{"id":"92d3664c-f6d4-439f-bf22-ccfdabff0d51","arxiv_id":"2504.13570","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Sparse nested arrays at a base station improve both sensing resolution and backscatter communication rates for a UAV swarm, and a sensing-assisted channel estimation method needs few pilots.","lead":"This paper designs a UAV swarm communication system where one leader transmits to a base station and nearby UAVs backscatter that signal to send their own data, while a sparse antenna array at the base station both communicates and senses the swarm. It derives beam patterns and channel estimation methods showing that L-shaped and planar nested arrays can resolve densely packed UAVs better than a conventional uniform array.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The O(1/M^2) LNA and O(1/M) PNA beamwidth advantage rests on unproven 'numerical simulation' conditions in Appendices A-C, and the Fig. 6(b) PNA parameters violate the stated sufficient condition, so the central resolution ordering is not established by the theorems.","rationale":"The reader's weakest assumption identifies the same load-bearing point: the tight beamwidth upper bounds in Theorems 1-3 are justified by numerical observations inside the proofs, and the sufficient conditions are asserted rather than derived. I agree with this, and I can make it more concrete: the PNA configuration used in Fig. 6(b) does not satisfy its own sufficient condition (M(s)1 >= M(d)2 M(s)2/(2M(d)1+1)), so the O(1/M) PNA bound is not available for the example used to illustrate the claimed advantage. This is an internal support gap, not a disagreement with the community's general view on sparse arrays; sparse apertures can indeed offer narrow beams. However, the paper's stated theorem should cover the simulated configurations, or the conditions should be verified for those configurations, or the scaling claims should be presented as empirical findings. The channel-estimation MSE result in Eq. (48) is also conditional on perfect angle estimates and the text comparing K+1 with M appears to have the inequality direction reversed; these are secondary but should be corrected. The integrated IS2AC symbiotic-radio system is plausible and the simulations are broadly consistent with the qualitative story, so a CONDITIONAL recommendation remains appropriate: the central analytic resolution ordering needs either a proof of the numerical-simulation conditions, a demonstration that the conditions hold for all reported parameter sets, or an explicit re-framing of those bounds as empirically validated rather than proven.","tokens_in":23559,"tokens_out":15095,"duration_ms":142640,"concrete_test":"Evaluate Eqs. (17) and (20) numerically on a fine grid in Delta_y with Delta_z=0 for: (i) the Fig. 6(b) PNA parameters M(d)1=0, M(d)2=9, M(s)1=3, M(s)2=1; (ii) the Fig. 6(c) LNA parameters My=8, Mz=8 with My,1=Mz,1=1, My,2=Mz,2=6; and (iii) a UPA with M=16. Locate the first local minimum of the resulting beam patterns and compare with the bounds in Theorems 1-3. If the PNA's first local minimum does not satisfy the claimed tight bound for its parameters, or if the LNA/PNA ordering versus UPA reverses under the full beam-pattern expression, then the resolution comparison must be reclassified as an empirical observation; if the bounds hold, the concern reduces to a proof gap and the existing CONDITIONAL verdict stands.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that, for the same number of physical antennas, LNA and PNA provide a narrower main-lobe beamwidth than UPA, with O(1/M^2) and O(1/M) scaling, respectively. This ordering is what drives the claimed sensing and, indirectly, the communication and channel-estimation gains. The proof chain runs through Theorems 1-3 and Appendices A-C, but in each appendix the tight upper bound is introduced as an unproved numerical observation: Appendix A states 'by numerical simulation, we found that when M(s)1 >= M(d)2 M(s)2/(2M(d)1+1)'; Appendix B states 'by numerical simulation'; Appendix C states 'by numerical simulation'. The derivative arguments preceding those observations establish only the coarse bounds (23)-(26), and they contain unjustified steps: the shared-element '-1' term is dropped, monotonicity of the Dirichlet-like factors is asserted without proof, and Appendix C says 'without loss of generality, assume My,1 = My,2 >= 2', which is not a legitimate WLOG step because My,1 and My,2 are different design parameters. More concretely, the PNA used in Fig. 6(b) has M(d)1=0, M(d)2=9, M(s)1=3, M(s)2=1, so the Theorem 1 sufficient condition reads 3 >= 9, which is false. For that illustrative PNA, the tight O(1/M) bound is not even applicable; the only guaranteed bound leaves BWy in the interval (4/7, 4), which does not by itself establish superiority over a UPA. Thus the paper's central resolution ordering is currently an empirical conjecture rather than a proven consequence of the array geometry.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a low-altitude UAV swarm symbiotic radio (SR) system in which a leading UAV acts as a primary transmitter and nearby UAVs act as passive backscatter devices. The base station is equipped with a 3D sparse MIMO array, specifically an L-shaped nested array (LNA) or a planar nested array (PNA), and the paper compares these with a conventional compact uniform planar array (UPA). The authors derive achievable rate expressions for the primary transmitter and the backscatter devices, analyze beam patterns and main-lobe beamwidths, propose an IS2AC-based channel estimation scheme that first estimates 2D angles via subspace methods and then estimates the complex path gains with few pilots, and provide simulation results showing that LNA and PNA outperform UPA in sensing and communication. The central quantitative claims are that, for a fixed number of physical antennas, LNA has O(1/M^2) and PNA has O(1/M) main-lobe beamwidth scaling, compared with O(1/sqrt(M)) for UPA, and that the proposed channel estimator achieves MSE (K+1)sigma^2/(tau Pt) versus M sigma^2/(tau Pt) for conventional training.","tokens_in":23939,"tokens_out":6664,"duration_ms":61736,"significance":"If the main theorems were fully proven, the paper would make a useful contribution by quantifying the sensing and communication benefits of 3D sparse MIMO in a symbiotic-radio UAV swarm setting. The system model and rate derivations in Section IV-A are standard and appear correct, and the channel estimation scheme is a sensible adaptation of the authors' prior IS2AC framework to sparse arrays. However, the central resolution-ordering claim is not established by the proof as written: the tight beamwidth bounds in Theorems 1-3 rely on unproved statements introduced as 'by numerical simulation' inside the appendices, the LNA proof contains an invalid 'without loss of generality' step, and the PNA example used in Fig. 6(b) violates the stated sufficient condition. The stress-test concern is therefore confirmed: the O(1/M^2) and O(1/M) beamwidth advantages are currently empirical conjectures rather than theorems. The MSE comparison in Section V-B also contains a reversed inequality condition.","major_comments":[{"comment":"The tight upper bounds in Theorems 1-3 are not proven. In each appendix the decisive step is an unverified numerical observation: Appendix A states 'by numerical simulation, we found that when M(s)1 >= M(d)2 M(s)2/(2M(d)1+1)', Appendix B states a similar condition, and Appendix C states 'by numerical simulation, we found that when My,2 >= 3(My,1+1)'. These conditions are the only mechanism that converts the coarse bounds (23)-(26) into the claimed O(1/M^2) and O(1/M) beamwidth scalings used in Section IV-C.4. The coarse bounds alone are insufficient; for example, for PNA with M(d)1=0, Theorem 1 guarantees only 4/7 < BWy < 4, which does not establish superiority over a UPA. The phrase 'very close to' is also not a formal mathematical statement. The central resolution ordering is therefore a conjecture unless these numerical conditions are proved or replaced by explicit covering arguments.","section":"Section IV-C, Appendices A-C"},{"comment":"The step 'Without loss of generality, assume My,1 = My,2 >= 2' is not a legitimate WLOG reduction, because My,1 and My,2 are independent design parameters. The ordering Delta_y,5 < Delta_y,4 < Delta_y,6 <= Delta_y,3 used to establish the bound (25) depends on this equality, and the paper does not prove the result for the general case. Notably, the example in Fig. 15 uses My,1=1, My,2=6, which violates the assumed equality. The theorem statement applies to all LNA parameter values, but the proof only addresses a restricted and inconsistently chosen subset.","section":"Appendix C"},{"comment":"The PNA parameters used in the illustrative beam pattern comparison, M(d)1=0, M(d)2=9, M(s)1=3, M(s)2=1, do not satisfy the sufficient condition of Theorem 1. The condition reads M(s)1 >= M(d)2 M(s)2/(2M(d)1+1) = 9, but M(s)1=3, so the tight upper bound does not apply to this configuration. The only guaranteed bound is 4/7 < BWy < 4, which does not by itself show superiority over the UPA shown in the same figure. Figure 6(b) therefore cannot be cited as evidence for the O(1/M) PNA beamwidth claim.","section":"Section VI, Fig. 6(b)"},{"comment":"The comparison sentence 'When the number of PT and BDs K+1 is larger than the number of antennas M, our proposed IS2AC-based channel estimation method can achieve better estimation performance compared with the traditional scheme' states the opposite of what the MSE expressions imply. The proposed MSE is (K+1)sigma^2/(tau Pt) and the conventional MSE is M sigma^2/(tau Pt), so the proposed method is better when K+1 < M, not when K+1 > M. Moreover, for K+1 > M the matrix A^H(Theta,Phi)A(Theta,Phi) in (47) is rank-deficient, so the LS estimate in (47) is not defined. This condition must be corrected, and the requirement M >= K+1 for the LS estimator should be stated explicitly.","section":"Section V-B, Eq. (48)"}],"minor_comments":[{"comment":"There is a typo: 'To obatin the CSI' should read 'To obtain the CSI'.","section":"Section V-B"},{"comment":"The derivative in Eq. (55) is written as d(.)/d(Delta y), but the expression is a derivative with respect to Delta z; the notation should be corrected.","section":"Appendix B, Eq. (55)"},{"comment":"The statement that UPA has O(1/sqrt(M)) beamwidth assumes that My,u and Mz,u both scale as sqrt(M). This scaling assumption should be stated explicitly.","section":"Section IV-C.4"},{"comment":"The phrase 'very close to' is not a precise mathematical claim; the authors should replace it with explicit inequalities or with a statement that the bound is a numerical conjecture.","section":"Theorems 1-3"},{"comment":"The MSE result (48) is quoted from [37] with 'following a similar derivation', but since it is a load-bearing result for the paper's comparison, the derivation should be included or the exact correspondence to [37] should be stated with equation references.","section":"Section V-B, Eq. (48)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript builds heavily on the authors' own prior work ([14], [34], [37]) and on standard sparse-array results ([18], [25], [30], [31]); the incremental contribution is the application to the UAV-SR scenario with beamwidth and MSE analysis. The main concern is not lack of novelty but the fact that the central beamwidth theorems are not actually proven. If the numerical-observation conditions cannot be rigorously established in a revision, the claims should be downgraded to conjectures supported by simulations, and the manuscript should be evaluated on that weaker basis. The reversed inequality in the MSE comparison and the invalid WLOG step in Appendix C are concrete errors that must be fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is worth a look for the 2D nested-array beam-pattern analysis, but the central claim—that for the same number of antennas, LNA and PNA beat UPA on main-lobe width by O(1/M^2) and O(1/M)—is not actually established by the theorems. The proof chain in Appendices A–C reaches the tight upper bounds only through \"by numerical simulation, we found...\" steps. That's the load-bearing part, and it's currently a conjecture, not a proof.\n\nWhat's genuinely new: Theorems 1–4 give explicit bounds on main-lobe width for LNA and PNA, and the SLH formula (27) is a useful closed form. The system model combining symbiotic radio with sparse MIMO at the BS is coherent, and the rate derivations are standard and look correct. The IS2AC-based channel estimation scheme is a reasonable adaptation of the authors' prior work; MSE formula (48) follows from their earlier derivation, and the simulations back the qualitative ordering.\n\nThe soft spots are real. The \"by numerical simulation\" conditions inside the proofs are the crux: if those conditions fail, the claimed O(1/M^2) advantage for LNA isn't proven. The issues are compounded by at least one parameter inconsistency: the PNA in Fig. 6(b) has M(s)1=3, M(d)2=9, M(s)2=1, so the Theorem 1 condition M(s)1 ≥ M(d)2 M(s)2/(2M(d)1+1) becomes 3 ≥ 9, which is false. For that example, the guaranteed bound on BWy is only (4/7, 4), which doesn't by itself beat UPA. The \"without loss of generality, assume My,1 = My,2\" in Appendix C is also not legitimate; those are distinct design parameters. The lower bounds in Theorems 1 and 3 are fine; it's the upper bounds that carry the scaling claim, and they're unproven.\n\nThe MSE comparison assumes perfect angle estimates, which the paper acknowledges; that's a minor caveat, not a fatal one. There's no code or simulation detail, so exact reproduction is impossible.\n\nWho's this for? People working on sparse-array ISAC or symbiotic radio who want a concrete extension of 1D nested-array beam-pattern analysis to 2D. The idea is plausible and the simulations are suggestive, but the theory needs another pass: either prove the sufficient conditions or reclassify them as assumptions and calibrate the claims accordingly, and fix the parameter inconsistency in Fig. 6(b).\n\nMy recommendation: send it to peer review. The core idea and derivations are worth engaging, and the gaps are fixable in revision. But the paper as it stands overclaims the proven scaling.","headline":"The paper's central beamwidth-ordering theorem is the load-bearing claim, and right now it's supported by unproved numerical observations rather than proof; the idea is plausible and worth refereeing, but the theory needs another pass.","tokens_in":24492,"tokens_out":3240,"would_cite":false,"duration_ms":26579,"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":"L-shaped sparse arrays sharpen UAV swarm sensing and rates","keywords":["symbiotic radio","UAV swarm","3D sparse MIMO","nested array","beam pattern","super-resolution sensing","channel estimation","integrated sensing and communication"],"falsifier":"Choose an LNA with parameters violating the stated condition, for example $M_{y,1}=3$ and $M_{y,2}=4$ so that $M_{y,2} < 3(M_{y,1}+1)=12$, compute the y-axis beam pattern $G_{\\mathrm{lna}}(\\Delta_y,0)$ numerically, and locate the first local minimum. If the main-lobe width is not close to $4/((M_{y,1}+1)M_{y,2})$ and the $\\mathcal{O}(1/M^2)$ upper bound fails, then the tight bound of Theorem 3 is not generally valid.","tokens_in":2081,"feed_emoji":"📡","tokens_out":4984,"duration_ms":100341,"temperature":0.7,"pith_summary":"The paper studies a low-altitude UAV swarm in which one leading UAV transmits to a base station while the other UAVs backscatter the same signal to send their own data without consuming extra spectrum or power. It argues that the base station's antenna geometry is the key resource: for a fixed number of physical antennas, a 3D sparse MIMO layout, specifically an L-shaped nested array (LNA) or a planar nested array (PNA), produces a much narrower main lobe and therefore finer angular resolution for densely packed UAVs than a conventional compact uniform planar array (UPA). From the beam-pattern analysis, the main-lobe beamwidth scales as $\\mathcal{O}(1/M)$ for PNA and $\\mathcal{O}(1/M^2)$ for LNA versus $\\mathcal{O}(1/\\sqrt{M})$ for UPA. The paper couples this sensing sharpness with a channel-estimation scheme that first finds all UAV directions using super-resolution sensing without pilots and then estimates the path gains with very few pilots, reaching a channel MSE of $(K+1)\\sigma^2/(\\tau P_t)$ instead of $M\\sigma^2/(\\tau P_t)$ for conventional training. If correct, the same hardware can serve denser swarms with less pilot overhead.","feed_headline":"L-shaped sparse arrays sharpen UAV swarm sensing and rates","feed_subtitle":"Same antenna count, narrower beam and lower channel-estimation error than compact arrays in symbiotic radio links.","key_machinery":"The load-bearing object is the difference co-array of a nested array: by taking differences of physical antenna positions, a small sparse array synthesizes a much larger virtual uniform array, and that virtual aperture is what provides super-resolution. For the LNA, two orthogonal one-dimensional nested arrays along the y and z axes give separable one-dimensional virtual arrays, and a pair-matching step using a permutation matrix associates the estimated elevation and azimuth angles. For the PNA, a compact uniform planar array on one side of the origin and a sparse uniform planar array on the other produce a contiguous two-dimensional difference co-array, and two-dimensional spatial smoothing restores the rank needed for MUSIC. The beam-pattern analysis in Theorems 1-4 converts this geometry into quantitative claims about main-lobe width, and the prominent side-lobe height analysis makes explicit the tradeoff between resolution and grating lobes.","core_discovery":"The paper's central claim is that integrated super-resolution sensing and symbiotic communication can be realized in a UAV swarm with a sparse 3D MIMO base station, and that sparse nested geometries outperform compact uniform arrays on both sensing and communication: they give a narrower main lobe, better separation of UAVs in angle, higher achievable backscatter-device sum rates, and lower channel-estimation error. For the L-shaped nested array, the main-lobe width on the y-axis is upper bounded by $4/((M_{y,1}+1)M_{y,2})$ under the condition $M_{y,2} \\geq 3(M_{y,1}+1)$, against $4/M_{y,u}$ for the uniform planar array, which yields the $\\mathcal{O}(1/M^2)$ versus $\\mathcal{O}(1/\\sqrt{M})$ scaling. The sensing-assisted estimator builds a virtual array from the difference co-array, applies a super-resolution subspace algorithm such as MUSIC to estimate elevation and azimuth angles without dedicated pilots, pair-matches those angles, and then estimates all path gains by least squares using very few pilots. The resulting MSE is $(K+1)\\sigma^2/(\\tau P_t)$ for the proposed scheme versus $M\\sigma^2/(\\tau P_t)$ for conventional pilot-based training, and the simulations show LNA and PNA maintaining better estimation and rate performance as the number of UAVs grows.","pith_inferences":["The virtual-array viewpoint suggests the same sparse geometries could support joint angle estimation and beam tracking for a moving swarm, since the direction estimates come from data symbols and can be refreshed without additional pilot overhead.","The parameter conditions verified numerically in the appendices are likely sufficient but not necessary; a closed-form proof of the tight beamwidth bounds would let designers choose the exact dense/sparse split that minimizes beamwidth for a fixed grating-lobe budget.","The MSE comparison has a natural regime boundary where $K+1$ equals $M$; operating on either side of that boundary determines whether the sensing-assisted estimator or conventional training is more efficient, and a systematic simulation sweep across that boundary would make the intended operating regime precise.","A testable extension is to adapt the dense/sparse split of the LNA and PNA to the instantaneous angular spread of the swarm: add more sparse elements when UAVs are tightly packed and shift toward dense elements when grating lobes would dominate."],"forward_implications":["For a fixed number of physical antennas, the L-shaped nested array gives the narrowest main lobe with $\\mathcal{O}(1/M^2)$ beamwidth scaling, the planar nested array is intermediate with $\\mathcal{O}(1/M)$, and the conventional uniform planar array is widest with $\\mathcal{O}(1/\\sqrt{M})$, so dense UAV swarms are separable in angle only with the sparse geometries.","The proposed sensing-assisted channel estimator reaches MSE $(K+1)\\sigma^2/(\\tau P_t)$ with only a few pilots; since conventional training gives $M\\sigma^2/(\\tau P_t)$, the estimator is preferable when $K+1 < M$.","Sparse geometries improve backscatter-device sum rate when CSI is estimated, especially when the number of UAVs is large or the antenna count is moderate, because the sharper beam pattern reduces inter-user interference.","The grating-lobe analysis shows a design tradeoff: more sparse elements improve resolution but raise prominent side-lobe heights, so the dense/sparse split should be chosen according to how tightly the UAVs are packed.","Because the super-resolution angle estimates use both pilot and data symbols, the proposed scheme removes the need for dedicated pilot training for angle acquisition, reducing overhead in the swarm scenario."],"supporting_citations":[{"why":"Supplies the nested-array construction and the difference co-array virtual array without holes, which is the basis for the sparse MIMO sensing gain.","marker":"[18]"},{"why":"Provides the planar nested array configuration whose difference co-array contains contiguous elements, used for the PNA design.","marker":"[30]"},{"why":"Supplies the two-dimensional array processing and spatial smoothing method used for PNA angle estimation.","marker":"[31]"},{"why":"Provides the beam-pattern analysis framework for nested arrays, including main-lobe beam width and side-lobe metrics, which the paper extends to LNA and PNA.","marker":"[34]"},{"why":"Gives the pair-matching operation for L-shaped nested arrays used to associate the separately estimated one-dimensional angles.","marker":"[25]"},{"why":"Defines the MUSIC super-resolution algorithm that estimates directions without requiring known pilot symbols.","marker":"[36]"},{"why":"Provides the prior IS2AC channel-estimation MSE analysis that the paper adapts to the sparse-array scenario and uses as the conventional-training baseline.","marker":"[37]"},{"why":"Establishes the parasite symbiotic-radio setup with equal symbol rates, which underlies the backscatter communication model.","marker":"[35]"}],"fun_headline_variants":["Sparse MIMO narrows beams for UAV swarm sensing and rates","Nested arrays sharpen UAV swarm sensing and backscatter rates","Sparse 3D MIMO boosts UAV swarm localization and comms","Super-resolution sensing with symbiotic backscatter for UAV swarms","LNA and PNA arrays cut beam width, lift UAV swarm rates"],"cache_read_input_tokens":26496,"weakest_assumption_plain":"The tight beamwidth upper bounds for the L-shaped and planar nested arrays rely on parameter-size conditions, such as $M_{y,2} \\geq 3(M_{y,1}+1)$ for the LNA, that the appendices verify only by numerical simulation rather than by proof; if those conditions fail, the claimed $\\mathcal{O}(1/M^2)$ beamwidth advantage for the LNA is not established.","fun_headline_variants_meta":{"raw":{"variants":["Sparse MIMO narrows beams for UAV swarm sensing and rates","Nested arrays sharpen UAV swarm sensing and backscatter rates","Sparse 3D MIMO boosts UAV swarm localization and comms","Super-resolution sensing with symbiotic backscatter for UAV swarms","LNA and PNA arrays cut beam width, lift UAV swarm rates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000475,"raw_usage":{"total_tokens":2457,"prompt_tokens":1142,"completion_tokens":1315,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":758,"completion_tokens_details":{"reasoning_tokens":1224}},"tokens_in":758,"tokens_out":1315,"duration_ms":9378,"temperature":1.0,"reasoning_tokens":1224,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:05:33.457909+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Choose an LNA with parameters violating the stated condition, for example $M_{y,1}=3$ and $M_{y,2}=4$ so that $M_{y,2} < 3(M_{y,1}+1)=12$, compute the y-axis beam pattern $G_{\\mathrm{lna}}(\\Delta_y,0)$ numerically, and locate the first local minimum. If the main-lobe width is not close to $4/((M_{y,1}+1)M_{y,2})$ and the $\\mathcal{O}(1/M^2)$ upper bound fails, then the tight bound of Theorem 3 is not generally valid.","supporting_citations":[{"cited_title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom,","cited_arxiv_id":null,"evidence_quote":"Supplies the nested-array construction and the difference co-array virtual array without holes, which is the basis for the sparse MIMO sensing gain."},{"cited_title":"Nested arrays in two dimensions, Part I: Geometrical considerations,","cited_arxiv_id":null,"evidence_quote":"Provides the planar nested array configuration whose difference co-array contains contiguous elements, used for the PNA design."},{"cited_title":"Nested arrays in two dimensions, Part II: Application in two dimensional array processing,","cited_arxiv_id":null,"evidence_quote":"Supplies the two-dimensional array processing and spatial smoothing method used for PNA angle estimation."},{"cited_title":"Integrated sensing and communication with nested array: Beam pattern and performance analysis,","cited_arxiv_id":null,"evidence_quote":"Provides the beam-pattern analysis framework for nested arrays, including main-lobe beam width and side-lobe metrics, which the paper extends to LNA and PNA."},{"cited_title":"2-D direction finding with pair-matching operation for L-shaped nested array,","cited_arxiv_id":null,"evidence_quote":"Gives the pair-matching operation for L-shaped nested arrays used to associate the separately estimated one-dimensional angles."},{"cited_title":"Multiple emitter location and signal parameter estimation,","cited_arxiv_id":null,"evidence_quote":"Defines the MUSIC super-resolution algorithm that estimates directions without requiring known pilot symbols."},{"cited_title":"Little pilot is needed for channel estimation with integrated super-resolution sensing and communication,","cited_arxiv_id":null,"evidence_quote":"Provides the prior IS2AC channel-estimation MSE analysis that the paper adapts to the sparse-array scenario and uses as the conventional-training baseline."},{"cited_title":"Symbiotic radio: A new communication paradigm for passive Internet-of-Things,","cited_arxiv_id":null,"evidence_quote":"Establishes the parasite symbiotic-radio setup with equal symbol rates, which underlies the backscatter communication model."}],"review_version":1}