{"id":"539a9172-3962-4564-ba3f-963ce2e7721f","arxiv_id":"2506.02760","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Repetition-based joint transmission of SSBs with orthogonal phase patterns improves initial access coverage by combining power from multiple base stations without channel state information.","lead":"This paper tests whether several base stations can send the same 5G synchronization signal together, using pre-set phase patterns, so that phones anywhere in the area get a stronger signal during initial connection. In simulations with four base stations and line-of-sight links, the scheme gave up to 6 dB more signal-to-noise than each station transmitting on its own, using the same total resources.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proof of consistent JT gain compares a single joint beam to an independent baseline using the same closest-BS beam, not the best joint beam against the best independent beam; the greedy selection does not guarantee the needed beam coverage.","rationale":"I reviewed the analytical core and the greedy selection. The Hadamard phase construction is correct: with orthogonal phase rows, the combined SNR in Eq. (10) equals B/N0 times the sum of per-BS received powers, independent of channel phases, so the transmit-diversity mechanism is sound. The resource accounting is also fair: both schemes use B × N_Ind total SSB transmissions when N_Joint = N_Ind. The load-bearing gap is in the transition from Eq. (12) to the universal conclusion. Equation (12) is a per-pair comparison: for a fixed joint beam tuple, it compares JT with the independent case using the same f_k from the closest BS. Real independent transmission, however, transmits all N_Ind beams and the UE takes the best one, so the true baseline is γ_Ind = B ρ_k/N0 max_f |h_k^H f|^2. Since the greedy selection in Eq. (15) maximizes coverage without any constraint that every independent beam of the closest BS appears in some selected joint tuple, the max-to-max inequality is not guaranteed. This is the same concern the reader identified, and I agree it is the weakest assumption. A counterexample search is the direct way to settle whether the claim fails or merely lacks proof. Therefore the verdict remains CONDITIONAL: qualify the claim or prove the missing beam-coverage condition.","tokens_in":9336,"tokens_out":11775,"duration_ms":117437,"concrete_test":"Run a counterexample search: for B=2 or B=3 BSs with small DFT codebooks (N_Ind=2 or 3) over a dense UE grid, implement the greedy selection (15) and compute, at each UE, the max JT SNR (maximum over selected joint beams of B/N0 Σ_b |√ρ_b h_b^H f_b|^2) and the max independent SNR (B/N0 max_f |√ρ_k h_k^H f|^2 from the closest BS k). If any UE has independent SNR exceeding the JT SNR, the 'consistently outperforms' claim is false as stated. Also record whether the selected joint beam set covers every codebook index of every BS; absence of coverage combined with any violation would confirm the proof gap.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (12) is derived under the explicit assumption that the closest BS uses the same beamformer f_k in both the JT and the independent scheme. But the actual independent baseline transmits all N_Ind codebook beams (each repeated B times) and the UE selects the best one, so its SNR is γ_Ind = B ρ_k/N0 max_f |h_k^H f|^2, not the same-f_k expression in (11). The greedy selection in (15) chooses N_Ind joint beam tuples to maximize coverage but does not guarantee that, for every UE location, the selected set contains a tuple whose k-th component equals the UE's optimal independent beam from the closest BS. If that beam is absent, the best joint SNR can be lower than the best independent SNR, and Δγ in (12) can be negative; the nonnegativity in (12) only holds for the per-pair comparison with a matched beam, not for the max-to-max comparison that the 'consistently outperforms' conclusion requires. Thus the central claim is not established by the equations unless the greedy selection is shown to cover every independent beam of the closest BS for every location, a condition that is neither stated nor proven.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a joint transmission (JT) scheme for synchronization signal blocks (SSBs) during initial access. Multiple base stations (BSs) transmit the same SSB using a fixed set of complementary (Hadamard-like) phase patterns, and the UE coherently combines the repeated receptions, so that the combined SNR becomes a coherent sum of per-BS power terms even without transmitter CSI. To limit overhead, a greedy algorithm selects N_Joint = N_Ind joint beam tuples from the full (N_Ind)^B set. The authors claim that under equal resource budgets JT of SSBs consistently outperforms independent SSB transmission, with simulation results showing up to 6 dB SNR gain for a 4-BS, 4-antenna line-of-sight deployment.","tokens_in":9584,"tokens_out":4284,"duration_ms":46975,"significance":"If the central claim is established, the work is a useful and novel contribution: it offers a CSI-free way to obtain constructive multi-BS gain during initial access, and it quantifies a coverage improvement over standard independent SSB sweeping. The analytical step from Eq. (9) to Eq. (10) is correct, and the proposal is not fitted to simulation data; the Hadamard phase design is a constructive, transparent mechanism. The main significance hinges on whether the claimed 'consistent outperformance under equal resources' is actually proven, which is where the manuscript currently falls short.","major_comments":[{"comment":"The comparison that supports the 'consistently outperforms' claim is not the comparison actually made by the UE. The independent baseline in Eq. (11) uses the same beamformer f_k as the JT scheme, but an independent UE selects the best of all N_Ind codebook beams from its closest BS, so its SNR is proportional to max_f |h_k^H f|^2, not to |h_k^H f_k|^2 for an arbitrary or matched f_k. Consequently, the nonnegativity of Δγ in Eq. (12) only proves that JT with a particular tuple containing the same f_k beats independent transmission using that same f_k; it does not prove that the best selected joint beam beats the best independent beam. The greedy selection in Eq. (15) does not guarantee that, for every UE location, the selected N_Ind joint tuples include a tuple whose k-th component is the UE's optimal independent beam from the closest BS. If that beam is missing, the max-to-max SNR difference can be negative, and the central claim is not established. The authors need to either prove a coverage condition ensuring every independent beam of every potential closest BS appears in at least one selected joint tuple, or weaken the claim to a conditional one.","section":"Section III-A, Eqs. (11)-(13)"},{"comment":"The greedy selection rule as written is not well defined. The objective in Eq. (15) uses γ_Joint-Comb_max, which is defined in Eq. (14) as the maximum over all joint beams at the UE location; this quantity does not depend on the candidate tuple (f_1,...,f_B) over which the argmax is being taken. As a result, every candidate tuple receives the same objective value, so the selection step cannot distinguish beams. The maximization should use the SNR achieved by the candidate tuple itself, e.g., γ_Joint-Comb(f_1,...,f_B) at the uncovered grid points, or the notation must be revised to make clear what is being maximized. This is a load-bearing issue because the beam selection procedure is the core of the resource-constrained design.","section":"Section III-B, Eq. (15)"},{"comment":"The claim that the reduced-cooperation strategy leaves the relative SNR 'nearly unchanged' is asserted rather than derived. Eqs. (16) and the surrounding text argue that omitted BSs have negligible power, but no formal bound is given on the resulting SNR difference relative to the fixed-cooperation scheme, and the dependence on the threshold α is not analyzed. Since this section is presented as an additional contribution, the authors should either provide a quantitative error bound or clearly state that this part is heuristic and supported only by the simulation in Fig. 6.","section":"Section III-C"}],"minor_comments":[{"comment":"The index in the transmit amplitude √ρ_k inside the summation over b should be √ρ_b; as written, the sum uses a fixed k for every term.","section":"Eq. (2)"},{"comment":"There are typographical issues in the author block, e.g., 'Fi nland' and 'antt i.tolli', which should be corrected in the final version.","section":"Abstract and author block"},{"comment":"The statement that the simulation grid is 'scaled by a factor of 100 relative to the wavelength' is puzzling; please clarify whether the physical carrier frequency of 7.5 GHz is actually used in the path-loss model or whether the geometry is purely illustrative.","section":"Section IV, simulation setup"},{"comment":"The selected joint beam matrix J has the property that each column contains all four DFT beam indices, which is exactly the kind of beam-coverage condition needed to support the max-to-max comparison in Major Comment 1. This property is not commented on in the text; making it explicit would strengthen the simulation evidence and help the reader understand why the greedy choice works in this example.","section":"Eq. (17)"}],"recommendation":"major_revision","confidential_remarks":"The core idea is promising and the analytical derivation of Eq. (10) is sound, but the central claim of consistent outperformance currently rests on a mismatched comparison between joint and independent baselines. The authors should either prove the required beam-coverage condition for the greedy selection or significantly soften the claim. I do not see this as a reject: the issue is fixable within the manuscript's scope by adding a condition, a proof, or a more careful statement of the result, plus a corrected greedy selection description."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know about this paper is that it takes a standard open-loop diversity trick—repeating a transmission with orthogonal phase patterns so that non-coherent BSs still add constructively at any UE—and applies it to SSB initial access, which nobody in the cited literature has done. That is a real, incremental new application. The analytical step from Eq. (9) to Eq. (10) is correct: Hadamard phase sequences kill the cross terms, leaving a sum of per-BS SNR terms. And the resource-fair setup, N_Joint = N_Ind, is a sensible way to compare against independent transmission. The simulation shows up to 6 dB SNR gain and a coverage improvement for one LoS geometry. The mechanism is plausible.\n\nThe soft spot is the proof of universal outperformance. Eq. (12) compares JT to an independent baseline that uses the same closest-BS beam f_k, but the actual independent scheme transmits all N_Ind beams and the UE picks the best one. The greedy selection is not shown to contain, for every UE location, the joint tuple whose k-th component equals that closest-BS best beam. If that beam is absent, the max-to-max SNR difference could be negative. So the 'consistently outperforms' conclusion is not established from the equations alone. The simulation suggests the gain holds for the specific geometry, but the claim needs qualification: either prove a matching condition or state it as 'can outperform' rather than 'consistently outperforms.'\n\nThere are also reproducibility issues. The path loss model is not given, the alpha threshold in Eq. (16) is never specified, and there is no random UE drop or Monte Carlo over positions. No code or data are provided, so I could not reproduce the 6 dB figure. These are standard omissions for a conference paper, but they make the quantitative results less convincing.\n\nWho should read it: anyone working on initial access, SSB beam design, or multi-BS coordination in 5G/6G. It is a good idea for a workshop paper, and the core concept is worth knowing. My verdict: send it to peer review, but request a pass that either fixes the comparison proof or softens the claim, and reports simulation parameters properly.","headline":"A genuinely new CSI-free JT-for-SSB idea with a correct core derivation, but the blanket 'consistently outperforms' claim is not fully proven and the simulations are under-specified.","tokens_in":775,"tokens_out":1948,"would_cite":true,"duration_ms":39440,"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":"Joint transmission of SSBs with fixed Hadamard phase patterns gives CSI-free constructive gain at initial access.","keywords":["initial access","SSB coverage","joint transmission","synchronization signal block","beam sweeping","Hadamard phase sequences","coherent combining","5G NR"],"falsifier":"Simulate the four-base-station setup on a fine grid and, for each grid point, compare the joint SNR from the greedy-selected beam tuple with the SNR the closest base station would get by transmitting its own best independent beam with the same repetition budget; any grid point with a negative SNR gap would contradict the claim that joint transmission consistently outperforms independent transmission.","tokens_in":9160,"feed_emoji":"📡","tokens_out":8501,"duration_ms":74820,"temperature":0.7,"pith_summary":"The paper aims to establish that joint transmission of synchronization signal blocks (SSBs) from several base stations can improve initial-access coverage even though the transmitters have no channel state information. It proposes repeating each SSB under a small set of fixed phase configurations and having the user equipment coherently combine the repetitions, so that signals from different base stations add constructively at every location. When the joint scheme uses the same number of beam patterns as the independent baseline, the derived SNR gap is non-negative, and a four-base-station line-of-sight simulation shows up to 6 dB relative gain. If correct, this gives a channel-agnostic way to strengthen initial access without power boosting or extra densification.","feed_headline":"Hadamard phase codes give 6 dB SSB gain with no CSI","feed_subtitle":"Four towers repeat each sync block with orthogonal phase patterns, and UEs combine them for up to 6 dB.","key_machinery":"The load-bearing object is the complementary phase set: $B$ phase configurations across $B$ base stations, chosen as rows of a Hadamard matrix of order $B$ (for $B=4$, $\\{(0,0,0,0), (0,\\pi,\\pi,0), (0,\\pi,0,\\pi), (0,0,\\pi,\\pi)\\}$). When the user equipment coherently combines the $B$ repetitions, the identity $\\gamma_{\\mathrm{Joint-Comb}} = \\frac{B}{N_0}\\sum_b |\\sqrt{\\rho_b} h_b^H f_b|^2$ (Eq. 10) makes the cross terms vanish, leaving only the sum of per-base-station powers. The second mechanism is greedy joint-beam selection: from $(N_{\\mathrm{Ind}})^B$ possible joint beam tuples, the algorithm picks $N_{\\mathrm{Ind}}$ tuples that cover the largest remaining uncovered area, keeping the beam-pattern count equal to the independent baseline.","core_discovery":"The paper claims that lack of channel state information need not prevent joint transmission of SSBs. By repeating each SSB with phase offsets drawn from an orthogonal Hadamard set, the base stations make the user equipment's coherent combining reduce to a sum of per-base-station powers, with all cross terms vanishing. With the joint beam-pattern count set equal to the independent baseline, the SNR gap against independent SSB transmission is non-negative, and the four-base-station line-of-sight simulation shows up to 6 dB gain. The paper further claims that adapting the cooperating set to the base stations that dominate at each location preserves the relative gain while reducing the number of SSB transmissions.","pith_inferences":["The same Hadamard-combining trick could be applied to other broadcast signals that reach a user without channel state information, such as paging or positioning reference signals.","The paper simulates line-of-sight propagation only; testing the phase code under frequency-selective or non-line-of-sight channels would show how much constructive gain survives when per-base-station channel phases vary.","The greedy selection in Eq. (15) is what determines whether the non-negative gap in Eq. (12) holds location by location; an implementation that guarantees the closest base station's independent beam is always included in the selected joint beam would make the theoretical claim airtight."],"forward_implications":["With equal SSB resources, joint transmission with complementary phases yields a non-negative SNR gain over independent SSB transmission at every user location.","In the four-base-station line-of-sight setup, coverage probability at a 10 dB reference SNR rises from about 66% to 94%.","Up to 6 dB relative SNR gain is achievable with four cooperating base stations, with the largest gains in the central region where multiple base stations contribute comparably.","Selecting only the dominant base stations per location cuts the number of SSB transmissions from 16 to 10 while leaving the relative SNR gain nearly unchanged."],"supporting_citations":[{"why":"Supplies the 5G NR SSB and DFT-codebook baseline against which the joint scheme is compared.","marker":"[8]"},{"why":"Shows the connected-mode gains of joint transmission that motivate applying the same idea to initial-access SSBs.","marker":"[10]"},{"why":"Represents an adaptive SSB allocation approach that assumes independent SSB transmission, the assumption this paper replaces with joint transmission.","marker":"[9]"}],"fun_headline_variants":["Hadamard-coded SSB JT: 6 dB gain without CSI","4 BSs + phase repetition: SSB coverage up 6 dB","No-CSI joint SSB transmission yields 6 dB SNR gain","Orthogonal phase codes for SSB JT: +6 dB coverage","Repetition-based SSB JT: constructive gain, no CSI"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof that joint transmission always wins assumes that, for every user location, the joint beam selection includes the same best beam from the closest base station that the independent scheme would use; if the greedy selection ever violates this, the guaranteed non-negative gain can break.","fun_headline_variants_meta":{"raw":{"variants":["Hadamard-coded SSB JT: 6 dB gain without CSI","4 BSs + phase repetition: SSB coverage up 6 dB","No-CSI joint SSB transmission yields 6 dB SNR gain","Orthogonal phase codes for SSB JT: +6 dB coverage","Repetition-based SSB JT: constructive gain, no CSI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000489,"raw_usage":{"total_tokens":2371,"prompt_tokens":874,"completion_tokens":1497,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":490,"completion_tokens_details":{"reasoning_tokens":1403}},"tokens_in":490,"tokens_out":1497,"duration_ms":11693,"temperature":1.0,"reasoning_tokens":1403,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:17:36.730043+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the four-base-station setup on a fine grid and, for each grid point, compare the joint SNR from the greedy-selected beam tuple with the SNR the closest base station would get by transmitting its own best independent beam with the same repetition budget; any grid point with a negative SNR gap would contradict the claim that joint transmission consistently outperforms independent transmission.","supporting_citations":[{"cited_title":"Dahlman, S","cited_arxiv_id":null,"evidence_quote":"Supplies the 5G NR SSB and DFT-codebook baseline against which the joint scheme is compared."},{"cited_title":"Evaluation of joint transmission CoMP in C-RAN based LTE-A HetNets with large coordination areas,","cited_arxiv_id":null,"evidence_quote":"Shows the connected-mode gains of joint transmission that motivate applying the same idea to initial-access SSBs."},{"cited_title":"An initial access optimization algorithm for millimeter wave 5G NR net works,","cited_arxiv_id":null,"evidence_quote":"Represents an adaptive SSB allocation approach that assumes independent SSB transmission, the assumption this paper replaces with joint transmission."}],"review_version":1}