequency domain (FD) input-output (I/O) relation between CP-OFDM carriers, acquiring which is otherwise difficult with traditional time-frequency signal processing. Using this FD I/O relation, we estimate the received FD pilot signal which is then canceled from the received FD signal, resulting in a data-only signal. Joint detection of all CP-OFDM data carriers from this data-only signal equalizes the effect of ICI. Numerical simulations of the standardized 3GPP TDL-C channel shows that in high mobility scenarios, the proposed DD domain sensing based CP-OFDM achieves significantly better spectral efficiency when compared to that achieved by traditional CP-OFDM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a concrete overlay method to sense the DD channel with a ZC pilot and derive the FD I/O matrix for standard CP-OFDM, but the gains depend on an unverified stationarity assumption and simulation results whose details are not shown.

read the letter

The main move is to overlay a Zadoff-Chu pilot on CP-OFDM data carriers, acquire the effective channel in the delay-Doppler domain, convert that estimate into the full frequency-domain input-output relation, cancel the pilot contribution, and then jointly detect the data carriers to equalize ICI. This is presented as new for conventional CP-OFDM rather than a full waveform change.

The processing chain is laid out clearly and stays close to existing OFDM hardware, which is a practical strength. Running the comparison on the standardized 3GPP TDL-C channel is also reasonable for a mobility test case, and the abstract claims a clear spectral-efficiency improvement in high-mobility conditions.

The soft spots are straightforward. All performance claims rest on numerical simulations whose parameters, number of runs, exact baselines, and error bars are not visible. More critically, the method treats the DD-domain filter as stationary so that one pilot observation yields an accurate FD I/O matrix. The TDL-C model produces only approximately sparse and stationary DD representations when Doppler spread is non-negligible relative to symbol rate; any residual mismatch would directly affect pilot cancellation and the subsequent joint detection. Without a derivation bound or error analysis in the visible text, it is unclear how much of the reported gain survives that approximation.

This is for engineers and researchers working on incremental fixes for high-mobility 5G/6G links who want to keep CP-OFDM at the transmitter. A reader focused on concrete receiver steps and standard-channel results will find it worth reading.

It deserves peer review because the problem is real, the approach is specific, and the gaps are fixable with more derivation and simulation detail rather than fundamental.

Referee Report

2 major / 1 minor

Summary. The paper proposes DD domain sensing based CP-OFDM, in which a Zadoff-Chu pilot is overlaid on standard CP-OFDM data carriers. At the receiver, delay-Doppler processing acquires an effective DD-domain channel filter asserted to be stationary; this estimate is used to construct the full frequency-domain input-output matrix between subcarriers, cancel the pilot contribution, and perform joint detection that equalizes ICI. Numerical simulations on the 3GPP TDL-C channel are reported to show substantially higher spectral efficiency than conventional CP-OFDM in high-mobility regimes.

Significance. If the central derivation holds, the approach offers a practical route to improve Doppler resilience of existing CP-OFDM waveforms by adding only an overlaid pilot and DD-domain post-processing, without waveform redesign. The use of a known ZC sequence for DD sensing and the subsequent reconstruction of the FD I/O relation constitute a concrete technical contribution; the standardized TDL-C simulations provide an initial, reproducible testbed for the claimed gains.

major comments (2)

[Abstract] Abstract: the claim that the effective DD-domain channel filter “is stationary in the DD domain” and thereby yields an exact frequency-domain I/O relation is stated without derivation, approximation bound, or error analysis for the TDL-C tapped-delay-line model. Because pilot cancellation and joint detection are built directly on this reconstructed matrix, any unquantified modeling error propagates into the equalized symbols and undermines the reported spectral-efficiency improvement.
[Numerical simulations] Numerical simulations (referenced in abstract): the performance claim rests on simulations whose setup (Doppler spread values, pilot power allocation, exact baseline CP-OFDM receiver, number of Monte-Carlo runs, error bars) is not described. Without these details it is impossible to assess whether the observed gain is robust or an artifact of particular parameter choices.

minor comments (1)

[Abstract] Acronyms CP-OFDM, ZC, ICI, and TDL-C should be defined at first use in the abstract and introduction for readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments. We address each major comment below and will revise the manuscript to strengthen the presentation of the central claims and simulation details.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the effective DD-domain channel filter “is stationary in the DD domain” and thereby yields an exact frequency-domain I/O relation is stated without derivation, approximation bound, or error analysis for the TDL-C tapped-delay-line model. Because pilot cancellation and joint detection are built directly on this reconstructed matrix, any unquantified modeling error propagates into the equalized symbols and undermines the reported spectral-efficiency improvement.

Authors: We agree that the abstract states the stationarity property concisely. The full manuscript derives the effective DD-domain channel filter from the Zadoff-Chu pilot processing and shows how it yields the frequency-domain I/O matrix; however, an explicit approximation analysis and error bound for the TDL-C model is not provided. In the revision we will add a dedicated subsection deriving the FD I/O relation with a first-order error bound that quantifies the modeling mismatch for the TDL-C tapped-delay-line structure. revision: yes
Referee: [Numerical simulations] Numerical simulations (referenced in abstract): the performance claim rests on simulations whose setup (Doppler spread values, pilot power allocation, exact baseline CP-OFDM receiver, number of Monte-Carlo runs, error bars) is not described. Without these details it is impossible to assess whether the observed gain is robust or an artifact of particular parameter choices.

Authors: We acknowledge that the simulation parameters were not reported in sufficient detail. The revised manuscript will include an expanded simulation-setup subsection specifying the Doppler spreads (corresponding to the 3GPP high-mobility TDL-C scenarios), the pilot-to-data power allocation ratio, the exact baseline CP-OFDM receiver (standard per-subcarrier MMSE equalization), the number of Monte-Carlo realizations, and error bars on all plotted curves. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses external pilot estimate to obtain I/O relation

full rationale

The paper's chain consists of transmitting an overlaid ZC pilot, acquiring the DD-domain channel filter via DD processing, asserting its stationarity, and deriving the FD I/O matrix from that estimate to enable pilot cancellation and joint detection. This is a direct estimation-plus-derivation procedure whose output is not forced by construction from the input data or by any self-citation chain. No equations reduce a claimed prediction to a fitted parameter, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled via citation. The stationarity claim is an assumption whose validity can be checked externally against the TDL-C model; it does not create a definitional loop inside the paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the central claim rests on one domain assumption about stationarity and on the existence of a complete FD I/O relation that can be computed from the DD filter. No free parameters or invented entities are mentioned.

axioms (1)

domain assumption The effective DD domain channel filter is stationary in the DD domain.
Explicitly invoked in the abstract as the reason DD-domain processing can acquire the filter and derive the FD I/O relation.

pith-pipeline@v0.9.1-grok · 5736 in / 1370 out tokens · 47520 ms · 2026-06-26T11:57:22.861824+00:00 · methodology

discussion (0)

Reference graph

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