{"id":"0e69f658-3a69-4a13-8f1f-bdfa293391b9","arxiv_id":"2506.03438","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A block coordinate descent hybrid precoding algorithm with a satellite interference penalty cuts LEO satellite interference-to-noise by 22.4 dB while keeping multiuser sum-rate within about 3% of existing hybrid solutions.","lead":"This paper proposes a beamforming algorithm for hybrid MIMO base stations that reduces interference to LEO satellites while serving downlink users. In simulations, it meets satellite protection thresholds far more often than baseline methods while keeping user data rates almost unchanged.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equations (11)–(12) appear to be gradients of the sum-rate term, not of the cost C in (9); as printed, Algorithm 1 would drive UE rate down, so the reported INR/rate results cannot be reproduced from the manuscript.","rationale":"Read in good faith, the central claim is that the proposed hybrid precoder simultaneously nulls LEO interference and preserves multiuser rate. For that claim to hold, Algorithm 1 must be a valid descent method for the cost C in (9). The manuscript's own equations fail that test: (10e)-(12) contain a wrong index and reversed signs for the rate term. This is more load-bearing than the LOS channel assumption, because it breaks the algorithm even under the paper's idealized channel model. The reader's weakest assumption (Sec. II-A, Eq. 2) is a real modeling limitation, but it affects the realism of the results; the gradient inconsistency affects whether the proposed algorithm as described can produce the reported numbers at all. I therefore recommend REJECT in the current form, contingent on the finite-difference check. If the check instead shows that the printed equations are valid under the authors' gradient convention, the concern does not land and the reader's CONDITIONAL verdict would remain appropriate.","tokens_in":8723,"tokens_out":15568,"duration_ms":175934,"concrete_test":"Run a finite-difference check of (9) at a random small instance (e.g., N_T=4, N_RF=2, U=1, N=1): numerically compute ∂C/∂Re(FBB) and ∂C/∂Im(FBB) (and analogously for FRF) and compare the descent direction with (11)-(12). If the projected update increases C, or if the log-term signs are opposite and N_{u,j} should read M_u FRF FBB e_j (FBB e_j)^H, the concern lands; then the paper should be revised with a full derivation (or code) before its claims are accepted.","verdict_should_be":"REJECT","load_bearing_attack":"Sec. IV-B defines C(FRF,FBB) = -Σ log(1+SINR_u)+λ||HSat FRF FBB||_F^2 and Algorithm 1 minimizes C by subtracting the printed gradients (11)-(12). For the log term, the correct gradient of -R_u (writing b_j=FBB e_j and G_j=H_u^H w_u w_u^H H_u FRF b_j b_j^H) is -G_u/(den_u+num_u)+Σ_{j≠u} num_u/(den_u(den_u+num_u)) G_j (up to a factor absorbed in the step size and the Hermitian adjoint term). Equation (11) has the opposite signs, and its auxiliary N_{u,j} in (10e) uses e_u instead of e_j, so the interference-part gradient is not the derivative of any term in (9). For U=1 and λ=0, the printed update FBB←FBB-α∇FBB C moves the digital precoder in the direction that reduces |H_u FRF FBB|^2, i.e., it lowers rate instead of raising it. Thus Algorithm 1 as documented cannot produce the 2.69%-rate-loss, 22.4 dB-INR-reduction results in Figs. 2-5 unless the implemented code uses a different (corrected) gradient. Because the derivation is omitted and no code is provided, the central claim currently rests on an unverifiable, internally inconsistent description.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper addresses spectrum coexistence between a terrestrial base station (BS) with a hybrid MIMO architecture and LEO satellite uplinks in the upper mid-band. The authors propose a block coordinate descent (BCD) algorithm with projected gradient descent that alternately updates the analog and digital precoders to maximize UE sum-rate while penalizing the beamforming gain toward known satellite directions. The cost function in (9) combines the negative sum-rate and a satellite interference penalty weighted by λ_sat. Simulations using Wireless InSite channels claim that the proposed method reduces the mean satellite INR by 22.4 dB compared to the DFT-Codebook + BD baseline and stays within 2.69% of the HF baseline sum-rate, while violating the -20 dB INR protection threshold in only 0.05% of trials.","tokens_in":9041,"tokens_out":5011,"duration_ms":49650,"significance":"The problem of enabling terrestrial-satellite coexistence in FR3 is timely and relevant, and the proposed approach is a natural extension of existing hybrid precoding techniques with a satellite interference penalty. If the algorithm performs as claimed, the paper would offer a useful engineering contribution. However, the central technical content currently rests on the closed-form gradients in (11) and (12), which are stated without derivation and appear to be incorrect. Because the derivation is omitted and no code is provided, the reported numerical results are not reproducible from the manuscript as written. The simulation methodology itself is standard (Wireless InSite channels, CDF comparisons, multiple baselines), and the authors are explicit about the hand-tuned parameters, which is a strength in transparency but also a limitation in generality.","major_comments":[{"comment":"The closed-form gradients (11) and (12) are not gradients of the cost function C in (9), as printed. For the rate term, the gradient of -log(1+SINR_u) has a negative coefficient on the desired-signal derivative and a positive coefficient on the inter-user interference derivative; equations (11) and (12) have the opposite signs. In addition, the auxiliary variable N_{u,j} in (10e) is defined with e_u instead of e_j, so the interference-part term in (11) is not the derivative of any component of (9). Concretely, for U=1 and λ_sat=0, Algorithm 1 updates F_BB in the direction that reduces the received signal power, lowering the UE rate rather than maximizing it. Therefore the results in Figs. 2-5 cannot be reproduced from the manuscript as written. The authors must correct the gradients, supply the full derivation, and ideally provide the code or a reproducible description of the implemented update.","section":"Sec. IV-B, Eqs. (10)-(12) and Algorithm 1"},{"comment":"The statement \"Because of a lack of space, we omit the derivation here\" is not acceptable for the paper's central algorithmic contribution. The correctness of (11) and (12) is load-bearing: Algorithm 1 explicitly relies on these expressions, and the simulation results depend on their validity. The derivation should be included in the manuscript or in a supplementary document, with the chain rule for complex Wirtinger derivatives spelled out.","section":"Sec. IV-B, after Eq. (9)"},{"comment":"The performance improvement is reported for specific hand-tuned values of the penalty parameter λ_sat (5, 7, 9) and a fixed step size α=10^-4, with no sensitivity analysis. Since the INR reduction is a direct consequence of minimizing the penalty term in (9), the reported 22.4 dB improvement is not an independent prediction but a property of the chosen objective. The authors should report how the results vary with λ_sat and α, and justify the selection mechanism, or the claims should be tempered to reflect the dependence on these free parameters.","section":"Sec. V-C and Figs. 4-5"},{"comment":"The BS-to-satellite channel is modeled as a single line-of-sight steering vector determined solely by the satellite position, ignoring multipath, satellite antenna pattern/orientation, atmospheric effects beyond a pathloss factor, and ephemeris errors. The authors should discuss the robustness of the nulling performance to deviations from this idealized model, since a mismatch between the assumed steering vector and the actual channel could substantially weaken the interference suppression. At minimum, a sensitivity analysis with angle errors or a discussion of the LOS-only assumption's scope would substantiate the practical claims.","section":"Sec. II-A, Eq. (2)"}],"minor_comments":[{"comment":"The abstract and introduction state that the algorithm \"optimizes the precoding within the set of precoders that null the interference to the satellite,\" but the actual formulation in (9) is a penalty-based method that does not guarantee exact nulling. The wording should be aligned with the mathematical formulation.","section":"Abstract and Sec. I"},{"comment":"The steering vector notation a_T(θ,φ) is used for the URA but the angle convention (azimuth and elevation) is only loosely described. Please define the array response explicitly, including the element spacing and the meaning of θ and φ.","section":"Sec. II-A, Eq. (2)"},{"comment":"The text states that the LEO satellite orbits at an altitude of 100 km, which is unrealistically low for a LEO satellite (typical altitudes are 400-1200 km). This is likely a typo and should be corrected, as it materially affects the channel model and pathloss.","section":"Sec. V-B"},{"comment":"The curves for \"Proposed w/o nulling\" and \"HF w/o nulling\" are described but are difficult to distinguish in the figures due to similar line styles. Please use more distinct markers or colors, and add a legend entry for each baseline in every subplot.","section":"Fig. 2 and Fig. 3"},{"comment":"The update F_RF ← exp(j ∠(F_RF - α∇_{F_RF} C)) is a standard unit-modulus projection, but for complex matrices the notation should be clarified: the exponential and angle are applied entry-wise. Please state this explicitly.","section":"Algorithm 1, line 12"},{"comment":"The claim that the proposed method \"contributes to reducing harmful interference\" is based on a single ITU-style protection threshold of -20 dB INR. The manuscript should clarify whether this threshold is frequency-dependent and whether the conclusions are sensitive to the chosen threshold.","section":"Sec. V-C"}],"recommendation":"major_revision","confidential_remarks":"The gradient error in Sec. IV-B is serious and undermines the reproducibility of the central simulation results. I would encourage the editor to request the authors to provide a corrected derivation, the complete gradient expressions, and possibly the simulation code as supplementary material. Even with corrections, the technical novelty is incremental over existing hybrid precoding with penalty-based objectives, so the revision should also strengthen the discussion of the method's practical advantages and limitations. The paper's length constraints may need to be revisited to accommodate the omitted derivation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper tackles a real problem: letting terrestrial base stations in FR3 coexist with LEO satellites by designing hybrid precoders that null interference to the satellite. That is worth reading. The system model is standard, the simulation setup uses Wireless InSite urban channels, and the authors compare against four baselines including fully digital and hybrid nulling schemes. On the surface, the reported INR improvement (22.4 dB mean reduction, 0.05% threshold violation vs 7.7% for DFT+BD) is striking, and the sum-rate loss is small.\n\nBut there is a load-bearing problem in the algorithm description. Equations (11)-(12) claim to be gradients of the cost function C in (9), but they have the wrong sign for the sum-rate term. For U=1 and λ=0, the printed update FBB ← FBB - α∇FBB C moves the digital precoder in the direction that reduces |w*H F b|^2, i.e., it decreases the UE rate rather than increasing it. The auxiliary variable N_{u,j} in (10e) also uses e_u instead of e_j, so it does not correspond to any term in the cost. The authors omit the derivation \"because of a lack of space\" and provide no code. So as printed, Algorithm 1 cannot produce the claimed rate/INR results. Either the equations are typesetting errors and the implementation used correct gradients, or the implementation has the same sign error; we have no way to verify.\n\nThis is a major issue, not a minor one, because the central empirical claim rests on an unverifiable and internally inconsistent description. The omission of the derivation and code would be problematic even if the signs were right, since the step size and penalty parameter are hand-tuned.\n\nWhat is genuinely new: the specific problem formulation (penalty-based hybrid precoding for satellite nulling) and the BCD/PGD approach seem not to appear in prior work, and the comparison against multiple hybrid baselines is fair.\n\nIf the gradient equations can be corrected and verified (ideally with code or a complete derivation), this could be a useful contribution. As it stands, I would not trust the results. The paper deserves a serious referee, but only with the expectation of heavy revision—the authors need to fix the math, include a derivation, and share the implementation.\n\nFor a reading group, it is a good example of why printed gradient expressions need checking. For citing, I'd hold off until a corrected version appears.\n\nRecommendation: send it to peer review, but the reviewers should be instructed to verify the gradients and require code or a full derivation.","headline":"Relevant coexistence problem and a plausible BCD/PGD approach, but the printed gradient expressions have the wrong sign for the sum-rate term, so the reported results cannot be reproduced from the manuscript.","tokens_in":9546,"tokens_out":7668,"would_cite":false,"duration_ms":78290,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Hybrid precoding nulls LEO satellite interference while keeping sum-rate close to baselines.","keywords":["hybrid precoding","LEO satellite coexistence","spectrum sharing","interference nulling","projected gradient descent","block coordinate descent","upper mid-band FR3","multiuser MIMO"],"falsifier":"Run the same algorithm in a scenario where the satellite channel includes a strong multipath component or a small angle error, and measure the fraction of trials in which the satellite interference-to-noise ratio exceeds -20 dB; if that fraction rises well above 0.05%, the nulling claim fails.","tokens_in":8525,"feed_emoji":"📡","tokens_out":2082,"duration_ms":24207,"temperature":0.7,"pith_summary":"This paper proposes a beamforming algorithm for hybrid MIMO base stations that suppresses interference to LEO satellites in shared spectrum while preserving downlink sum-rate. The algorithm alternates between analog and digital precoder updates using block coordinate descent with projected gradient steps, guided by a cost function that penalizes satellite interference. Simulations show it reduces mean satellite interference-to-noise ratio by 22.4 dB versus the best hybrid baseline and meets the -20 dB protection threshold in 99.95% of trials, with only a 2.69% rate loss. The significance is a practical path to spectrum coexistence in the upper mid-band without exclusion zones or full digital arrays.","feed_headline":"Hybrid precoding cuts LEO satellite interference 22.4 dB","feed_subtitle":"BCD with projected gradients keeps sum-rate within 3% of baselines while meeting the -20 dB INR threshold in 99.95% of trials.","key_machinery":"The central mechanism is a block coordinate descent (BCD) algorithm with projected gradient descent (PGD) applied alternately to the analog precoder $\\mathbf{F}_{\\mathrm{RF}}$ and the digital precoder $\\mathbf{F}_{\\mathrm{BB}}$. The cost function is $C(\\mathbf{F}_{\\mathrm{RF}}, \\mathbf{F}_{\\mathrm{BB}}) = -\\sum_u \\log(1+\\mathrm{SINR}_u) + \\lambda_{\\mathrm{Sat}} \\operatorname{tr}(\\mathbf{F}_{\\mathrm{BB}}^* \\mathbf{F}_{\\mathrm{RF}}^* \\mathbf{H}_{\\mathrm{Sat}}^* \\mathbf{H}_{\\mathrm{Sat}} \\mathbf{F}_{\\mathrm{RF}} \\mathbf{F}_{\\mathrm{BB}})$, whose closed-form gradients with respect to both precoders are derived. Each update projects the analog entries onto the unit-modulus circle and normalizes the digital precoder to the power constraint, allowing the algorithm to null satellite directions while maximizing user rates.","core_discovery":"The paper establishes that a hybrid MIMO precoder can simultaneously maintain near-baseline multiuser sum-rate and dramatically suppress interference to LEO satellites by optimizing a penalty-based objective. The key result is a block coordinate descent algorithm with projected gradient descent that alternates between the analog and digital precoders, using closed-form gradients of a cost function that includes both negative sum-rate and a satellite interference penalty weighted by a tunable parameter. Across simulated urban scenarios with two satellites and two UEs, the proposed method achieves satellite interference-to-noise ratios far below the -20 dB protection threshold in 99.95% of trials, outperforming both DFT-codebook and hybrid factorization baselines while staying within 2.69% of the best hybrid sum-rate.","pith_inferences":["If the satellite channel departs from the single-line-of-sight steering vector assumption, the nulling may degrade; tracking the satellite's angle and adding robustness to channel uncertainty would likely preserve the protection guarantee.","The same penalty-based BCD framework could be adapted to protect other incumbent receivers, such as fixed satellite service earth stations or radio astronomy sites, by replacing the satellite channel matrix with the corresponding interference channel.","A testable extension is to combine the proposed precoder with dynamic $\\lambda_{\\mathrm{Sat}}$ scheduling based on satellite ephemeris updates, potentially improving sum-rate during satellite passes while still satisfying the protection criterion."],"forward_implications":["Base stations in the upper mid-band can share spectrum with LEO satellites without relying on exclusion zones or coordination overhead.","Hybrid MIMO architectures, which are practical at FR3 frequencies, can provide satellite protection comparable to fully digital nulling at a fraction of the hardware cost.","The penalty parameter $\\lambda_{\\mathrm{Sat}}$ gives operators a tunable trade-off between satellite interference and terrestrial sum-rate, enabling dynamic coexistence policies.","The algorithm's fixed-step projected gradient design keeps computational complexity low enough for real-time precoder updates as satellites move.","The approach can be extended to arbitrary numbers of satellites and users, as demonstrated with two satellites and two UEs, while maintaining the protection threshold."],"supporting_citations":[{"why":"Establishes the line-of-sight channel model for the BS-to-satellite link and motivates interference nulling for terrestrial-satellite coexistence.","marker":"[7]"},{"why":"Provides the projected gradient descent method and block coordinate descent framework used in the proposed algorithm.","marker":"[10]"},{"why":"Shows prior use of penalty-method objective functions in hybrid precoding designs, which the paper adapts for satellite interference.","marker":"[12]"},{"why":"Supplies the block diagonalization technique used in the fully digital and hybrid baseline precoders.","marker":"[17]"},{"why":"Defines the -20 dB interference protection criterion that the paper uses to evaluate harmful interference probability.","marker":"[19]"},{"why":"Motivates the hybrid MIMO architecture as a practical base station configuration in the upper mid-band.","marker":"[8]"}],"fun_headline_variants":["Hybrid precoder cuts LEO satellite interference by 22.4 dB","Beamforming nulls satellite interference, keeps sum-rate within 3%","MIMO precoding shields LEO satellites, meets -20 dB in 99.95% trials"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes the base station-to-satellite channel is a single line-of-sight steering vector determined only by the satellite's known position, ignoring multipath, satellite antenna pattern, and ephemeris errors.","fun_headline_variants_meta":{"raw":{"variants":["Hybrid precoder cuts LEO satellite interference by 22.4 dB","Beamforming nulls satellite interference, keeps sum-rate within 3%","MIMO precoding shields LEO satellites, meets -20 dB in 99.95% trials"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000321,"raw_usage":{"total_tokens":1760,"prompt_tokens":848,"completion_tokens":912,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":464,"completion_tokens_details":{"reasoning_tokens":842}},"tokens_in":464,"tokens_out":912,"duration_ms":10234,"temperature":1.0,"reasoning_tokens":842,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:02:55.251568+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same algorithm in a scenario where the satellite channel includes a strong multipath component or a small angle error, and measure the fraction of trials in which the satellite interference-to-noise ratio exceeds -20 dB; if that fraction rises well above 0.05%, the nulling claim fails.","supporting_citations":[{"cited_title":"Terres trial-satellite spectrum sharing in the upper mid-band with interference nu lling,","cited_arxiv_id":null,"evidence_quote":"Establishes the line-of-sight channel model for the BS-to-satellite link and motivates interference nulling for terrestrial-satellite coexistence."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the projected gradient descent method and block coordinate descent framework used in the proposed algorithm."},{"cited_title":"Digital and Hybrid Precoding Designs in Massive MIMO with Low-Resolution ADCs","cited_arxiv_id":"2409.17638","evidence_quote":"Shows prior use of penalty-method objective functions in hybrid precoding designs, which the paper adapts for satellite interference."},{"cited_title":"Zero-forc ing methods for downlink spatial multiplexing in multiuser mimo channe ls,","cited_arxiv_id":null,"evidence_quote":"Supplies the block diagonalization technique used in the fully digital and hybrid baseline precoders."},{"cited_title":"Interference protection criteria phase 1-co mpilation from existing sources,","cited_arxiv_id":null,"evidence_quote":"Defines the -20 dB interference protection criterion that the paper uses to evaluate harmful interference probability."},{"cited_title":"Hybrid digital and analog beamform ing design for large-scale antenna arrays,","cited_arxiv_id":null,"evidence_quote":"Motivates the hybrid MIMO architecture as a practical base station configuration in the upper mid-band."}],"review_version":1}