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arxiv: 2606.26420 · v1 · pith:A57BCDH5new · submitted 2026-06-24 · 📡 eess.SP

MIMO Zak-OTFS: Channel Estimation, Detection, and Throughput Analysis

Faraz Barati , Rahul Kumar Jaiswal , Saif Khan Mohammed , Ronny Hadani , Jeffrey G. Andrews This is my paper

Pith reviewed 2026-06-26 00:38 UTC · model grok-4.3

classification 📡 eess.SP
keywords MIMO Zak-OTFSchannel estimationdelay-Doppler domainCP-OFDMDoppler dispersionpilot-to-data power ratiothroughput analysisinter-carrier interference
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The pith

MIMO Zak-OTFS derives its full system model directly from the physical multipath channel and identifies a performance crossover with CP-OFDM.

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

The paper extends Zak-OTFS modulation to multiple-input multiple-output systems by deriving a complete end-to-end model straight from the physical multipath channel. It introduces structured pilot placement in the delay-Doppler domain to support efficient channel estimation. Evaluations on the standardized CDL-C model show that Zak-OTFS robustness to Doppler and inter-carrier interference carries over to MIMO, with a crossover point where CP-OFDM performs better only at low SNR and low Doppler. The crossover locations for SNR and Doppler are inversely related, and Zak-OTFS shows greater sensitivity to high pilot-to-data power ratios while sharing a similar optimal ratio with CP-OFDM.

Core claim

We first derive a complete system model for MIMO Zak-OTFS based directly on the physical multipath channel. We then propose an efficient channel estimation method using structured pilot placement in the delay-Doppler domain. The proposed approach demonstrates that the advantages of Zak-OTFS observed in SISO scenarios extend to MIMO systems, particularly its robustness to Doppler and inter-carrier interference. We identify a fundamental crossover behavior: CP-OFDM performs slightly better at low SNR and low Doppler, while Zak-OTFS excels at higher SNR or under severe Doppler dispersion, with the crossover points for SNR and Doppler shifting inversely to each other.

What carries the argument

The complete system model for MIMO Zak-OTFS obtained by direct mapping from the physical multipath channel, which enables structured pilot placement in the delay-Doppler domain for channel estimation.

If this is right

  • Zak-OTFS maintains its Doppler and ICI robustness when extended from SISO to MIMO.
  • CP-OFDM is preferable only below the identified SNR and Doppler thresholds; Zak-OTFS is preferable above them.
  • Crossover SNR and crossover Doppler are inversely related, so raising one threshold lowers the other.
  • Zak-OTFS exhibits increased sensitivity to high pilot-to-data power ratios compared with CP-OFDM while sharing the same optimal ratio.

Where Pith is reading between the lines

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

  • Pilot design rules developed here could be tested on other delay-Doppler waveforms to check whether the same crossover pattern appears.
  • If hardware impairments shift the reported crossover points, the model would need an additional impairment term before being used for link adaptation.
  • Throughput gains at high Doppler suggest the framework may favor Zak-OTFS in vehicular or high-speed train scenarios once the pilot overhead is accounted for.

Load-bearing premise

The standardized CDL-C channel model together with the chosen structured pilot placement accurately reproduces the estimation accuracy and interference behavior that would appear in real deployments without unmodeled hardware impairments or synchronization errors.

What would settle it

Measurements in an actual high-mobility MIMO deployment that produce crossover SNR or Doppler values different from those obtained under the CDL-C model with the same pilot structure.

Figures

Figures reproduced from arXiv: 2606.26420 by Faraz Barati, Jeffrey G. Andrews, Rahul Kumar Jaiswal, Ronny Hadani, Saif Khan Mohammed.

Figure 1
Figure 1. Figure 1: SISO Zak-OTFS System Model input–output relationship, in which the MN × 1 vector con￾taining all received symbols is expressed as the product of an MN × MN effective channel matrix and the corresponding MN × 1 vector of transmitted information symbols: y = Hx + n (23) Where y ∈ CMN×1 , x ∈ CMN×1 , n ∈ CMN×1 , H ∈ CMN×MN . C. MIMO Zak OTFS Here we consider a MIMO system with Nt transmit and Nr receive anten… view at source ↗
Figure 2
Figure 2. Figure 2: MIMO Zak-OTFS System Model. The received match-filtered continuous DD domain sig￾nal at the rth receive antenna is given by y wrx r,dd(τ, ν) = N Pt−1 t=0 h r,t eff(τ, ν)∗σx wtx t,dd(τ, ν) + n wrx r,dd(τ, ν) where n wrx r,dd(τ, ν) = wrx(τ, ν) ∗σ nr,dd(τ, ν) and nr,dd(τ, ν) is the DD representa￾tion (Zak transform) of the time-domain AWGN at the rth re￾ceive antenna. Sampling y wrx r,dd(τ, ν) on the informat… view at source ↗
Figure 3
Figure 3. Figure 3: Permutation method. III. METHODOLOGY In SISO Zak-OTFS, the channel filter heff[k, l] is estimated from the channel response to a single DD pulse (pilot) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pilot separation strategies in the delay–Doppler (DD) plane: (a) SISO, (b) separation in Doppler only, (c) separation [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Uncoded 4QAM BER vs TSNR for Perfect CSI with [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: NMSE vs TSNR for Different Pilot Placement [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Different Pilot Placement Strategies comprising [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: illustrates the spectral efficiency vs maximum Doppler shift of the two modulation schemes at the fixed 12 dB TSNR [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Throughput and NMSE versus TSNR for Zak-OTFS [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

Zak-Orthogonal Time Frequency Space (Zak-OTFS) modulation has demonstrated substantial performance gains over cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM) in highly time- and frequency-selective channels. In this paper, we extend Zak-OTFS to a multiple-input multiple-output (MIMO) framework. We first derive a complete system model for MIMO Zak-OTFS based directly on the physical multipath channel; ours is the first work to do so. We then propose an efficient channel estimation method using structured pilot placement in the delay-Doppler (DD) domain. The proposed approach is evaluated under the standardized CDL-C channel model, demonstrating that the advantages of Zak-OTFS observed in SISO scenarios extend to MIMO systems, particularly its robustness to Doppler and inter-carrier interference (ICI). We identify a fundamental crossover behavior: CP-OFDM performs slightly better at low SNR and low Doppler, while Zak-OTFS excels at higher SNR or under severe Doppler dispersion. Furthermore, we show that the crossover points for SNR and Doppler shift inversely to each other. We also observe that Zak-OTFS, particularly with MIMO, exhibits increased sensitivity to high values of pilot-to-data power ratio (PDR), but has a similar optimal PDR as 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.

Referee Report

2 major / 2 minor

Summary. The paper extends Zak-OTFS to MIMO by deriving a complete system model directly from the physical multipath channel (claimed as the first such derivation), proposes an efficient DD-domain channel estimation scheme using structured pilot placement, and evaluates the approach under the standardized CDL-C model. It reports that Zak-OTFS advantages over CP-OFDM extend to MIMO, with a crossover behavior where CP-OFDM is slightly better at low SNR/low Doppler while Zak-OTFS excels at higher SNR or severe Doppler (with inverse crossover dependence), plus increased sensitivity to high PDR values but similar optimal PDR.

Significance. If the system model derivation is complete and the simulation results hold under the stated assumptions, the work would provide a useful analytical and practical foundation for MIMO Zak-OTFS in doubly-selective channels, clarifying operating regimes relative to CP-OFDM and highlighting PDR sensitivity. The use of a standardized channel model aids reproducibility, though the absence of machine-checked proofs or open code is noted.

major comments (2)
  1. [Numerical results section] Numerical results / simulation setup (around the crossover SNR/Doppler figures): the reported crossover points and MIMO robustness claims rest on idealized CDL-C simulations with structured DD pilots; the manuscript does not model hardware impairments (phase noise, I/Q imbalance, residual timing/frequency offsets) that would alter effective Doppler/ICI statistics and could shift or eliminate the claimed advantage regions.
  2. [Channel estimation and detection sections] Channel estimation and detection sections: while the system model is derived from the physical multipath channel, the evaluation of estimation accuracy and throughput does not include an ablation or sensitivity analysis showing how unmodeled synchronization errors would affect the PDR sensitivity and crossover observations.
minor comments (2)
  1. [System model] Notation for MIMO channel matrices and DD-domain transformations should be cross-checked for consistency between the system model derivation and the simulation parameter tables.
  2. [Figures in numerical results] Figure captions for throughput vs. SNR/Doppler curves should explicitly state the number of Monte Carlo realizations and whether error bars are shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive comments on our manuscript. We address the major comments point by point below, clarifying the scope and assumptions of the work.

read point-by-point responses

  1. Referee: [Numerical results section] Numerical results / simulation setup (around the crossover SNR/Doppler figures): the reported crossover points and MIMO robustness claims rest on idealized CDL-C simulations with structured DD pilots; the manuscript does not model hardware impairments (phase noise, I/Q imbalance, residual timing/frequency offsets) that would alter effective Doppler/ICI statistics and could shift or eliminate the claimed advantage regions.

    Authors: The numerical results are obtained under the standardized CDL-C channel model with the assumptions of the derived system model, which is standard practice for establishing baseline performance in doubly selective channels. Hardware impairments such as phase noise or I/Q imbalance are not modeled, as incorporating them would require additional specific impairment models and parameters outside the current scope focused on the MIMO Zak-OTFS derivation and DD-domain estimation. The reported crossover points and robustness claims hold under these conditions; extensions to include impairments are left for future work. revision: no

  2. Referee: [Channel estimation and detection sections] Channel estimation and detection sections: while the system model is derived from the physical multipath channel, the evaluation of estimation accuracy and throughput does not include an ablation or sensitivity analysis showing how unmodeled synchronization errors would affect the PDR sensitivity and crossover observations.

    Authors: The system model derivation and subsequent evaluation assume ideal synchronization, consistent with the physical multipath channel model used throughout the paper. No ablation study on synchronization errors is included because such errors are not part of the stated model assumptions, and modeling their distributions would require additional analysis beyond the paper's focus on channel estimation accuracy and throughput under CDL-C. The PDR sensitivity and crossover observations are presented under the given assumptions; sensitivity to synchronization errors can be investigated in follow-on studies. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation from physical channel is independent

full rationale

The paper states it derives the MIMO Zak-OTFS system model directly from the physical multipath channel (first such work). Channel estimation and performance claims rest on evaluation under the external standardized CDL-C model, with no evidence of fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations in the derivation chain. The central claims (crossover behavior, robustness) are simulation-based against an independent benchmark rather than reducing to the paper's own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no concrete information on free parameters, axioms, or invented entities; the ledger is therefore empty.

pith-pipeline@v0.9.1-grok · 5775 in / 1176 out tokens · 24239 ms · 2026-06-26T00:38:52.728748+00:00 · methodology

discussion (0)

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Reference graph

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