{"id":"5b9a3e9f-763f-4f8d-a47b-de5e38285388","arxiv_id":"2411.13188","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Rate-splitting with a three-stage decoding order yields larger inner bounds for sensing-communication coexistence than OMA- and NOMA-inspired schemes.","lead":"This paper proposes splitting a wireless user's message into two parts so a base station can decode one part, estimate a radar target, then decode the second part, letting communication and radar share the same spectrum with less interference. The authors derive rate limits and the optimal power split, and show the approach beats two existing spectrum-sharing methods in simulations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (9) inverts the variance inequality: (8d) lower-bounds the Fisher information, so the resulting CRLB is an upper bound on estimation variance, not the stated lower bound; (13)-(14) inherit the reversed direction.","rationale":"The central claim is that the RS-inspired decoding order sc,1 → radar → sc,2 enlarges the sensing-communication inner bound relative to OMA- and NOMA-inspired schemes. The proof chain is (8c)->(9)->(10),(12)->(13),(14). The weakest load-bearing link is the inequality direction in (9). I checked the algebra: (8c) is exact for the Gaussian interference model; the Cauchy-Schwarz step to (8d) is valid and gives a lower bound on J. Consequently the quantity on the RHS of (9) is an upper bound on the CRLB, not a lower bound on the variance. The paper states the opposite. This is a mathematical error in a key step. However, the error is conservative: if the matched-filter estimator reaches the CRLB, then the true variance is no larger than the RHS of (9), so plugging that RHS into (10) and (12) produces a pessimistic REIR and a pessimistic Rc,2. The plotted RS curve therefore sits southwest of the true achievable region; fixing the direction would move the curve up and right, which would only improve RS's relative standing. Thus the central claim is not threatened by this error, but the written derivation is not rigorous. The reader's verdict of CONDITIONAL with corrections is appropriate. I disagree slightly with the reader's choice of weakest_assumption: the white-noise residual model in (4) is an inherited approximation that affects all schemes equally, whereas the reversed inequality in (9) is an internal inconsistency that can be resolved by an independent check. The concrete test above settles the direction effect quantitatively. If the corrected curve still dominates, the paper should be accepted after a minor revision; if not, the claimed trade-off would need substantial reappraisal.","tokens_in":8385,"tokens_out":23462,"duration_ms":225078,"concrete_test":"Recompute the RS inner bounds in Fig. 3 using the exact Fisher information from (8c) (keeping the Sherman-Morrison correction term) instead of the lower bound in (8d), for the same Table I parameters, and using the corrected inequality σ2_est ≤ C in (13) and (14). Then compare the resulting (Rest, Rc) curve with the OMA- and NOMA-inspired inner bounds. If the corrected RS curve still lies to the northeast of the baselines (higher Rc for each Rest), the central claim is robust to the direction error; if it crosses or lies below, the claimed superiority is an artifact of the reversed inequality.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim depends on (13)-(14) being valid inner bounds. The derivation of (9) from (8c) is where the argument breaks. In (8c), the Sherman-Morrison formula gives the exact Fisher information J(τr) for the Gaussian model in (7). The step to (8d) uses Cauchy-Schwarz to show |h^H r'_τr|^2 ≤ ||h||^2||r'_τr||^2, which implies J ≥ |ar|^2Pr||r'_τr||^2/(σn^2+|bc|^2Pc,2). Thus (8d) is a lower bound on J. Because the CRLB is 1/J, the correct statement is σ2_τr,est ≤ (σn^2+|bc|^2Pc,2)/(2γ^2B^2(TB)|ar|^2Pr), with ≤, not ≥ as written in (9). Section II.C then substitutes this 'variance' into the REIR bound (10) and the second-stream interference (12), so (13) and (14) are affected. If the estimator achieves the (smaller) true CRLB, then using the right-hand side of (9) as the variance makes the REIR bound in (13) a conservative lower bound (the RHS is smaller than the true attainable rate) and makes Rc,2 in (14) conservative as well; correcting the sign therefore shifts the RS curve northeast in Fig. 3 and strengthens the claimed dominance over OMA/NOMA. Nevertheless, the printed inequality in (9) is not a consequence of (8d), and the paper does not rigorously establish the inner bounds as written. The authors must either reverse the inequality in (9) and re-derive (13)-(14) with the correct directions, or rephrase the Cramer-Rao step as a pessimistic variance assumption.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a rate-splitting (RS)-inspired scheme for an uplink integrated sensing and communication (ISAC) scenario in which a base station simultaneously serves a communication user and estimates a radar target's delay. The communication user splits its message into two streams, and the receiver uses a fixed decoding order sc,1 → radar → sc,2. The authors derive bounds on the ergodic data information rate (DIR) for communication and the ergodic radar estimation information rate (REIR), together with a closed-form expression for the power-split factor α that maximizes DIR. They compare the RS scheme with OMA- and NOMA-inspired baselines and report that RS yields a more favorable sensing–communication trade-off, with the RS curve beginning at the NOMA point for α=0 and extending toward higher DIR at the cost of lower REIR.","tokens_in":8757,"tokens_out":18213,"duration_ms":173331,"significance":"If the bounds are valid, the work is a useful conceptual extension of rate-splitting from digital communication to a framework that treats the sensing signal as a non-orthogonal interferer that is partially decoded and partially noise. The closed-form optimal power split and the explicit recovery of the NOMA case at α=0 are positive features, and the simulation results corroborate the analytical curves. The central qualitative claim—that decoding-order flexibility from message splitting improves the trade-off relative to OMA and NOMA—is plausible and, if properly argued, would be a solid addition to the ISAC literature. However, the technical derivation contains a sign error in the Cramér-Rao step that must be corrected before the inner bounds are rigorously established.","major_comments":[{"comment":"The inequality in Eq. (9) is reversed. Equation (8d) is a lower bound on the Fisher information J(τr): J ≥ |ar|^2 Pr ||r'_τr||^2 / (σ_n^2 + |bc|^2 Pc,2). Since the CRLB is the reciprocal of J, the expression on the right-hand side of (9) is an upper bound on the variance, not a lower bound. The correct statement is σ^2_{τr,est} ≤ (σ_n^2 + |bc|^2 Pc,2) / (2γ^2B^2(TB)|ar|^2Pr), assuming the usual unit-energy pulse h with ||h||^2=1. The phrase 'a more pessimistic CRLB' in the text preceding (9) is also inconsistent: a lower bound on J gives an upper bound on the CRLB, not a larger CRLB. This is load-bearing because equations (12), (13) and (14) all use the variance expression from (9). Please correct the direction and rephrase the step as a pessimistic variance assumption (an upper bound on the true CRLB) rather than as the CRLB itself.","section":"Section II.C, Eqs. (8a)–(9)"},{"comment":"Assuming Eq. (9) is corrected to an upper bound, the derivation of the inner bounds in (13) and (14) must be made explicit. If the authors intend to use the pessimistic variance (the upper bound on the CRLB), they should state that this produces conservative bounds: the actual achievable REIR and second-stream DIR are at least as large as the printed expressions when the receiver uses the true CRLB-achieving estimator. If, instead, they intend to use the true CRLB, the directions and the numerical results in Fig. 3 change, shifting the RS curve northeast and strengthening the claimed advantage over the baselines. Either way, the current derivation does not rigorously establish the inner bounds as written because the chain from (8d) to (13)–(14) relies on a false inequality. Please provide a short, explicit argument that the variance value used in (12) leads to valid inner bounds (or update the bounds to use the true CRLB).","section":"Section III, Eqs. (13)–(14)"}],"minor_comments":[{"comment":"The text refers to sc,2(t) as an 'unknown random constant amplitude', but sc,2(t) is a time-varying unit-variance communication stream. The subsequent derivation treats sc,2 as a random scalar multiplying a deterministic unit-energy pulse h, which is a specific modeling choice. Please clarify this assumption, e.g., by stating that the communication signal is modeled as a known pulse shape with random amplitude over the radar processing interval.","section":"Section II.C, Eq. (5)–(7)"},{"comment":"The optimal α is found by setting the derivative to zero, but the paper does not verify that the stationary point is a maximum (second derivative condition) or discuss what happens when multiple stationary points exist. A brief check or a note that the boundary cases were examined would make the derivation complete.","section":"Section III, Eq. (16)"},{"comment":"Reference [9] is incomplete: 'pp. 1–1' lacks the volume and year details. Please complete the bibliographic information.","section":"References"},{"comment":"Figure 4 would be clearer with labeled axes and a caption explaining what is plotted (presumably the optimal α as a function of communication range). Currently the y-axis label is missing.","section":"Section IV, Fig. 4"},{"comment":"There are several typographical and typesetting issues, including inconsistent power notation in (15) (e.g., 'P 3 bc' instead of P_bc^3) and a minor grammar error ('communications stream' in Section II.B). A careful proofread is recommended.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper's contribution is incremental but relevant: it applies the RS principle to the sensing-communication coexistence problem and shows a plausible trade-off improvement. The main obstacle is the incorrect direction in the CRLB inequality, which is a genuine technical error but appears fixable without changing the overall framework. If the authors correct the inequality and reframe the pessimistic variance assumption, the central claims can be salvaged. The lack of a released code or full simulation details is not a blocker for a journal publication in this subfield, but the derivation needs to be rigorous."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper's RS-inspired decoding order is a reasonable and modest extension of the NOMA baseline, and the main performance claim is likely correct. However, the CRLB inequality in (9) is printed backwards, which needs fixing.\n\nWhat's new: the three-stage decoding order (sc,1 → radar → sc,2) and the closed-form optimal power split. The framework generalizes the NOMA-inspired scheme in [5], and the NOMA case is recovered at α=0. The analytical bounds match simulations, which supports the derivations.\n\nThe major issue: (8d) lower-bounds the Fisher information, so the CRLB is an upper bound on the estimation variance, not a lower bound. The correct inequality in (9) is ≤, not ≥. Because the RHS is then a pessimistic variance estimate, (13) and (14) remain conservative inner bounds; correcting the direction shifts the RS curve northeast, strengthening the claimed advantage over OMA/NOMA. So the central insight stands, but the derivation as written is mathematically inconsistent.\n\nMinor concerns: the residual radar echo model in (4) assumes white noise with a specific variance; this is an approximation from [5] and should be stated as such. Also, an independent check of the optimal α formula (16) reportedly gives a different factor of two. That should be double-checked, though it doesn't change the qualitative conclusions.\n\nBottom line: this is a solid subfield contribution. The paper is worth peer review; the authors need to fix the inequality direction and re-derive the bounds accordingly, and verify (16). After that, it publishes.\n\nFor your decisions: I'd bring it to a reading group to discuss the CRLB error, and I'd cite it in spectrum-sharing work.","headline":"A rate-splitting ISAC scheme that likely works, but the printed CRLB inequality is backwards and needs fixing before publication.","tokens_in":9258,"tokens_out":3776,"would_cite":true,"duration_ms":38181,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Splitting an uplink message and decoding it around the radar echo yields a better sensing-communication trade-off than OMA or NOMA coexistence.","keywords":["radar-communications coexistence","rate-splitting (RS)","successive interference cancellation (SIC)","integrated sensing and communication (ISAC)","ergodic data information rate","ergodic radar estimation information rate","power-split optimization","Cramér–Rao lower bound"],"falsifier":"Run the joint receiver with a radar waveform whose spectrum is not flat, for example a pulse-shaped waveform with a non-rectangular envelope, and compare the measured residual interference power after predicted-return subtraction with $P_{\\mathrm{r}} |a_{\\mathrm{r}}|^2 \\gamma^2 B^2 \\sigma^2_{\\tau_r,\\mathrm{proc}}$; a systematic mismatch means equation (4) and the bounds built on it do not correctly describe the scheme.","tokens_in":8166,"feed_emoji":"📡","tokens_out":13792,"duration_ms":120922,"temperature":0.7,"pith_summary":"The paper asks how a base station can simultaneously receive an uplink communication message and estimate the range of a radar target without letting one function starve the other. It answers by splitting the user's message into two superposed streams and decoding them around the radar estimation step, first stream, then radar echo, then second stream, so that interference between sensing and communication is partly decoded and partly treated as noise. The authors derive inner bounds on the ergodic data information rate and the ergodic radar estimation information rate, together with a closed-form expression for the power split that maximizes the communication rate. They show that, for the adopted model, this rate-splitting scheme yields a more favorable sensing-communication trade-off than OMA- and NOMA-inspired baselines, with NOMA-inspired behavior recovered as a special case. The result offers a systematic, analytically tractable way to tune non-orthogonal coexistence of sensing and communication.","feed_headline":"Rate splitting beats OMA and NOMA in radar-communication trade-off","feed_subtitle":"Splitting one uplink message lets a joint receiver decode around radar estimation, widening the achievable rate region.","key_machinery":"The load-bearing object is the rate-split transmit signal $x(t)=\\sqrt{P_{c,1}} s_{c,1}(t)+\\sqrt{P_{c,2}} s_{c,2}(t)$, where $s_{c,1}$ and $s_{c,2}$ are independently encoded streams of one user's message, combined with the SIC decoding order $s_{c,1} \\to$ radar $\\to s_{c,2}$ at the base station. Rate-splitting means the message is split into two parts that are superposed at the transmitter and sequentially decoded at the receiver, giving a continuous set of operating points indexed by $\\alpha$. The mathematical engine is the Cramér–Rao lower bound for radar time-delay estimation under Gaussian interference from $s_{c,2}$: the Fisher information step, simplified via the Sherman–Morrison formula and a Cauchy–Schwarz bound, produces the conservative estimator variance in (9), which feeds the REIR bound (13) and the interference term in (12). The closed-form power split (16) follows from setting the derivative of $R_{c,1}+R_{c,2}$ to zero and solves for the DIR-maximizing operating point.","core_discovery":"The paper's central claim is that inter-functionality interference in an uplink ISAC receiver should be treated as a controllable resource rather than something to be entirely avoided or fixed in a rigid order. The communication user rate-splits its message into two superposed streams; the joint radar-communication receiver decodes the first stream with the predicted radar echo subtracted, estimates the radar time delay while the second stream acts as interference, and then decodes the second stream after removing the estimated echo. The achievable trade-off is described by inner bounds (13) for the ergodic radar estimation information rate and (14) for the ergodic data information rate, parameterized by the power split $\\alpha=P_{c,2}/P_c$. The paper shows that as $\\alpha$ moves from 0 to 1, this region improves on the OMA- and NOMA-inspired bounds for the system model considered, with $\\alpha=0$ exactly recovering the NOMA-inspired bounds, and it gives the closed-form $\\alpha^{\\mathrm{RS}}_{\\max}$ in (16) that maximizes the communication rate.","pith_inferences":["The paper analyzes a single communication user; a natural next step is to combine RS with multiple users, where each user's streams could be inserted at different points of the radar estimation chain, though the resulting rate region is not derived here.","The closed-form split $\\alpha^{\\mathrm{RS}}_{\\max}$ depends on the target's process noise and radar power, so an adaptive implementation that recomputes the split as the target moves would be a practical refinement the paper leaves implicit.","The flat-spectrum residual-echo assumption is likely the first thing to test experimentally: if real residuals are colored, the CRLB and the claimed region would need correction, but the splitting idea itself would remain applicable."],"forward_implications":["The NOMA-inspired coexistence scheme becomes a special case of the RS scheme at $\\alpha=0$, so a design already using NOMA-inspired SIC can switch to RS without losing that operating point.","The closed-form optimal split means the DIR-maximizing point can be computed from the channel gains, radar power, bandwidth, and target process noise without numerical search over $\\alpha$.","Because $\\alpha$ controls how much of the communication signal interferes with radar estimation, the scheme gives operators a continuous knob to shift the operating point between sensing accuracy and communication rate.","The same decoding-and-estimation ordering can be applied to radar parameters other than range, since the CRLB structure carries over, a direct extension the paper states."],"supporting_citations":[{"why":"Supplies the co-existence inner-bound approach, the radar-communication signal model, the CRLB, and the OMA/NOMA baseline bounds used for comparison.","marker":"[5]"},{"why":"Supplies the rate-splitting principle and the superposition-coded transmit signal structure used to split the uplink message into two streams.","marker":"[7]"},{"why":"Provides the multiple-access perspective on ISAC and the ergodic DIR/REIR metrics that frame the performance comparison.","marker":"[2]"},{"why":"Provides the predicted-radar-return suppression model and the semi-integrated OMA-to-NOMA approach the derivation builds on.","marker":"[3]"},{"why":"Warrants marginalizing the Gaussian likelihood over the interfering communication stream, the step that yields the CRLB in (9).","marker":"[12]"},{"why":"Supports the rate-splitting transmission and SIC decoding principle behind the transmit signal in (1).","marker":"[8]"}],"fun_headline_variants":["Rate-splitting widens ISAC trade-off beyond OMA/NOMA","Splitting messages improves radar-communication coexistence","RS-inspired ISAC achieves better sensing-communication balance","Closed-form power split optimizes uplink ISAC rate"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole calculation treats the leftover radar echo after subtracting the predicted return as white noise with power $P_{\\mathrm{r}} |a_{\\mathrm{r}}|^2 \\gamma^2 B^2 \\sigma^2_{\\tau_r,\\mathrm{proc}}$; if real residual echoes are correlated or non-Gaussian, the CRLB and the rate bounds change.","fun_headline_variants_meta":{"raw":{"variants":["Rate-splitting widens ISAC trade-off beyond OMA/NOMA","Splitting messages improves radar-communication coexistence","RS-inspired ISAC achieves better sensing-communication balance","Closed-form power split optimizes uplink ISAC rate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001523,"raw_usage":{"total_tokens":6112,"prompt_tokens":971,"completion_tokens":5141,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":587,"completion_tokens_details":{"reasoning_tokens":5082}},"tokens_in":587,"tokens_out":5141,"duration_ms":35929,"temperature":1.0,"reasoning_tokens":5082,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:47:14.991457+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the joint receiver with a radar waveform whose spectrum is not flat, for example a pulse-shaped waveform with a non-rectangular envelope, and compare the measured residual interference power after predicted-return subtraction with $P_{\\mathrm{r}} |a_{\\mathrm{r}}|^2 \\gamma^2 B^2 \\sigma^2_{\\tau_r,\\mathrm{proc}}$; a systematic mismatch means equation (4) and the bounds built on it do not correctly describe the scheme.","supporting_citations":[{"cited_title":"Inner bounds on performance of radar and communications co-existence,","cited_arxiv_id":null,"evidence_quote":"Supplies the co-existence inner-bound approach, the radar-communication signal model, the CRLB, and the OMA/NOMA baseline bounds used for comparison."},{"cited_title":"Rate-Splitting Multiple Access for 6G—Part I: Principles, Applications and Future Works,","cited_arxiv_id":null,"evidence_quote":"Supplies the rate-splitting principle and the superposition-coded transmit signal structure used to split the uplink message into two streams."},{"cited_title":"NOMA for integrating sensing and communications toward 6G: A multiple access perspective,","cited_arxiv_id":null,"evidence_quote":"Provides the multiple-access perspective on ISAC and the ergodic DIR/REIR metrics that frame the performance comparison."},{"cited_title":"Semi-Integrated-Sensing-and-Communication Semi- ISaC: From OMA to NOMA,","cited_arxiv_id":null,"evidence_quote":"Provides the predicted-radar-return suppression model and the semi-integrated OMA-to-NOMA approach the derivation builds on."},{"cited_title":"On the rela- tionship of the Cramer-Rao lower bound and channel capacity in an interfered binary channel through the log-likelihood ratio,","cited_arxiv_id":null,"evidence_quote":"Warrants marginalizing the Gaussian likelihood over the interfering communication stream, the step that yields the CRLB in (9)."},{"cited_title":"Rate splitting for MIMO wireless networks: A promising PHY-layer strategy for LTE evolution,","cited_arxiv_id":null,"evidence_quote":"Supports the rate-splitting transmission and SIC decoding principle behind the transmit signal in (1)."}],"review_version":1}