{"id":"d9e67f23-a151-4e21-882c-d75a1de46118","arxiv_id":"2412.12590","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A zero-feedback FDD MIMO ISAC precoding framework uses observed Fisher information for error covariance estimation and RSMA with NEPv-based power iteration to maximize spectral efficiency under a beam pattern constraint.","lead":"This paper designs a precoding method for a cellular base station that simultaneously communicates with users and senses the environment, without users sending back channel information. It uses uplink training signals to reconstruct downlink channels and splits messages to manage interference, improving spectral efficiency while shaping the sensing beam.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (63) omits the non-reciprocal DL gain term in Eq. (4), so the ECM understates CSI error for η<1 and the claimed RSMA robustness is not established.","rationale":"The reader's weakest assumption targeted the validity of the observed-Fisher-information ECM and the diagonal approximation. I agree with that area, but the sharpest problem is more specific and more internal: Eq. (63) cannot in principle estimate the β-induced component of e_k because β is absent from the UL likelihood. This is not merely an external validation gap; the paper's own channel model in Eq. (4) and reconstruction rule in Eq. (9) create an error term that the proposed ECM structurally omits. Since the central contribution is to feed Σhat into the RSMA precoder (40)–(43) to mitigate imperfect DL CSI, a biased-low Σhat undermines the claimed SE gains and the sensing–communication trade-off in the simulation section. The fix is concrete and likely straightforward: add the covariance of sqrt(1−η²) Σ_ℓ β_{k,ℓ} u(τ,θ) to Eq. (63), or justify that this term is negligible at the simulated parameters. The paper has genuine strengths: it clearly identifies partial reciprocity as a key assumption, supplies extensive simulations, and provides an explicit limitation discussion in Remark 5. I did not find a more load-bearing objection; the Algorithm 1 ν-update typo and the omitted Q_k derivation are reproducibility issues but secondary to the biased ECM. Conditional acceptance remains the appropriate verdict: the framework is plausible and the gap is identifiable, but the current evidence does not fully support the headline claims as written.","tokens_in":25775,"tokens_out":6860,"duration_ms":65443,"concrete_test":"Run a Monte Carlo experiment with the exact model in Eqs. (1)–(4), (7), (9), (10) at η=0.9 and the Fig. 3 settings (N=8, K=4, M=4, SNR=35 dB). For each drop compute the empirical covariance C_k = (1/T) Σ (h_k−ĥ_k)(h_k−ĥ_k)^H over T independent β and noise realizations, and compare its diagonal and trace with Eq. (63). Then rerun the SE-vs-T_mse comparison in Fig. 3 with η=1.0 (no β term) and with η=0.9, keeping everything else fixed. If the GPI-ISAC-RS gain over GPI-ISAC-noRS is much smaller at η=1.0, or if the empirical trace exceeds the estimated trace by an amount on the order of (1−η²)σ_path², the claimed SE gain rests on the omitted partial-reciprocity error and the paper should be revised to add that term to Σhat.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (4) models the DL path gain as α^dl = η α^ul + sqrt(1−η²)β, with β independent of α^ul. Eq. (9) reconstructs the DL gain as η \\hat{α}^ul. Hence the DL CSI error e_k = h_k − ĥ_k contains an irreducible, statistically independent component sqrt(1−η²) Σ_ℓ β_{k,ℓ} u(τ,θ), whose per-path variance is (1−η²)σ_path². The observed Fisher information in Eq. (58) is built from the UL likelihood function of P_k = {α^ul, τ, θ}; it has no sensitivity to β. The Jacobian transformation in Eq. (61) can only propagate the UL parameter-estimation error into the DL channel; it cannot create or estimate the β component. Therefore Eq. (63) cannot be the arg-min of E[(e_k e_k^H − Σhat)^2] claimed in Eq. (61) unless η=1 or σ_path=0. Since all ISAC simulations set η=0.9, the omitted variance is non-negligible. Moreover, the diagonal assumption in Eq. (63) is inconsistent with the β term: E[β_ℓ β_{ℓ'}^*] is diagonal in paths, but after multiplication by the array response, the antenna-domain covariance has off-diagonal entries (1−η²)σ_path² e^{j2π(n−m)φ_ℓ}. The RSMA precoder in Eqs. (40)–(43) uses Σhat to allocate common/private power and to whiten interference from imperfect CSI; a systematically low-biased Σhat tilts the optimization toward aggressive spatial multiplexing and can inflate the reported SE and the claimed sensing–communication trade-off in Figs. 3–4. The paper's validation of Eq. (63) points to prior work [24, Fig. 1], but the current channel model (4) is more general; the missing β term is not covered by that reference as presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a zero-feedback precoding framework for FDD MIMO-ISAC systems. The downlink channel is reconstructed from uplink training via 2D-NOMP, and an error covariance matrix (ECM) is estimated from the observed Fisher information of the uplink parameter estimates. This ECM is used in an RSMA-based precoder that maximizes a lower bound on the ergodic sum spectral efficiency under a beam-pattern MSE constraint. The precoder is obtained by a generalized power iteration derived from a nonlinear eigenvalue problem with eigenvector dependency (NEPv). The numerical results claim that the method provides precise beam pattern control, high SE, and a favorable sensing-communication trade-off without CSI feedback.","tokens_in":26172,"tokens_out":8271,"duration_ms":71357,"significance":"If the results are correct, the paper offers a meaningful advance: it removes CSI feedback overhead in FDD ISAC, which is a major practical barrier, and it combines RSMA with a Fisher-information-based error covariance estimate in a scalable NEPv framework. The paper gives a self-contained KKT derivation, a complexity analysis, and extensive simulations including detection probability, SCNR extension, and large-antenna regimes. However, the central component—the ECM estimation—has a modeling gap: the estimator in Eq. (63) omits the independent non-reciprocal DL gain component in Eq. (4). Because the RSMA precoder relies on this covariance to allocate power and whiten interference, the reported SE and trade-off improvements are not established for the stated channel model. The validation of the ECM refers to the authors' prior work [24], which does not cover the generalized non-reciprocal gain model.","major_comments":[{"comment":"The estimated ECM in Eq. (63) is biased low because it omits the independent non-reciprocal DL gain component β in Eq. (4). The reconstruction in Eq. (9) sets `\\hat{α}^dl = η \\hat{α}^ul`, but the true DL gain is η α^ul + sqrt(1−η²) β. The observed Fisher information I(\\hat{P}_k) in Eq. (58) is computed from the UL likelihood and has no sensitivity to β, which is independent of α^ul and not observed from UL training. The Jacobian Q_k in Eq. (61) can only propagate the covariance of the UL parameter estimation errors; it cannot account for the variance of β. Consequently, Eq. (63) omits a contribution with per-path variance (1−η²)σ_path². Since the simulations set η=0.9, this is a non-negligible systematic under-estimate. Because the RSMA SINR expressions in Eqs. (40)–(43) and the precoder updates in Eqs. (66)–(73) depend directly on \\Σhat, the SE gains shown in Figs. 3–4 and the claimed sensing–communication trade-off are not reliable for the model in Eq. (4). The validation via [24, Fig. 1] does not cover this generalized model.","section":"Section IV, Eq. (63)"},{"comment":"The diagonal approximation in Eq. (63) is inconsistent with the sparse geometric channel model. Even if the β components are independent across paths, after multiplication by the array response u(τ,θ) the antenna-domain error covariance has off-diagonal entries proportional to (1−η²)σ_path². The justification by reference to a 'rich scattering' environment [34] does not apply to the 2D-NOMP reconstruction error in Eqs. (1)–(10), which is based on a deterministic multipath model. Since the off-diagonal terms enter the RSMA interference terms through \\Σhat in Eqs. (40)–(43), discarding them can systematically misallocate common/private power and distort the reported SE.","section":"Section IV, Eq. (63)"},{"comment":"The Jacobian matrix Q_k(f) is not derived; the paper only states that 'its derivation is straightforward' and refers to [22]. This step is load-bearing because the Jacobian must map the four UL parameters (real/imaginary gain, delay, angle) to the DL channel vector and must incorporate the partial-reciprocity scaling in Eq. (9). Without the explicit expression or a derivation, the reader cannot verify that the inverse observed Fisher information is transformed correctly, and the error propagation argument in Eq. (61) remains incomplete. Please provide the explicit form of Q_k(f) or a detailed derivation.","section":"Section IV, Eq. (61)"},{"comment":"The convergence argument in Eqs. (74)–(81) is a perturbative analysis around a fixed point and assumes \\bar{p}^{(t−1)} is already close to \\bar{p}†. The paper does not provide a global convergence guarantee, and the initialization of \\bar{p}^{(0)} is unspecified. In addition, the outer-loop condition in Algorithm 1 ('while |ν^{(n)}−ν^{(n−1)}|≥ε_ν or n≤n_max') appears to be a typo: with 'or' the loop always runs to n_max, making the first condition irrelevant. Please correct this condition and state precisely what convergence result is claimed.","section":"Section V, Proposition 1 and Algorithm 1"}],"minor_comments":[{"comment":"The algorithm states 'Construct matrix L(\\bar{p}^{(t−1)},ν^{(n)}) with (33); Construct matrix R(...) with (34);' but equations (33) and (34) are the MSE constraint and the norm constraint, not the matrix definitions. The intended references are likely Eqs. (67) and (68). Also, the variable \\zeta_mse is not defined before it is used in the MSE feasibility check.","section":"Algorithm 1"},{"comment":"The symbol η is overloaded: in Eq. (4) it denotes the partial-reciprocity gain coefficient, while in Eq. (44) it is the LogSumExp smoothing parameter. Please rename one of them to avoid confusion.","section":"Notation"},{"comment":"The figure caption orders the subplots as '(a) Achieved MSE and (b) Ergodic sum SE', but the text refers to Fig. 3-(a) as the ergodic sum SE and Fig. 3-(b) as the achieved MSE. The caption and text should be made consistent.","section":"Fig. 3 caption"},{"comment":"In Eq. (10) and the following line, the reconstructed DL channel uses \\hat{\\phi}^{ul}_{k,ℓ,s}, which appears to be a typo: it should be \\hat{\\phi}^{dl}_{k,ℓ,s} or a notation that makes the DL frequency dependence explicit.","section":"Eq. (11)"},{"comment":"The values of the LogSumExp smoothing parameter η and the bisection bounds (ν_min, ν_max) are not reported. Since these are user-specified free parameters, please provide their values and, ideally, a brief sensitivity study.","section":"Simulation setup"},{"comment":"The complexity analysis refers to a matrix \\Omega(\\bar{p}) that is never defined. The statement should refer to the matrix inverted in the algorithm, presumably R(\\bar{p},ν) or the matrix K(\\bar{p},ν).","section":"Remark 6"}],"recommendation":"major_revision","confidential_remarks":"The central concern is the ECM bias: if the authors can modify the estimator to include the β contribution and re-run the simulations, the framework may be salvageable. Please note that the validation of the key ECM component is by reference to the authors' prior work [24], and the NEPv-GPI method is also from the same group; independent verification would strengthen the paper. The manuscript does not include a code release, which makes the numerical claims harder to reproduce."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a genuine integration: zero-feedback FDD DL reconstruction, observed-Fisher-information ECM, RSMA, and NEPv-based precoding for ISAC. That combination is new, and the optimization machinery is competently put together. Second, the ECM estimate that the whole RSMA robustness argument leans on has a gap. With the non-reciprocal gain model in Eq. (4), the DL reconstruction error contains an independent beta component that the UL observed Fisher information cannot see. Equation (63) therefore understates the true CSI error for eta < 1, and every simulation uses eta = 0.9. This is not a corner case.\n\nWhat the paper does well: the system model is clearly laid out, the SE lower bounds are standard and correctly derived, and the KKT conditions leading to the NEPv form are worked through in detail. The sensing beam-pattern MSE is neatly expressed as a quadratic form in the vectorized precoder, and the complexity comparison against SDR is fair. The experiments are broad, covering beam patterns, SE vs. target MSE, SNR behavior, detection probability, SCNR, and large-scale antennas. The authors also include honest remarks about partial reciprocity assumptions and where the method degrades.\n\nThe soft spots are real but not all equal. The Jacobian Q_k is never derived, the diagonal covariance assumption is strong, and the key validation of Eq. (63) points to the authors' own prior figure, which does not cover the more general channel model used here. The algorithm pseudocode also has an unclear Lagrange multiplier update and leaves the bisection bounds unspecified. These are fixable. The omitted beta term is the load-bearing one: unless the ECM is corrected or the channel model restricted to etas close to 1, the reported SE gains and trade-off curves in Figs. 3-4 are likely optimistic.\n\nWho gets value: readers working on low-overhead FDD systems or ISAC precoding will find the framework and the optimization approach useful, even if the numerical claims need revisiting. It deserves a serious referee, but the referee should push hard on the ECM derivation and ask for either a correction that includes the beta variance or a narrowed claim about when the estimate is valid. I would not cite it in its current form, but I would watch a revised version.","headline":"Solid integration of zero-feedback FDD channel reconstruction with RSMA and NEPv for ISAC, but the error covariance estimate omits the non-reciprocal DL gain term and may overstate the claimed robustness.","tokens_in":26776,"tokens_out":1873,"would_cite":false,"duration_ms":19072,"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":"FDD MIMO-ISAC precoding can run with zero downlink CSI feedback: reconstruct each user's channel from uplink training, estimate the reconstruction error's covariance from the uplink signal, and let RSMA manage the resulting interference.","keywords":["integrated sensing and communication (ISAC)","frequency division duplex (FDD)","zero-feedback CSI acquisition","partial channel reciprocity","error covariance estimation","observed Fisher information","rate-splitting multiple access (RSMA)","nonlinear eigenvalue problem (NEPv)"],"falsifier":"Take a measured FDD channel with strong spatial correlation and a larger UL-DL frequency gap, reconstruct the downlink channel with 2D-NOMP, and compare the true per-antenna error covariance against the diagonal $\\hat{\\boldsymbol{\\Sigma}}_k$ from Eq. (63); if off-diagonal entries are non-negligible or the trace systematically misses the realized MSE, the RSMA precoder will misallocate power and the claimed SE gains should shrink in the corresponding simulations.","tokens_in":25558,"feed_emoji":"📡","tokens_out":9994,"duration_ms":79548,"temperature":0.7,"pith_summary":"This paper claims that an FDD MIMO base station can run integrated sensing and communication without any downlink CSI feedback. The idea is to reconstruct each user's downlink channel from uplink training signals using partial reciprocity, estimate the covariance of the reconstruction error from observed Fisher information, and then design an RSMA precoder that maximizes ergodic sum spectral efficiency while keeping the sensing beam pattern within a target mean-squared error. If the error-covariance estimate is accurate, the scheme removes feedback latency and overhead while still managing the interference that imperfect CSI and radar symbols create. The payoff is a practical low-latency route to joint communication and sensing in FDD bands, a regime where feedback cost usually dominates.","feed_headline":"Zero-feedback FDD ISAC precoder beats state-of-the-art baselines","feed_subtitle":"Reconstructed downlink channels plus an estimated error covariance let RSMA keep spectral efficiency while shaping the sensing beam.","key_machinery":"The load-bearing object is the estimated error covariance matrix $\\hat{\\boldsymbol{\\Sigma}}_k$, obtained as the diagonal of $Q_k^H(f)\\,I^{-1}(\\hat{P}_k)\\,Q_k(f)$, where $I(\\hat{P}_k)$ is the observed Fisher information of the uplink channel parameters and $Q_k(f)$ is the Jacobian mapping uplink parameter errors to downlink channel errors. This matrix converts unknown CSI imperfection into a concrete quadratic penalty inside each user's SINR, making the imperfect-CSI precoding problem tractable. Two further mechanisms carry the optimization: rate-splitting multiple access (RSMA), whose common stream is decoded by every user and helps mitigate the interference caused by imperfect CSI and radar symbols, and the nonlinear-eigenvalue reformulation, which turns the KKT stationarity condition $L(\\bar{p},\\nu)\\bar{p} = \\zeta(\\bar{p},\\nu) R(\\bar{p},\\nu)\\bar{p}$ into a fixed-point iteration for the leading eigenvector of $R^{-1}L$. The Lagrange multiplier $\\nu$ acts as a dial between communication and sensing: small $\\nu$ favors sum SE, large $\\nu$ enforces the beam-pattern MSE constraint.","core_discovery":"The central claim is that missing downlink channel error statistics—normally unavailable without feedback—can be synthesized from uplink observations alone. Because the 2D-NOMP uplink parameter estimator operates near the Cramér-Rao bound, the paper evaluates the negative Hessian of the uplink log-likelihood at the estimated parameters (the observed Fisher information), maps its inverse through the Jacobian to the downlink channel, and uses only its diagonal as the error covariance matrix $\\hat{\\boldsymbol{\\Sigma}}_k$. Feeding this covariance into the SINR expressions turns the RSMA precoding problem into a nonlinear eigenvalue problem with eigenvector dependency; the proposed generalized power iteration updates the precoder and the Lagrange multiplier alternately, with the multiplier controlling how strictly the beam-pattern MSE constraint is enforced. The paper reports that this zero-feedback design achieves higher ergodic sum SE than the ISAC baselines across target MSE levels and SNRs, while matching or improving the achieved sensing beam-pattern MSE and sidelobe suppression.","pith_inferences":["If the observed-Fisher-information estimate proves as faithful in hardware as in simulation, the same recipe could attach to any uplink estimator that operates near its Cramér-Rao bound, making it a general zero-feedback ISAC design pattern rather than a 2D-NOMP-specific fix.","The diagonal-only covariance assumption is the most fragile piece: in spatially correlated channels, off-diagonal error terms could leak through the SINR bounds, and an extension to full covariance or a diagonal inflation factor would be a natural fix.","The stated partial-reciprocity condition is tied to moderate UL-DL frequency separation; sweeping the frequency gap and locating where the SE advantage over feedback-based baselines disappears would map the method's operational range.","A hybrid design could add a low-rate feedback link that only corrects the common-stream rate allocation, using the error-covariance estimate to decide when such correction is needed."],"forward_implications":["Downlink CSI feedback can be dropped entirely in FDD MIMO-ISAC, removing the multi-millisecond feedback loop and the overhead that scales with antenna and user count.","The sensing beam pattern remains controllable to a prescribed MSE even though the precoder is built from reconstructed, imperfect CSI, and users see less sensing-induced interference than with the SDMA or SDR baselines.","The same optimization machinery extends to other sensing metrics: the paper formulates an SCNR-constrained variant and shows the beam pattern steers toward targets and away from clutter.","Precoder updates are a generalized power iteration, so per-iteration complexity scales as $O(N^3(K+M))$ rather than the semidefinite-programming cost of earlier ISAC designs.","The relative SE advantage narrows as the number of antennas grows because channel vectors become more orthogonal, but the zero-feedback RSMA design still outperforms the GPI-ISAC baseline at 128 antennas."],"supporting_citations":[{"why":"Establishes the partial-reciprocity model (shared delay, angle, and path number) that lets the downlink channel be reconstructed from uplink signals.","marker":"[19]"},{"why":"Provides the 2D-NOMP uplink parameter estimator whose near-Cramér-Rao-bound MSE justifies replacing the true error covariance with the observed Fisher information inverse.","marker":"[21]"},{"why":"Describes the Newtonized orthogonal matching pursuit algorithm used for the gridless 2D-NOMP parameter extraction.","marker":"[23]"},{"why":"Prior zero-feedback FDD RSMA work showing that the estimated error covariance matches the actual MSE; the paper's covariance validation and RSMA framing build directly on it.","marker":"[24]"},{"why":"Analyzes channel extrapolation in FDD massive MIMO and supplies the CRLB-based error characterization used for the downlink reconstruction error.","marker":"[22]"},{"why":"Supplies the statistical result that the inverse observed Fisher information optimally estimates realized squared error, the theoretical basis for using it as the error covariance.","marker":"[37]"},{"why":"Introduces the generalized power iteration and nonlinear-eigenvalue approach for RSMA precoding that the proposed solver adapts.","marker":"[25]"},{"why":"Supplies the GPI-ISAC beamforming baseline and the joint beamforming framework this paper extends with RSMA and zero feedback.","marker":"[2]"},{"why":"Establishes rate-splitting multiple access for joint radar and communications, the interference-mitigation rationale for splitting messages in ISAC.","marker":"[4]"}],"fun_headline_variants":["No-feedback FDD ISAC precoder lifts spectral efficiency","Uplink-only CSI reconstructs downlink, no feedback needed","Fisher information turns uplink into downlink CSI for FDD","Zero-feedback FDD ISAC: RSMA precoder beats baselines"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole scheme rests on the assumption that the base station can accurately guess how wrong its downlink channel reconstruction is—and that the guess needs no off-diagonal terms—using only the uplink training signal.","fun_headline_variants_meta":{"raw":{"variants":["No-feedback FDD ISAC precoder lifts spectral efficiency","Uplink-only CSI reconstructs downlink, no feedback needed","Fisher information turns uplink into downlink CSI for FDD","Zero-feedback FDD ISAC: RSMA precoder beats baselines"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000719,"raw_usage":{"total_tokens":3231,"prompt_tokens":948,"completion_tokens":2283,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":564,"completion_tokens_details":{"reasoning_tokens":2208}},"tokens_in":564,"tokens_out":2283,"duration_ms":15198,"temperature":1.0,"reasoning_tokens":2208,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:57:29.309251+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a measured FDD channel with strong spatial correlation and a larger UL-DL frequency gap, reconstruct the downlink channel with 2D-NOMP, and compare the true per-antenna error covariance against the diagonal $\\hat{\\boldsymbol{\\Sigma}}_k$ from Eq. (63); if off-diagonal entries are non-negligible or the trace systematically misses the realized MSE, the RSMA precoder will misallocate power and the claimed SE gains should shrink in the corresponding simulations.","supporting_citations":[{"cited_title":"Eliminating channel feedback in next-generation cellular networks,","cited_arxiv_id":null,"evidence_quote":"Establishes the partial-reciprocity model (shared delay, angle, and path number) that lets the downlink channel be reconstructed from uplink signals."},{"cited_title":"Efficient downlink channel reconstruction for FDD multi-antenna systems,","cited_arxiv_id":null,"evidence_quote":"Provides the 2D-NOMP uplink parameter estimator whose near-Cramér-Rao-bound MSE justifies replacing the true error covariance with the observed Fisher information inverse."},{"cited_title":"Splitting messages in the dark- rate-splitting multiple access for FDD massive MIMO without CSI feedback,","cited_arxiv_id":null,"evidence_quote":"Prior zero-feedback FDD RSMA work showing that the estimated error covariance matches the actual MSE; the paper's covariance validation and RSMA framing build directly on it."},{"cited_title":"Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information,","cited_arxiv_id":null,"evidence_quote":"Supplies the statistical result that the inverse observed Fisher information optimally estimates realized squared error, the theoretical basis for using it as the error covariance."},{"cited_title":"Rate-splitting multiple access for downlink MIMO: A generalized power iteration approach,","cited_arxiv_id":null,"evidence_quote":"Introduces the generalized power iteration and nonlinear-eigenvalue approach for RSMA precoding that the proposed solver adapts."}],"review_version":1}