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CSI-Free Positioning of Movable Antennas for IoT Networks: A Compositional Kernelized Bandit

Wonseok Choi, Yunseob Tae, Jeongjae Lee, Songnam Hong

arXiv:2610.01285v1eess.SP

TL;DR

CSI-free multi-antenna positioning must be learned from scalar rate feedback after actuator-limited moves, even as the channel changes during transit. The paper combines a pairwise compositional kernel with CoMoveUCB’s persistent target selection and proves sublinear dynamic regret with polynomial dependence on array size. Simulations report that CoMoveUCB outperforms fixed, measure-then-optimize, and reachability-confined benchmarks across tested loadings.

  • Problem

    CSI-free positioning is difficult because configurations can be evaluated only after actuator-limited relocation, during which the channel changes and scalar feedback arrives without CSI.

    Source: §I · p. 1, A. System Model · p. 3

  • Method

    The paper uses a compositional kernel retaining antenna-pair interactions and CoMoveUCB, which selects and persistently approaches a target over the joint configuration space.

    Source: §I · p. 2

  • Results

    CoMoveUCB outperforms fixed, measure-then-optimize, and reachability-confined benchmarks across tested loadings, with sublinear dynamic regret and polynomial dependence on array size.

    Source: §VI · p. 10

  • Takeaways & Limitations

    The reported results support repositioning a movable-antenna array under realistic actuation limits for the tested IoT settings.

    Source: §VI · p. 10

Abstract

from arXiv · show

Movable antenna (MA) arrays reshape the propagation channel by mechanically changing the element positions, which suits Internet-of-Things access points whose devices cannot adapt on their own. Existing position optimization assumes the channel is known at every candidate configuration. In practice a configuration can be evaluated only after the array has moved there, over several slots limited by the actuator speed, during which the channel changes. We formulate the positioning of M MAs serving K < M devices without channel state information as a nonstationary kernelized bandit over the joint configuration space, driven by a single scalar rate feedback per slot under a reachability constraint and an actuation-energy cost. Since the information gain of a standard kernel grows exponentially with M , and the multiuser sum rate depends on the positions through a sum of per-antenna terms, we design a compositional kernel that retains interactions up to antenna pairs. On this kernel we propose CoMoveUCB, which selects a target configuration over the whole feasible set by coordinate ascent and retains it under a persistence rule. We prove sublinear dynamic regret with a polynomial dependence on M . Simulations show that CoMoveUCB outperforms fixed, measure-then-optimize, and reachability-confined benchmarks across loadings, confirming the value of repositioning an MA array under realistic actuation limits.

I. INTRODUCTION

CSI-free positioning becomes a sequential learning problem when antennas must move before a configuration can be measured, while the reward changes during transit. The paper formulates joint multi-antenna positioning under mechanical constraints and proposes a compositional-kernel bandit with a sublinear dynamic-regret guarantee.

I. INTRODUCTION

  • With movement-limited measurements, channel changes can make each observation outdated before the next, turning position selection into a sequential decision problem.CSI acquisition across candidate configurations incurs pilot overhead; the array also transmits from intermediate positions during transit.Source: §I · p. 1
  • For multiple antennas, coupled multiuser rewards, scalar feedback for an M-dimensional action, and joint target search rule out independent single-antenna learners.A generic joint-space kernel also has information gain that grows exponentially with M.Source: §I · pp. 1–2
  • The proposed compositional kernel retains interactions up to antenna pairs, keeping learning complexity polynomial in M rather than exponential under a generic kernel.Its pairwise structure is motivated by the additive per-antenna structure of the multiuser sum rate.Source: §I · p. 2
  • CoMoveUCB selects a joint target, retains it under a persistence rule, and approaches it within actuation limits while achieving sublinear dynamic regret under standard assumptions.The guarantee uses an information-gain subadditivity bound and a travel bound for antennas moving toward a common target.Source: §I · p. 2
  • CoMoveUCB outperforms fixed, random, measure-then-optimize, and reachability-confined policies charged the same movement cost; an ablation attributes most gain to optimistic target selection and the compositional kernel.The supplied passage reports the comparison and attribution without giving numerical benchmark values.Source: §I · p. 2

A. System Model

  • The AP serves K<M devices with a spaced linear array, receives one noisy scalar per slot, and moves toward a target under a per-slot stroke limit.Mechanical delay depends on the largest antenna displacement, while energy accumulates across all antenna displacements.Source: A. System Model · pp. 2–3

B. Problem Formulation

The objective is cumulative reward net of actuation energy, but the reward is revealed only causally through noisy observations. Dynamic regret compares the policy with an equally constrained oracle, which is useful analytically but computationally intractable beyond small arrays.

B. Problem Formulation

  • The policy seeks to maximize accumulated reward after subtracting actuation energy.The reward sequence is revealed only causally through noisy observations.Source: B. Problem Formulation · p. 3
  • For M=6, the oracle's dynamic program has about 4 × 10^9 grid states, so it serves as an analytical reference rather than a simulation benchmark.The oracle is intractable to compute beyond small arrays.Source: B. Problem Formulation · p. 3
  • The regret objective is sublinear in T with high probability, so time-averaged performance approaches that of the oracle as the horizon grows.The oracle knows the reward sequence in advance but shares the policy's initial position, reachability constraint, and actuation-energy cost.Source: B. Problem Formulation · p. 3

III. COMPOSITIONAL KERNELIZED BANDIT

CoMoveUCB estimates the reward over the joint antenna configuration space using a compositional kernel and a sliding-window estimator. The kernel retains unary and pairwise interactions, reflecting the reward structure while keeping information gain polynomial in the number of antennas.

A. Reward Estimation with a Compositional Kernel

  • Reward estimates use kernel ridge regression over the w most recent observations, balancing spatial correlation against temporal staleness.The window length w balances estimation noise against the staleness of older observations.Source: A. Reward Estimation with a… · p. 4
  • The pairwise truncation follows from the Gram-matrix structure, with higher-order interactions expected to weaken as K/M decreases and conditioning improves.The additive Gram structure holds for any channel model, while conditioning is channel-dependent; the approximation grows looser as K/M approaches unity.Source: A. Reward Estimation with a… · p. 4
  • The kernel combines physics-informed unary terms with pairwise terms that encode antenna-pair separation and dependence on absolute positions.The pairwise products represent effects including blockage attenuation, path angular spread, and cross terms between distinct paths.Source: A. Reward Estimation with a… · p. 4
  • The compositional kernel retains interactions through antenna pairs, yielding polynomial rather than exponential information gain as the number of antennas grows.A standard kernel on the joint space has information gain that grows exponentially with M; the proposed kernel couples every antenna pair.Source: A. Reward Estimation with a… · p. 4

B. Movement-Aware Selection over the Joint Configuration

CoMoveUCB selects a target over the full joint configuration space while accounting for the effects of movement, then approaches it within actuator limits. A persistence rule limits redirection, and coordinate ascent provides a nondecreasing approximate target search.

B. Movement-Aware Selection over the Joint Configuration

  • Movement incurs actuation energy, transit reward loss, and estimate staleness, while only the energy cost appears explicitly in the regret objective.Transit loss and staleness enter through the reward collected at the array’s current position rather than at its target.Source: B. Movement-Aware Selection over the… · pp. 4–5
  • In Fig. 2, Local-UCB remains at the reachable peak while CoMoveUCB targets a peak over the whole configuration space and approaches it one stroke per slot.The figure shows one coordinate of the acquisition function, with faint curves representing neighboring slots.Source: Figure 2 · p. 5
  • The algorithm selects a joint target over the full feasible set and approaches it as far as the actuators permit each slot.It retains the target unless another configuration exceeds it by margin ∆, limiting redirection at a loss of at most ∆ per slot.Source: B. Movement-Aware Selection over the… · p. 5

C. Coordinate Ascent for Target Selection

  • Coordinate ascent starts from the previous target and retains the incumbent, so its acquisition value does not decrease, but a fixed number of rounds need not find the global maximizer.Each coordinate is updated over a finite grid satisfying the antenna-spacing constraint.Source: C. Coordinate Ascent for Target… · p. 5

D. Complexity

The per-slot procedure has polynomial dependence on the number of antennas, unlike exhaustive joint maximization. With one antenna, CoMoveUCB reduces to the single-antenna algorithm.

D. Complexity

  • Updating the Gram-matrix Cholesky factor costs O(w^3) from scratch or O(w^2) when sliding the window by one observation.Evaluating the kernel between the new observation and the window requires O(M^2w) operations.Source: D. Complexity · p. 6
  • The per-slot cost depends polynomially on M, in contrast to the O(G^M) cost of exhaustive joint maximization.The factor M inside the coordinate-ascent cost arises from pairwise kernel terms, and the factor w from posterior variance.Source: D. Complexity · p. 6
  • For M = 1, the pairwise kernel terms vanish and CoMoveUCB reduces to the single-antenna algorithm of [11].Coordinate ascent becomes exhaustive search over the grid X_g.Source: D. Complexity · p. 6

IV. REGRET ANALYSIS

The analysis establishes sublinear dynamic regret under stated kernelized-bandit assumptions. It bounds information gain and travel in the joint configuration space, while assuming exact target maximization.

IV. REGRET ANALYSIS

  • CoMoveUCB has a sublinear dynamic-regret bound, with information gain polynomial in M and travel bounded for M coordinates moving toward a common target.The travel analysis accounts for delay and energy governed by different norms.Source: §IV · p. 6

A. Preliminaries

  • The guarantee assumes reward functions lie in the kernel RKHS with bounded norm and range, and that observation noise is conditionally zero-mean and sub-Gaussian.The reward and noise conditions are stated in Assumptions 1 and 2.Source: A. Preliminaries · p. 6
  • The analysis assumes exact maximization of the acquisition function, while coordinate ascent approximates it for larger configuration spaces.The stated exact-selection assumption separates the statistical analysis from the combinatorial optimization problem.Source: A. Preliminaries · p. 6

B. Information Gain of the Compositional Kernel

The compositional kernel’s information gain is bounded by decomposing it into unary and pairwise components and applying subadditivity. This yields polynomial rather than exponential dependence on array size, at the cost of model error relative to a joint-space squared exponential kernel.

B. Information Gain of the Compositional Kernel

  • The kernel has M unary and pairwise components, each depending on at most two coordinates, so subadditivity yields an information-gain bound polynomial in M.The decomposition and subadditivity establish the array-size scaling used in the analysis.Source: B. Information Gain of the… · pp. 6–7
  • The compositional-kernel bound replaces the squared-exponential bound on the joint space, at the cost of model error.Unary and pairwise summands are bounded through their lower-dimensional projections and component rates.Source: B. Information Gain of the… · pp. 6–7
  • For positive-semidefinite kernel components, the information gain of their sum is no greater than the sum of their individual information gains.The bound is applied inductively to the compositional kernel’s components.Source: B. Information Gain of the… · pp. 6–7

C. Bounding the Travel

The travel analysis bounds movement by partitioning the horizon into journeys with fixed targets. Monotone coordinate motion limits travel and transit duration on each journey, so total movement is charged to target changes.

C. Bounding the Travel

  • With a fixed target, each coordinate moves monotonically toward its target component, bounding a journey’s total ℓ1 travel by MD.Across at most Nsw + 1 journeys, this gives the total travel bound in terms of target replacements.Source: C. Bounding the Travel · p. 7
  • A journey has at most D/ρmax transit slots because each transit slot reduces the remaining ℓ∞ distance by ρmax.Summing over journeys bounds the total transit slots by the number of target changes.Source: C. Bounding the Travel · p. 7
  • The analysis bounds actuation energy and transit loss together by C0(Nsw + 1).The target-switch count is controlled through the acquisition-function drift and the persistence margin.Source: C. Bounding the Travel · p. 7

D. Main Result

Under Assumptions 1–3, the theorem gives sublinear dynamic regret when the variation budget is o(T), for both a high-probability bound and its expected-regret counterpart. The guarantee depends on the information-gain and travel bounds, while approximate acquisition maximization can add a linear-in-horizon shortfall term.

D. Main Result

  • Combining the information-gain and travel bounds with the single-antenna regret decomposition yields the main guarantee.The proof accounts for confidence, actuation energy, transit loss, and grid approximation.Source: D. Main Result · pp. 7–8
  • Both the high-probability and expected-regret bounds are sublinear in T whenever VT = o(T), under Assumptions 1–3.The theorem’s bounds hide factors polylogarithmic in T and 1/δ.Source: D. Main Result · pp. 7–8
  • The regularity discussion distinguishes uniform smoothness under fixed-κ regularized zero-forcing from pure zero-forcing, which has the bound only with high probability when the array is large relative to the devices.The distinction concerns the analysis, not the reward-only observations used by the algorithm.Source: D. Main Result · p. 8
  • Approximate acquisition maximization with average shortfall εopt adds εoptT to the bound, which is sublinear only if εopt vanishes with T.At M = 4, K = 2, single-start ascent has εopt = 0.08 (0.03σf); three starts halve it at proportionate cost.Source: D. Main Result · p. 8

V. SIMULATION RESULTS

The simulation section evaluates CoMoveUCB against benchmark policies across loadings and reports an ablation study of its key components.

V. SIMULATION RESULTS

  • The evaluation compares CoMoveUCB with benchmark policies across loadings and includes an ablation study of key components.The supplied passage states the evaluation scope but gives no outcome comparisons.Source: §V · p. 8

A. Setup

The evaluation uses a six-antenna, four-device IoT access point over a 6,000-slot horizon, with piecewise-changing channels and constrained mechanical movement. Benchmarks share movement costs and reachability limits, while the reported figures compare objective gains over the fixed array and across loadings.

A. Setup

  • The main setup uses M = 6 antennas, K = 4 devices, a 6λ region, 6,000 slots, and 48 independent channel-and-noise realizations.The evaluated trajectory starts from an equally spaced placement over the central 60% of the region.Source: A. Setup · pp. 8–9
  • Each link has three paths, including a blocked line-of-sight path; the reward is regularized zero-forcing sum rate at 9 dB per-device SNR.The movement-cost coefficient is ce = 8 per λ, about one fifth of the stated boundary beyond which actuation energy exceeds any achievable rate gain.Source: A. Setup · pp. 8–9
  • The channel changes about every 58 slots on average, comparable to the approximately 58 slots needed for a full array reconfiguration.The environment includes 20 events and six device swaps per device over the horizon.Source: A. Setup · pp. 8–9
  • Estimator policies start from 40 spatial samples of a frozen channel snapshot, modeled as a pre-deployment site survey outside the evaluated slots.The evaluated trajectory itself remains subject to the reachability constraint.Source: A. Setup · p. 9

B. Benchmarks

  • The benchmark set includes fixed and random movement, sweep-and-hold, and learning policies; policies are charged the same actuation energy and subject to the same reachability constraint.Sweep-and-hold uses a 2,000-slot cycle, while GP-UCB shares CoMoveUCB’s kernel, window, and confidence parameter but does not price movement or transit loss.Source: B. Benchmarks · p. 9
  • The reported evaluation visuals compare objective gains over the fixed array and repeat the comparison across loadings.The window is set to w = 80, partly because the reward map changes about every 58 slots.Source: Figure 3 · p. 9, Table II · p. 9, A. Setup · p. 9

C. Comparison against the Benchmarks

CoMoveUCB gains more than benchmarks that either lack an estimator or restrict moves to one stroke, and it leads across tested loadings. Ablations attribute most of its gain to optimistic target selection and pairwise kernel terms, while persistence reduces travel without measurable reward loss.

C. Comparison against the Benchmarks

  • Sweep-and-hold gains 0.44, but its rigid translation never adjusts antenna spacing and its 2,000-slot hold becomes outdated against a map changing about every 58 slots.Random movement falls 0.90 bit/s/Hz per slot below the fixed array because its actuation energy is not offset by rate gain.Source: C. Comparison against the Benchmarks · pp. 9–10
  • CoMoveUCB gains 1.70 bit/s/Hz per slot, versus 1.17 for GP-UCB, and its margin over GP-UCB is 0.53 ± 0.07.The policies share the estimator, kernel, window, and confidence parameter; CoMoveUCB searches targets over the whole configuration space and prices movement.Source: C. Comparison against the Benchmarks · pp. 9–10
  • Across K = 2, 3, and 4, CoMoveUCB leads; its margin over Sweep-and-hold grows from 0.30 ± 0.04 to 1.26 ± 0.09 bit/s/Hz per slot.Its margin over GP-UCB varies between 0.43 ± 0.03 and 0.53 ± 0.07; the reported interpretation is that relative-position adjustment matters more as loading rises, while the benefit of looking beyond one stroke changes little.Source: C. Comparison against the Benchmarks · p. 10

D. Ablation

  • Optimistic target selection adds 0.70 ± 0.08 bit/s/Hz per slot over the posterior-mean target, with travel increasing from 70λ to 528λ.The uncertainty bonus draws the array toward unexplored configurations, among which it finds better ones.Source: D. Ablation · p. 10
  • Persistence leaves the objective unchanged within 0.07 ± 0.06 while reducing travel from 528λ to 466λ.The passage states that replacing a target before reaching it can keep the array in transit and make the regret bound vacuous if repeated.Source: D. Ablation · p. 10, Table III · p. 10
  • Replacing the compositional kernel with its unary part costs 0.72 ± 0.08 bit/s/Hz per slot and reduces travel from 466λ to 83λ.The unary estimator cannot represent how one antenna’s position changes the value of the others; the passage attributes identifying distant superior configurations to pairwise terms.Source: D. Ablation · p. 10, Table III · p. 10

VI. CONCLUSION

  • The compositional kernel retains interactions up to antenna pairs, and CoMoveUCB achieves sublinear dynamic regret with polynomial dependence on array size.The conclusion reports that simulations outperform fixed, measure-then-optimize, and reachability-confined benchmarks at every tested loading.Source: §VI · p. 10
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