{"id":"9cb34e04-e3fc-4b98-b210-a55cf0738afc","arxiv_id":"2507.12593","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In Zak-OTFS, the cross-ambiguity of received and transmitted random data is approximately the channel, so detected data can replace periodic pilots and enable pilot-free differential detection.","lead":"This paper proposes letting data symbols double as channel probes in Zak-OTFS, a delay-Doppler modulation, so that pilots need not be sent every frame. The receiver uses channel estimates from previously detected data to detect the next frame, trading a small amount of error propagation for full spectral efficiency.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq (16) is derived for the true transmitted frame, but the receiver substitutes detected symbols; the bootstrap replacement and finite-frame residual B[k,l] are unanalyzed, so the pilot-free claim rests on an unproven step.","rationale":"The paper's strongest claim is that detected data can replace pilots because A_{y,x} ≈ e_d h_eff. The derivation of this identity assumes knowledge of the true transmitted data, while the receiver only has detected data. This is the same gap the reader identified, and it is load-bearing: if decision errors or finite-frame leakage are not controlled, the channel estimate degrades, error propagation sets in, and the claimed reduction of pilot transmissions is not supported outside the specific simulated high-SNR regime. The paper itself acknowledges error propagation at low SNR and transmits a pilot frame every 30 frames, so the asymptotic identity is not sufficient for the actual algorithm. The index issue in Eq. (15) adds a correctness concern in the written derivation, though the intended autocorrelation argument is plausible. I do not see a fundamental flaw that would require rejection: the underlying idea is reasonable, the simulations are internally consistent, and the comparison with spread pilot is informative. The missing piece is an analysis of the decision-directed bootstrap and a bound on the finite-frame residual, which is exactly what a conditional acceptance should demand. The concrete test would distinguish between a benign implementation detail and a genuine gap between the analytic claim and the receiver behavior.","tokens_in":9130,"tokens_out":3291,"duration_ms":39179,"concrete_test":"Run a matched simulation at M=31, N=37 over VehA channels at SNR values 0, 10, 20, 25 dB comparing three receivers: (i) the proposed receiver using detected \\hat{X} in the cross-ambiguity; (ii) the same bootstrap but with the true X substituted at the channel-estimation step (genie channel estimate); (iii) the proposed receiver with the finite-frame residual B[k,l] removed by subtracting the known autocorrelation of the true data. If (i) is statistically indistinguishable from (ii), the detected-data substitution is benign; if (i) is measurably worse, Eq. (16) does not cover the actual receiver. Separately, plot E|B[k,l]|^2 for M=11, 31, 101 at fixed N to check that the residual decays with frame size; if it does not decay, the asymptotic argument is not the operative mechanism in the simulated regime.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that detected data can serve as pilots because the cross-ambiguity A_{y,x} approximates e_d h_eff (Eq. 16). However, Eqs. (11)-(16) compute A_{y,x} using the true transmitted data X. At the receiver only the detected frame \\hat{X} is available, so the actual quantity is A_{y,\\hat{x}}. Replacing X by \\hat{X} changes the residual B[k,l] in Eq. (14) from a data autocorrelation to a mixed data/decision-error term; no bound is provided for this term. Because the estimated channel is fed forward to detect the next frame, any decision errors propagate. Figure 2 shows that at SNR = 0 dB error propagation indeed occurs, and the authors insert a pilot frame every 30 transmissions to curb it; at 25 dB errors are 'small' but no analytical threshold is given. The undulations in Fig. 1c are precisely the nonzero finite-frame B[k,l], and Remark 1 contrasts this with spread pilot where B is exactly a delta. Additionally, Eq. (15) appears mis-indexed: solving 1{k=(k0-k1) mod M} gives k1 = k0 - k, not k1 = (k-k0)_M. The intended autocorrelation interpretation is plausible, but as written the derivation is not self-consistent. Thus the claim that periodic pilot transmission is alleviated depends on an unanalyzed decision-directed bootstrap and an unbounded finite-frame residual.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a decision-directed differential communication scheme for Zak-OTFS. It argues that the cross-ambiguity between the received frame and the data frame is approximately a scaled version of the effective delay-Doppler channel, so that detected data symbols can serve as implicit pilots. The receiver carries the channel estimate across frames, reducing pilot overhead while retaining full spectral efficiency. The paper provides an analytic derivation for known data, simulation results for 4-QAM and 16-QAM, comparisons with spread-pilot schemes, and a complexity analysis.","tokens_in":9383,"tokens_out":10024,"duration_ms":108019,"significance":"If the central claim holds, the scheme offers a practical way to reduce pilot overhead in Zak-OTFS without sacrificing spectral efficiency, with lower complexity than spread-pilot receivers. The paper identifies a meaningful problem, provides a plausible asymptotic mechanism, and demonstrates empirically that the data-only estimate improves with frame size. It also usefully displays the finite-frame residual in Fig. 1 and diagnoses error propagation in Fig. 2. However, the advertised analytic justification is incomplete because it is derived for known transmitted data rather than for detected symbols, and the finite-frame residual is not bounded; these gaps currently limit the strength of the contribution.","major_comments":[{"comment":"In the displayed definition of A_{X_p,k0,l0; X_p,k1,l1}[k,l], the indices (k1,l1) of the second pulsone appear both as parameters and as summation variables. The extra summation over k1,l1 makes the expression ill-defined as a cross-ambiguity between two specific pulsones; as written, the reduction to Eq. (6) does not follow from Eq. (4). Since Eq. (14) and the asymptotic estimate (16) rely on Eq. (6), this part of the derivation must be corrected.","section":"Section II-C, Eq. (4)"},{"comment":"The index substitution is inconsistent: from the condition 1{k=(k0-k1) mod M} in Eq. (14), the correct second summation index is k1 = (k0-k)_M, not (k-k0)_M, and similarly l1 = (l0-l)_N. As written, Eq. (15) describes a mirrored autocorrelation and is not the quantity arising from Eq. (14). The authors should correct the indices and re-verify that the asymptotic claim (16) remains valid after the correction.","section":"Section III, Eq. (15)"},{"comment":"The analytic derivation computes A_{y,x} with the true transmitted symbols X. In the proposed differential scheme, the receiver only has the detected frame \\hat{X}, so the actual residual in Eq. (14) becomes a mixed data/decision-error term. The paper does not analyze how decision errors affect B or the subsequent channel estimate, and the statement that Eq. (16) holds 'asymptotically' is not accompanied by a formal limit or concentration argument. Because the estimated channel is used to detect the next frame, error propagation is a first-order concern; this omission leaves the central 'detected data as pilots' claim unproven.","section":"Section III, Eqs. (11)-(16)"},{"comment":"The results show that at SNR=0 dB the instantaneous NMSE grows between pilot insertions and that the scheme requires a pilot frame every 30 transmissions; at 25 dB the error propagation is small but no analytical threshold is given. The abstract's claim that the scheme 'alleviates' the need for periodic pilots is compatible with these results, but the paper should state precisely under what conditions the reduced pilot rate is reliable and how the 30-frame period is chosen.","section":"Section IV-A, Fig. 2"}],"minor_comments":[{"comment":"The vector x is described as the vector of transmitted symbols in the time-domain, while the surrounding text discusses DD-domain data symbols; the notation should be aligned.","section":"Section II-A, Eq. (1)"},{"comment":"Even after fixing the summation-variable issue, the notation should clearly distinguish the indices of the two pulsones from the summation indices.","section":"Section II-C, Eq. (4)"},{"comment":"Please specify whether the approximation is in expectation or with high probability, and over what asymptotic regime (frame size, constellation size) it is intended to hold.","section":"Section III, Eq. (16)"},{"comment":"The phrase 'the performance with DO frame is the lower bound for the performance with SP frame' is ambiguous; since lower BER is better, the intended ordering should be stated explicitly.","section":"Section IV-C"},{"comment":"The nine-subfigure layout is hard to read at print size; consider presenting a subset of the cases or using larger panels.","section":"Section IV, Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope and the problem is timely. The main technical gaps are in the derivation of the bootstrap estimate: the Eq. (15) index error is local, but the unanalyzed substitution of detected data for true data is load-bearing for the paper's core claim. If the authors can correct the derivation and provide at least a partial analysis or a clearly delimited operating regime for the decision-directed bootstrap, the paper could be a valid contribution. I do not see grounds for rejection, but the current version's central claim is stronger than what is proved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is that this paper is a credible, mostly honest application of classical decision-directed channel estimation to Zak-OTFS, but the central claim that detected data can replace pilots is not fully proven: the asymptotic result (16) is derived for the true transmitted frame, and the replacement by detected symbols is only simulated. That said, the paper is not sloppy. It explicitly identifies the residual B[k,l], shows the undulations in Fig. 1c, and admits that pilot frames are still inserted every 30 transmissions at low SNR. The sign error in Eq. (15) looks like a typo rather than a fatal flaw, since the intended autocorrelation interpretation is clear.\n\nWhat is actually new: applying differential/decision-directed communication to Zak-OTFS and showing that, for random data, the DD-domain cross-ambiguity between received and transmitted frames converges to the effective channel up to a scale. The derivation is short but clean, reusing known ambiguity-function identities. The complexity comparison is fair: DO avoids the pilot-removal step of spread pilot, which is a genuine saving. The numerical results back the qualitative claims, especially the effect of frame size on estimation accuracy in Fig. 3. No parameters are fitted, and the asymptotic statement is not circular by construction.\n\nThe soft spots: first, the detected-data step. The paper proves A_{y,x} ≈ e_d h_eff, then uses A_{y,\\hat{x}}. Decision errors change the residual B from a data autocorrelation to a mixed data/decision-error term, and no bound or analysis is given. Error propagation is visible at 0 dB in Fig. 2, and the fix is a periodic pilot frame. That does not kill the pilot-free claim at high SNR, but it makes the alleviation conditional. Second, the finite-frame residual B[k,l] is asserted to be small without a non-asymptotic bound. The undulations in Fig. 1c show it is present; the paper does not show it decays fast enough. Third, the comparison against spread pilot is fair only under the chosen equal-energy split; the α sweep helps, but the comparison does not cover all operating points. The index sign in Eq. (15) is minor but should be corrected.\n\nThis paper is for researchers working on OTFS receiver design and integrated sensing and communication. It deserves a serious referee, but the referee should push for an analysis of the detected-data bootstrap and a bound on the finite-frame residual. If those are added, the central claim becomes defensible as stated. My verdict: conditional accept, with revision.","headline":"A plausible specialization of decision-directed channel estimation to Zak-OTFS, but the pilot-free claim rests on an unanalyzed bootstrap and an unbounded finite-frame residual.","tokens_in":9948,"tokens_out":2211,"would_cite":false,"duration_ms":25605,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Zak-OTFS can estimate the channel from its own detected data, so periodic pilot symbols become optional resets only.","keywords":["Zak-OTFS","delay-Doppler domain","differential communication","channel predictability","cross-ambiguity function","pilot-free channel estimation","spectral efficiency","doubly-dispersive channel"],"falsifier":"Measure the instantaneous NMSE of the channel estimate from a data-only frame at a fixed SNR while increasing frame size $MN$; Eq. (16) predicts convergence to the scaled effective channel, so if the NMSE stops improving or stays well above the spread-pilot estimate at large frames, the central claim fails.","tokens_in":8861,"feed_emoji":"📡","tokens_out":9350,"duration_ms":96952,"temperature":0.7,"pith_summary":"The paper's aim is to make a Zak-OTFS wireless link work without regularly sending pilot symbols. It shows that the receiver can estimate the delay-Doppler channel from the data it has already detected, then use that estimate to detect the next frame, and repeat. The key analytical result is that the cross-ambiguity between a received frame and the transmitted data frame is, for large frames and random data, just the effective channel scaled by the data-symbol energy. Because the delay-Doppler channel changes slowly, the estimate stays valid across consecutive frames. The payoff is that all frame energy goes to data, spectral efficiency is full, and the receiver is simpler than a spread-pilot receiver while achieving better bit-error rate in simulation.","feed_headline":"Zak-OTFS turns detected data into pilots, ending periodic pilot waste","feed_subtitle":"Reusing detected symbols as pilots frees all frame energy for data and beats spread-pilot bit-error rate at lower cost.","key_machinery":"The load-bearing object is the DD-domain cross-ambiguity function $$A_{y,x}[k',l'] = \\frac{1}{MN}\\sum_{n=0}^{MN-1} y[n]x^*[n-k']$e^{{-j\\frac{2\\pi}}${MN}l'(n-k')},$$ which is the maximum-likelihood, model-free estimate of the effective channel. The sum in (13) is a twisted convolution of $h_{\\mathrm{eff}}$ with $B[k,l]$, a convolution variant that carries the quasi-periodic phase structure of the DD pulsones. The key identity is (16): with random data symbols and a large frame, the self-interference term $B[k,l]$ collapses to $e_d\\delta[k]\\delta[l]$, so the cross-ambiguity of a received data frame with the transmitted data frame is approximately $e_d h_{\\mathrm{eff}}[k',l']$. The differential recursion then alternates between detecting data from the current channel estimate and refreshing the estimate from the detected data.","core_discovery":"The central claim is that in Zak-OTFS a data frame can serve as its own pilot. The DD-domain cross-ambiguity $A_{y,x}[k',l']$ between the received frame $y$ and the transmitted data frame $x$ is shown to satisfy $$A_{y,x}[k',l'] \\approx e_d\\,h_{\\mathrm{eff}}[k',l'],$$ where $e_d$ is the average energy of the information symbols and $h_{\\mathrm{eff}}$ is the effective delay-Doppler channel. The identity follows because the interference term $B[k,l]$ in (14)--(15) averages to a scaled delta, $e_d\\,\\delta[k]\\delta[l]$, when data symbols are random and the frame is large. Hence the receiver can start from a pilot-assisted channel estimate, detect data, treat the detected frame as a pilot to update the estimate, and carry that estimate forward through the predictable DD channel. Periodic pilots are retained only as occasional resets to stop error propagation.","pith_inferences":["The paper does not discuss joint sensing, but if the bootstrap is stable the same detected-data channel estimate could simultaneously feed radar sensing in a Zak-OTFS sensing-and-communication system, yielding a continuous sensing stream without dedicated pilot frames.","A threshold-triggered pilot reset, based on observed NMSE or decoder confidence, could replace the fixed every-30-frames schedule and reduce pilot overhead further at low SNR, where the paper's Figure 2 shows error propagation building between resets.","Because the analysis assumes true data symbols in the cross-ambiguity, the practical robustness of the scheme hinges on the decision-error rate; one could test this by feeding the receiver correlated or coded data and measuring how quickly the estimate drifts.","Since Eq. (16) is asymptotic, the residual $B[k,l]$ is the quantity to watch for finite frames; quantifying its norm in terms of $M$, $N$, and constellation statistics would predict exactly when the pilot-free bootstrap starts to fail."],"forward_implications":["Pilot energy can be reallocated to data: a data-only frame carries the full frame energy in its information symbols, so the effective data SNR is higher than in point-pilot or embedded-pilot frames.","Spectral efficiency becomes full, matching the spread-pilot scheme while removing the separate pilot-removal stage, so receiver complexity is roughly halved relative to spread-pilot reception.","At SNR high enough that detection errors are rare, the bootstrap does not accumulate errors, and an occasional pilot frame every 30 frames is enough to reset the channel estimate.","Channel estimates obtained from data improve with frame size and are essentially independent of constellation size up to 256-QAM, matching the asymptotic form of the cross-ambiguity result."],"supporting_citations":[{"why":"It introduces Zak-OTFS as a delay-Doppler modulation whose channel is predictable, the property the differential scheme exploits.","marker":"[6]"},{"why":"It supplies the DD-domain system model and the construction of the channel matrix from the effective channel estimate, and it documents the point-pilot frame.","marker":"[7]"},{"why":"It defines the spread-pilot frame and the cross-ambiguity as the maximum-likelihood model-free channel estimate, and it serves as the full-spectral-efficiency baseline.","marker":"[9]"},{"why":"It provides the spread-pilot channel estimation used in the comparisons, and in Remark 1 its pilot cross-ambiguity is an exact delta.","marker":"[12]"},{"why":"It gives the time-domain input-output relation from which the cross-ambiguity derivation in Eq. (11) starts.","marker":"[11]"},{"why":"It supplies the inverse discrete Zak transform that maps DD pulsones to time-domain symbols.","marker":"[10]"},{"why":"It provides the turbo receiver baseline against which the proposed data-only-frame receiver is compared.","marker":"[14]"}],"fun_headline_variants":["Zak-OTFS data as pilots ends periodic pilot waste","Differential Zak-OTFS: reuse data, drop pilots, boost efficiency","Data-as-pilot Zak-OTFS achieves full spectral efficiency","Zak-OTFS turns data into pilots for higher energy and lower BER","No more pilot overhead with differential Zak-OTFS scheme"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The scheme assumes that the symbols the receiver detects are close enough to what was sent that re-estimating the channel from them is as good as using pilots; if decision errors or frame-size effects are too large, the estimate degrades and periodic pilot resets become necessary.","fun_headline_variants_meta":{"raw":{"variants":["Zak-OTFS data as pilots ends periodic pilot waste","Differential Zak-OTFS: reuse data, drop pilots, boost efficiency","Data-as-pilot Zak-OTFS achieves full spectral efficiency","Zak-OTFS turns data into pilots for higher energy and lower BER","No more pilot overhead with differential Zak-OTFS scheme"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000178,"raw_usage":{"total_tokens":1321,"prompt_tokens":995,"completion_tokens":326,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":611,"completion_tokens_details":{"reasoning_tokens":235}},"tokens_in":611,"tokens_out":326,"duration_ms":4230,"temperature":1.0,"reasoning_tokens":235,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:44:11.886119+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the instantaneous NMSE of the channel estimate from a data-only frame at a fixed SNR while increasing frame size $MN$; Eq. (16) predicts convergence to the scaled effective channel, so if the NMSE stops improving or stays well above the spread-pilot estimate at large frames, the central claim fails.","supporting_citations":[{"cited_title":"Zak-OTFS with Spread Carrier Waveforms","cited_arxiv_id":"2505.08079","evidence_quote":"It gives the time-domain input-output relation from which the cross-ambiguity derivation in Eq. (11) starts."},{"cited_title":"Discrete Zak transforms , polyphase transforms, and applications,","cited_arxiv_id":null,"evidence_quote":"It supplies the inverse discrete Zak transform that maps DD pulsones to time-domain symbols."},{"cited_title":"Zak-OTFS and Turbo Signal Processing for Joint Sensing and Communication","cited_arxiv_id":"2406.06024","evidence_quote":"It provides the turbo receiver baseline against which the proposed data-only-frame receiver is compared."}],"review_version":1}