{"id":"e81bbf64-1354-4871-a0a5-7e8a0f00fa57","arxiv_id":"2505.05914","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A speed-dependent stepper motor power model is introduced for movable antennas, and an energy-efficiency maximization algorithm (max speed, Dinkelbach power, enumerated position) shows the movable antenna system can beat fixed antennas in energy efficiency despite movement power.","lead":"The paper models the electricity needs of the small motor that physically moves a 'movable antenna', then finds the best antenna spot, speed, and transmit power to make the system's energy efficiency as high as possible.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The power model in Eq. (3) treats mechanical output power as electrical consumption, so the optimized EE and the claimed MA-over-FPA gain may not hold for a real stepper-driven system.","rationale":"The paper's optimization machinery (Dinkelbach plus enumeration) is internally coherent given the stated PM(v), and Proposition 1's derivative argument is correct under Eq. (3). However, Eq. (3) misidentifies the quantity being optimized: PM is mechanical output power, not electrical input power. The electrical input to a stepper motor is larger and, importantly, has a different speed dependence because resistive and core losses are largest at low speed/high current and are nonzero at no load. Changing PM(v) can overturn Proposition 1, since monotonicity in v depends on PM(v) decreasing fast enough relative to the transmission-time gain, and can overturn the numerical EE comparison against the FPA benchmark. The lead-screw relation v = l0 omega is also dimensionally inconsistent with screw kinematics; the correct conversion uses the screw lead, so the discretized position set and vmax are not justified. The reader identified the same core assumption and the pseudocode feasibility inversion; this pass agrees that the physical power model, not the Dinkelbach/enumeration structure, is the load-bearing weakness. A corrected physical model must be checked before the EE gains can be trusted, so the conditional verdict stands.","tokens_in":9682,"tokens_out":4622,"duration_ms":48990,"concrete_test":"Obtain the AM2224's electrical input power P_elec(v) from the manufacturer's datasheet or from a direct measurement of driver DC-bus voltage and current during constant-speed MA motion. Re-run Algorithm 1 with PM replaced by P_elec(v) and with the corrected lead-screw relation v = (L/(2*pi))omega. Then check: (i) Does EE still monotonically increase with v for every xt and P, as Proposition 1 requires? (ii) Does the corrected EE of the proposed scheme still exceed the FPA benchmark in Fig. 5? If either answer is no, the paper's central claim is an artifact of using mechanical output power as the consumption model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (3) defines PM = omega M(omega) = (v/l0) M(v/l0), which is the motor's mechanical output power, and then calls this the MA driver's power consumption. Electrical input power also includes resistive I^2R losses, core losses, and no-load losses, all of which are nonzero when the motor is spinning unloaded; the paper itself notes that the output power drops to zero at no load only in an unachievable ideal case. Since PM(v) enters the EE objective (6), Proposition 1's monotonicity proof and every Section V EE comparison are statements about mechanical output, not about energy actually drawn from the supply. The kinematic relation v = l0 omega is also not the lead-screw kinematics: for a screw with lead L, v = (L/(2*pi))omega, so the step size ds = omega_D l0 and vmax = omega_max l0 are not physically tied to the actuator. Either correction can change the shape of PM(v), and with it the optimal speed, position, power, and the headline conclusion that MA systems beat FPA. Algorithm 1's line 5 also inverts the feasibility check, but even a corrected implementation still optimizes the wrong physical objective until Eq. (3) is fixed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies energy-efficiency (EE) maximization for a single movable-antenna (MA) system driven by a stepper motor through a lead screw. The authors propose a power consumption model in which the driver power is the product of the motor's angular speed and its pull-out torque (Eqs. (3)-(4)), formulate an EE maximization problem over antenna position, moving speed, and transmit power (P1), prove that EE is monotonically increasing in speed (Proposition 1), and then solve the reduced problem by Dinkelbach's algorithm for the transmit power plus enumeration over candidate positions (Algorithm 1). Numerical results show that the proposed scheme can outperform fixed-position antenna (FPA) and other benchmarks in terms of EE despite the mechanical power consumption.","tokens_in":9976,"tokens_out":10673,"duration_ms":105335,"significance":"If the power model were physically faithful, the paper would offer a useful hardware-aware EE formulation and an efficient, provably convergent solution: Proposition 1's derivative computation is correct under the stated model, the Dinkelbach update in Eq. (15) is the standard and correct water-filling-like expression, and the enumeration over discrete MA positions is straightforward. The manuscript also makes no attempt to fit targets; the motor parameters come from a datasheet and the proof is self-consistent. However, the central model equates mechanical output power with electrical input power, and the stress-test concern is valid: Eq. (3) is not the power drawn from the supply. Because the model error is load-bearing for Proposition 1, the optimization, and all Section V conclusions, the claimed MA-over-FPA gain is not established. The framework is reusable, but the physical model and all downstream results need to be reworked.","major_comments":[{"comment":"Equation (3) identifies the stepper motor's power consumption with its mechanical output power PM = ω M(ω). The electrical power drawn from the supply is P_elec = V I = PM + P_loss, where resistive (I^2 R), core, and no-load losses remain positive even at no load; a stepper motor spinning unloaded does not consume zero power. Since PM enters Etotal in Eq. (1) and EE in Eq. (6), Proposition 1 and the Section V comparisons optimize and evaluate mechanical output power, not the energy actually drawn by the driver. The authors themselves note that the zero-power no-load condition is unachievable, which exposes the issue. Additionally, M(ω) in Eq. (4) is the pull-out torque, i.e., the maximum torque available before losing synchronism, not the torque actually developed for the given antenna load; the mechanical power required to move the antenna should be based on load torque. These are load-bearing problems: replacing PM by a realistic electrical input model changes the shape of f(v) and can invalidate the monotonicity conclusion in Proposition 1.","section":"§II-B, Eq. (3)"},{"comment":"The kinematic relation ω = v/l0, with l0 called the 'outer radius' of the lead screw, is not the kinematics of a lead screw. For a screw with lead L, the linear speed is v = (L/(2π))ω, and the displacement per step is (L/(2π))ωD, independent of the screw's outer radius. Using l0 changes the mapping between speed and angular speed, and therefore changes the shape of PM(v), the numerical values of vmax and ds, the candidate position set Ct, and all optimized positions reported in Section V. Figures 4-9 are specific to the radius-based mapping and need to be re-derived under correct lead-screw kinematics.","section":"§II-A and §II-B, v = l0ω and ds = ωD l0"},{"comment":"The feasibility check in line 5 is inverted. Constraint (11a) requires |xt-x0|/vmax ≤ T, so an infeasible candidate satisfies |xt-x0|/vmax > T. The code sets EE* = -∞ when the condition is < T, which is exactly when the position is feasible, and leaves truly infeasible positions to be processed. Under the simulation parameters all candidate positions are feasible, so the numerical figures are unaffected, but the algorithm as written does not enforce constraint (11a) in general and therefore does not solve (P2) as claimed.","section":"Algorithm 1, line 5"}],"minor_comments":[{"comment":"The text refers to 'Fig. 2(a)' when discussing the decreasing pull-out torque; the correct reference is Fig. 3(a).","section":"§IV-A, after Eq. (10)"},{"comment":"The step angle is stated as ωD = π/12 rad/s; the unit should be radians (or degrees), not rad/s.","section":"§V, simulation parameters"},{"comment":"The text says Fig. 3 plots quantities versus the load speed v, but the horizontal axes are labeled 'Angular speed (rad/s)'. The text and figures should be aligned, and the distinction between PM as output power and as electrical input consumption should be made explicit.","section":"Fig. 3 and §II-B"},{"comment":"In Eq. (5), R is a spectral efficiency in bit/s/Hz, while the EE in Eq. (6) is reported in bit/s/Joule; a bandwidth factor should be introduced, or the units should be stated consistently.","section":"Eqs. (5)-(6)"},{"comment":"The iteration indexing is confusing: with l=1 and P(l-1)=Pmax, the loop increments l before computing P(l). It would be clearer to state explicitly that η(0) is computed from the initial transmit power Pmax.","section":"Algorithm 1, iteration indexing"}],"recommendation":"major_revision","confidential_remarks":"The core modeling error in Eq. (3) is central enough that the numerical conclusions cannot be accepted as they stand. I recommend major revision rather than rejection because the optimization machinery is largely reusable and the model can, in principle, be corrected within the paper's stated scope; however, the authors should expect to re-derive the speed monotonicity and rerun all experiments under a realistic electrical input power model and correct lead-screw kinematics. There is no evidence of target fitting or circularity in the derivation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe short version: this paper adds a speed-dependent stepper-motor power model to the MA energy-efficiency literature, proves that under that model the optimal speed is always the maximum, and solves the rest with Dinkelbach plus enumeration. The optimization math is correct; the physical power model has two real gaps that a referee should push on.\n\nWhat is actually new: prior EE work on MAs ([18], [19]) treated motion power as a constant. This paper instead uses the pull-out-torque expression PM(v) = (v/l0) M(v/l0) from motor theory, and shows (Proposition 1) that EE still increases with v, so v=vmax is optimal. That monotonicity result is simple but correct, and the Dinkelbach power update (15) and enumeration (16) are standard but properly applied. The paper is honest that FPA is the feasible point xt=x0, so the headline MA-beats-FPA is not a free lunch, but the numerical section quantifies the gain.\n\nWhere it gets soft. First, Eq. (3) counts the motor's mechanical output power as the driver's power consumption. Real electrical input also includes I^2R, core, and no-load losses; the text even admits the output power goes to zero at no load, which a real motor never does. So the optimized EE and the recommended positions are about mechanical work, not energy drawn from the supply. Second, for a lead screw the linear speed is v = (lead/(2π))ω, not v = l0ω with l0 the outer radius. Using the radius overestimates the step size and changes the shape of PM(v). Either fix can shift the optimal position and the size of the MA gain. Third, Algorithm 1's feasibility check is inverted (the condition should be '>' not '<'). As written it would reset EE* to -∞ for every feasible candidate in the simulations; the figures imply the actual implementation used the correct check, but the pseudocode is wrong. These are not deep mathematical flaws, but they are exactly the kind of hardware-modeling mistakes that matter if the results are meant to guide system design.\n\nBottom line: the paper deserves peer review, and the algorithmic core holds up. The power model and the kinematics need correction or a clear statement that the results are for mechanical power only. A careful reader in the MA community will get value from the monotonicity result and the Dinkelbach enumeration, but shouldn't take the absolute EE numbers seriously until the model is fixed.\n\nI'd send it to a serious referee with instructions to push on the power model, not to reject on the optimization.","headline":"A correct but physically under-specified MA energy-efficiency paper: the optimization is sound, but the power model counts mechanical output as electrical consumption and the lead-screw kinematics are off.","tokens_in":10449,"tokens_out":6574,"would_cite":true,"duration_ms":64962,"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":"The paper establishes that a movable antenna driven by a stepper motor can achieve higher energy efficiency than a fixed antenna, provided the motor runs at maximum speed and position and transmit power are optimized.","keywords":["movable antenna","energy efficiency","stepper motor","mechanical power consumption","Dinkelbach algorithm","antenna position optimization","pull-out torque","wireless communications"],"falsifier":"Measure the stepper motor's actual input electrical power over the speed range of Fig. 3 with the antenna load attached; if it does not fall to near zero at $\\omega_{\\max}$, or if the linear speed follows the lead screw's pitch rather than $l_0\\omega$, then the monotonicity in Proposition 1 can break and an interior speed may be optimal.","tokens_in":9490,"feed_emoji":"⚡","tokens_out":6980,"duration_ms":69626,"temperature":0.7,"pith_summary":"This paper asks whether movable antennas remain worthwhile once the electricity used by their mechanical drivers is counted. It answers yes, under a power model taken from electric motor theory: a stepper-motor-driven movable antenna can achieve higher energy efficiency than a fixed-position antenna, despite the extra mechanical power. The key structural result is Proposition 1: for a fixed destination and transmit power, the system's energy efficiency increases with the antenna's moving speed, so the motor should always run at its maximum speed. With that speed fixed, the optimal transmit power is obtained in semi-closed form by Dinkelbach's algorithm and the optimal discrete position by enumeration. If correct, the paper turns moveable-antenna energy efficiency from an open question into a tractable optimization problem.","feed_headline":"Energy efficiency rises with motor speed in movable-antenna systems","feed_subtitle":"A stepper-motor-powered antenna beats a fixed one when it moves at top speed and balances position with power.","key_machinery":"The central object is the stepper-motor power function $P_M = \\omega M(\\omega)$, with $\\omega = v/l_0$ and pull-out torque $M(\\omega)$ decreasing in $\\omega$. The proof of Proposition 1 rewrites the objective as $\\mathrm{EE} = R(x_t, P)/(P + P_s + f(v)|x_t - x_0|)$ with $f(v) = P_M/(vT - |x_t - x_0|)$, and shows $f$ decreases with $v$ because $dM/d\\omega < 0$. That monotonicity is what forces $v = v_{\\max}$ and makes the remaining problem a one-dimensional power optimization plus a finite position search.","core_discovery":"The paper's central claim has two parts. First, in the modeled stepper-motor system, the energy efficiency $\\mathrm{EE}(P, x_t, v)$ is monotonically increasing in the moving speed $v$ for any fixed antenna destination and transmit power, because the motor's pull-out torque decreases with angular speed and the movement time shrinks as $v$ grows. Therefore the speed constraint binds: $v = v_{\\max}$ is optimal. Second, for any fixed position, the optimal transmit power is the unique solution of a concave Dinkelbach subproblem, given in closed form as $P = \\min\\left([1/(\\eta\\ln 2) - \\sigma^2/|h(x_t)|^2]^+, P_{\\max}\\right)$, and the optimal position is found by scanning the discrete candidate set. Numerical evaluation with the AM2224 stepper motor and a field-response channel model shows that the movable-antenna system outperforms the fixed-position antenna in energy efficiency, with optimized positions lying close to the initial position to save movement energy.","pith_inferences":["If the model were upgraded to electrical input power including resistive and core losses, $P_M$ would not vanish at high speed, and the monotonicity argument could yield an interior optimal speed; this is a testable extension, not a claim of the paper.","The paper's kinematic relation $v = l_0\\omega$ treats the lead screw's outer radius as the effective lever arm; with the standard lead-screw relation $v = (\\text{lead}/2\\pi)\\omega$, the step size and the power curve change, which would alter the optimized positions reported in Section V.","The same speed-monotonicity idea could be applied to multi-antenna or rotatable-antenna platforms, but only if their driver power also decreases with speed.","A direct measurement campaign comparing this motor model with input power readings from a real stepper driver would calibrate whether the claimed zero-power no-load point is physically reachable."],"forward_implications":["The optimal operating point for a stepper-motor movable antenna is to move at maximum speed for the entire positioning phase; slowing down never improves energy efficiency in this model.","With the speed fixed, the transmit-power subproblem has a water-filling-type closed-form solution, and scanning the candidate positions gives the global optimum in $O(J_x I_1)$ time.","The optimal antenna position generally sits close to the initial position rather than at the best channel point, because movement energy and movement delay penalize long trips.","As the channel coherence time grows, the mechanical-power penalty vanishes and the energy efficiency approaches the classical ratio $R/(P + P_s)$, matching earlier movable-antenna energy-efficiency studies.","A movable-antenna system can beat a fixed-position antenna in energy efficiency even with mechanical power counted, but only if position and transmit power are optimized jointly; rate-only optimization loses energy efficiency."],"supporting_citations":[{"why":"Supplies the stepper-motor power model $P_M = \\omega M(\\omega)$, the pull-out torque expression, and the assumption that acceleration and deceleration energy is negligible.","marker":"[20]"},{"why":"Supplies the field-response channel model and the movable-region discretization used for the system model and simulation.","marker":"[3]"},{"why":"Supplies the Dinkelbach fractional-programming framework and its convergence guarantee, used for the transmit-power update.","marker":"[21]"},{"why":"Supplies the AM2224 stepper-motor parameters used in the numerical results.","marker":"[24]"},{"why":"Prior movable-antenna energy-efficiency work with a motion-power model; serves as a baseline and motivates the need for a speed-dependent driver model.","marker":"[18]"},{"why":"Prior statistical-CSI movable-antenna energy-efficiency study; another baseline that treats driver power more coarsely and motivates this paper's model.","marker":"[19]"}],"fun_headline_variants":["Faster movement lifts energy efficiency in movable-antenna systems","Movable antennas beat fixed ones when moving at top speed","Stepper-driven antennas: Speed up for better energy efficiency","Optimal speed and power make movable antennas energy-efficient","Move fast, save energy: Movable antennas outperform fixed"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes the motor's electricity use equals its mechanical output $\\omega M(\\omega)$, which falls to zero at high speed, and that acceleration and deceleration cost nothing; if real electrical losses or start-up transients matter, top speed may not maximize efficiency.","fun_headline_variants_meta":{"raw":{"variants":["Faster movement lifts energy efficiency in movable-antenna systems","Movable antennas beat fixed ones when moving at top speed","Stepper-driven antennas: Speed up for better energy efficiency","Optimal speed and power make movable antennas energy-efficient","Move fast, save energy: Movable antennas outperform fixed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000638,"raw_usage":{"total_tokens":2956,"prompt_tokens":980,"completion_tokens":1976,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":1895}},"tokens_in":596,"tokens_out":1976,"duration_ms":16131,"temperature":1.0,"reasoning_tokens":1895,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:54:40.371217+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the stepper motor's actual input electrical power over the speed range of Fig. 3 with the antenna load attached; if it does not fall to near zero at $\\omega_{\\max}$, or if the linear speed follows the lead screw's pitch rather than $l_0\\omega$, then the monotonicity in Proposition 1 can break and an interior speed may be optimal.","supporting_citations":[{"cited_title":"Stepper Motors, Series AM2224,","cited_arxiv_id":null,"evidence_quote":"Supplies the AM2224 stepper-motor parameters used in the numerical results."},{"cited_title":"G lobally optimal movable antenna-enhanced multi-user communicati on: Discrete antenna positioning, motion power consumption, and imperf ect CSI,","cited_arxiv_id":null,"evidence_quote":"Prior movable-antenna energy-efficiency work with a motion-power model; serves as a baseline and motivates the need for a speed-dependent driver model."}],"review_version":1}