Source-linked AI summary
Cross-Band Movable-Antenna Communications under Frequency-Dependent Multipath
Guangchen Wang, Zhifeng Tang, Haiyao Yu, Nan Yang, Salman Durrani, Xiangyun Zhou
TL;DR
The paper addresses the limited study of movable-antenna spatial behavior across distinct bands under frequency-dependent multipath, where bands can favor different configurations despite sharing one physical layout. It models this setting, derives cross-band spatial relationships and bounds, and develops CAGO and CBGT; CAGO outperforms practical benchmarks while CBGT approaches CAGO performance at lower online computational cost.
Problem
Prior MA studies mainly address single-band or contiguous wideband transmission, leaving the cross-band configuration conflict under frequency-dependent multipath unexplored.
Source: §I · p. 2Method
The paper models shared propagation geometry with band-dependent multipath powers and phases, derives spatial scaling and performance bounds, and develops CAGO and CBGT for joint assignment, positioning, and precoding.
Source: §I · p. 2Results
CAGO consistently outperforms the considered practical schemes while remaining close to the independent-MA benchmark, and CBGT achieves near-CAGO sum-rate performance with substantially lower online computational cost.
Source: §V · pp. 12–13Takeaways & Limitations
CBGT with online refinement offers near-CAGO sum-rate performance at lower online computational cost for multi-band MA communication.
Source: §I · p. 2, §V · p. 13
Abstract
from arXiv · showhide
Movable antennas (MAs) provide additional spatial degrees of freedom by adapting their physical positions to the propagation environment. However, existing studies mainly focus on single-band or contiguous wideband transmission, leaving the cross-band spatial behavior of MAs under frequency-dependent multipath propagation largely unexplored. To address this gap, we investigate a downlink multi-band MA communication system where a common physical MA configuration is shared across multiple communication bands. Such sharing induces an inherent configuration conflict, as different bands often favor substantially divergent MA configurations. We first develop a frequency-dependent multipath channel model with shared propagation geometry but band-dependent multipath component powers and phases. Using this model, we formulate a sum-rate maximization problem by jointly optimizing user-band assignment, MA positioning, and transmit precoding. We further establish a cross-band spatial scaling relationship for the normalized channel power and derive both a position-independent channel gain upper bound and a sum-rate upper bound. Based on these results, we propose a cross-band analysis-guided optimization (CAGO) algorithm and a cross-band graph transformer (CBGT) to reduce online optimization complexity. Numerical results validate the derived cross-band spatial relationship and show that CAGO consistently outperforms the narrowband, wideband, and fixed-antenna benchmarks while remaining close to the idealized independent-MA benchmark. Additionally, CBGT with online refinement achieves near-CAGO sum-rate performance with substantially lower online computational cost, providing a practical framework for exploiting the spatial reconfiguration capability of MAs in multi-band communication systems.
I. Introduction
The paper addresses the unresolved cross-band configuration conflict that arises when a common movable-antenna layout serves bands with different spatial channel conditions. It models frequency-dependent multipath and jointly designs band assignment, antenna positions, and precoding, then develops analytical guidance and lower-cost optimization methods.
I. Introduction
- Existing MA studies focus on single-band or contiguous wideband settings, leaving unresolved how frequency-dependent multipath across distinct bands affects favorable antenna configurations.Different bands can favor different configurations, while frequent repositioning incurs delay and reduces effective transmission time.Source: §I · pp. 1–2
- The formulated design jointly optimizes user-band assignment, movable-antenna positioning, and transmit precoding to address cross-band configuration conflict and multiuser coupling.The shared layout must balance distinct spatial channel conditions across bands while assignment affects which users share frequency resources.Source: §I · p. 2
A. Multi-Band Multipath Channel Model
- The channel model shares propagation geometry across bands but allows multipath component powers and phases to vary with frequency, producing different spatial channel variations.The model attributes the differences to wavelength-dependent spatial phase and band-dependent relative multipath powers.Source: §I · p. 2, A. Multi-Band Multipath Channel Model · pp. 3–4
I. Introduction
- The analysis establishes a cross-band spatial scaling relationship for normalized channel power and derives position-independent channel-gain and sum-rate upper bounds.These results characterize how frequency-dependent multipath variations reshape favorable antenna positions across bands.Source: §I · p. 2
- CAGO uses the analytical results for screening, initialization, and joint optimization, while CBGT uses offline learning and lightweight online refinement to reduce online computational cost.Numerical results report that CAGO outperforms practical benchmarks while remaining close to the independent-MA benchmark, and CBGT achieves near-CAGO sum-rate performance at substantially lower online cost.Source: §I · p. 2
II. System Model
- The base station serves users over distinct bands using one common physical antenna configuration, while precoding can be designed independently for each band.Antenna positions lie within a predefined aperture and obey a minimum-spacing constraint.Source: §II · p. 3
B. Multi-Band Transmission
Each user is assigned to one communication band, and users sharing a band are spatially multiplexed with linear precoding. Because bands are orthogonal, interference is limited to users assigned to the same band.
B. Multi-Band Transmission
- Each user is assigned to exactly one communication band, and the users assigned to each band form that band’s user set.The binary assignment variable indicates whether a user is assigned to a given band.Source: B. Multi-Band Transmission · p. 4
- The base station uses linear precoding to spatially multiplex users assigned to the same band.Each user has a band-specific precoding vector and information symbol.Source: B. Multi-Band Transmission · p. 4
- Orthogonal frequency resources eliminate inter-band interference, so each user experiences multiuser interference only from users on the same band.The SINR expression underlies the corresponding achievable-rate expressions.Source: B. Multi-Band Transmission · p. 4
C. Problem Formulation
The section frames multi-band MA design as a coupled sum-rate optimization and characterizes how spatial channel behavior changes across bands. It derives a conditional cross-band scaling relationship and position-independent gain bounds.
C. Problem Formulation
- The design also enforces one assigned band per UE, minimum SINR requirements, a total-power limit, aperture limits, and minimum inter-MA spacing.These constraints accommodate heterogeneous UE quality-of-service requirements.Source: C. Problem Formulation · p. 5
- P1 jointly optimizes user-band assignment, MA positions, and transmit precoding despite binary decisions and coupling through interference and the shared MA configuration.Band assignment determines which UEs share frequency resources; the common configuration affects channels across all bands.Source: C. Problem Formulation · pp. 4–5
A. Cross-Band Spatial Channel Characteristics
- Normalized channel power is defined to isolate position-dependent spatial variation from band-dependent large-scale channel gain.The characterization first considers one MA communicating with one UE.Source: A. Cross-Band Spatial Channel… · p. 5
- When two bands share normalized MPC power profiles and pairwise MPC phase differences, their normalized spatial channel powers correspond under frequency-dependent spatial scaling for any displacement.The scaling compares band b1 at q0 + (fb2/fb1)d with band b2 at q0 + d.Source: A. Cross-Band Spatial Channel… · p. 5
- In practical channels, frequency-varying MPC powers and phases can produce different favorable and unfavorable MA locations across bands.Phase-difference changes shift constructive and destructive combinations; normalized power changes alter each MPC’s contribution.Source: A. Cross-Band Spatial Channel… · p. 5
- The propositions give position-independent channel-gain bounds for a single MA and for the channel vector with M MAs.The bound removes dependence on MA position and captures the normalized MPC power profile.Source: A. Cross-Band Spatial Channel… · pp. 5–6
- The bound assumes ideal coherent combining, which may be unattainable when finite-aperture MAs cannot align many MPCs simultaneously.It nevertheless provides a tractable basis for a system-level performance upper bound.Source: A. Cross-Band Spatial Channel… · pp. 5–6
B. Analytical Sum-Rate Upper Bound
The sum-rate upper bound relaxes the multi-band problem into band-level transmit-power and effective-spatial-dimension allocation. This convex bound provides an analytical benchmark and allocation guidance, but may be loose.
B. Analytical Sum-Rate Upper Bound
- The relaxed band-level problem optimizes transmit power and continuous effective spatial dimensions, yielding an analytical upper bound without enumerating user-band assignments.The relaxation enlarges the feasible set, with 0 ≤ r_b ≤ M and total effective spatial dimensions bounded by K.Source: B. Analytical Sum-Rate Upper Bound · p. 6
- The relaxed optimization is convex, and its optimal transmit-power allocation follows a waterfilling structure favoring bands with larger bandwidths or channel-gain bounds.The bound accounts for the finite total spatial degrees of freedom across bands.Source: B. Analytical Sum-Rate Upper Bound · p. 6
- The derived upper bound is tractable but may be loose because its derivation successively relaxes channel gain, precoding capacity, user SINR constraints, and discrete assignment.It is not a tight characterization of achievable sum rate.Source: B. Analytical Sum-Rate Upper Bound · p. 6
IV. Cross-Band Analysis-Guided Optimization
CAGO uses analytical channel-gain and sum-rate bounds to narrow the search and initialize joint optimization, then alternates precoding and antenna-position updates before refining assignments.
IV. Cross-Band Analysis-Guided Optimization
- CAGO screens infeasible user-band pairs using the channel-gain bound and uses the relaxed band-level solution to initialize user-band assignment and MA configuration.For fixed assignment, it alternates WMMSE precoder updates with MM antenna-position updates, then refines assignment through analysis-guided neighborhood search.Source: §IV · p. 7
A. Analysis-Guided Screening and Initialization
Analysis-guided screening and initialization use the channel-gain bound and relaxed band-level allocation to reduce the joint assignment and antenna-configuration search.
A. Analysis-Guided Screening and Initialization
- The position-independent channel-gain bound screens user-band pairs whose SINR requirement cannot be met even under an interference-free upper-bound condition.A screened pair is excluded by fixing its assignment variable to zero; if any user has no candidate band, the problem is infeasible.Source: A. Analysis-Guided Screening and… · p. 7
- The relaxed upper-bound solution guides assignment initialization through user-band suitability scores and target band loads based on preferred power and effective spatial-dimension allocations.The initial assignment is obtained by solving a reduced mixed-integer linear program that penalizes deviations from target loads.Source: A. Analysis-Guided Screening and… · p. 7
- The band contributing most to the analytical upper bound is chosen as an anchor for single-band position updates, and scaled, uniform, and anchor configurations form initialization candidates.Scaled configurations are only candidates: the exact spatial scaling relationship requires matching normalized MPC power profiles and pairwise MPC phase differences across bands, so candidates are evaluated using actual multi-band channels.Source: A. Analysis-Guided Screening and… · p. 7
- Candidate assignments and MA configurations are checked for SINR and power feasibility by solving a minimum-power problem, with feasible candidates supplying precoder initialization.The configuration with the largest sum rate after several precoding updates is selected as the initial MA configuration.Source: A. Analysis-Guided Screening and… · pp. 7–8
1) WMMSE-Based Precoding Update:
For fixed assignments and antenna positions, WMMSE updates precoders; for fixed assignments and precoding variables, MM updates the shared antenna configuration while maintaining feasibility.
1) WMMSE-Based Precoding Update:
- For fixed assignment and MA configuration, the rate objective is transformed into a WMMSE form, and equalizers, MSE weights, and precoders are successively updated until convergence.The precoder subproblem is a convex QCQP, and its MSE constraint guarantees the corresponding SINR requirement.Source: 1) WMMSE-Based Precoding Update · p. 8
2) MM-Based MA Position Update:
- For fixed assignment and precoding variables, MM constructs quadratic majorizers using band-dependent channel curvature to update the common MA positions.Inner approximations handle minimum spacing; accepted updates remain feasible for the original problem, with backtracking when the majorization condition fails.Source: 2) MM-Based MA Position Update · p. 8
C. Analysis-Guided Assignment Refinement and Overall Algorithm
CAGO refines user-band assignments by ranking moves and swaps analytically, then testing candidates against feasibility and actual sum rate. Its updates produce a convergent, non-decreasing sum-rate sequence, though global optimality is not guaranteed.
C. Analysis-Guided Assignment Refinement and Overall Algorithm
- CAGO accepts a move or swap only after feasibility checks and actual sum-rate evaluation; analytical scores order candidates rather than determine acceptance.Infeasible candidates are discarded, and only a candidate satisfying the acceptance condition is accepted.Source: C. Analysis-Guided Assignment… · pp. 8–9
D. Convergence and Computational Complexity
- The CAGO sum-rate sequence is non-decreasing and convergent, while fixed-assignment continuous-variable limit points are stationary under standard MM conditions.The sequence is bounded by the sum-rate upper bound; the stationary-point result assumes MM tightness and first-order consistency.Source: D. Convergence and Computational… · p. 9
- Assignment updates increase sum rate by at least ϵA, so only finitely many are accepted; complete move-and-swap evaluation yields neighborhood-local, not global, optimality.With a truncated neighborhood, local optimality applies only to evaluated candidates.Source: D. Convergence and Computational… · p. 9
- CAGO complexity scales as O(IO [IQ (IWCW + IBCQ) + NA (CF + IWCW)]), with analysis-guided screening reducing evaluated assignments to NA ≪ |N(A)|.Minimum-power feasible solutions initialize WMMSE updates, further reducing practical computational cost.Source: D. Convergence and Computational… · pp. 9–10
E. Cross-Band Graph Representation
The graph represents candidate user-band assignments and their cross-band competition, same-band interference, and coupling through a common MA configuration. Relation-aware attention updates node representations to encode these distinct relationships.
E. Cross-Band Graph Representation
- Candidate user-band pairs form graph nodes, with edges linking alternative bands for the same UE, different UEs on the same band, and a global node for the shared MA configuration.These relations represent cross-band competition, potential multiuser-interference coupling, and network-wide configuration information, respectively.Source: E. Cross-Band Graph Representation · p. 10
F. Relation-Aware Graph Transformer
- Relation-specific attention updates user-band embeddings to capture assignment coupling and intra-band interference, while the global embedding aggregates information about the common MA configuration.The node features incorporate frequency-dependent multipath characteristics and analytical quantities from the channel analysis.Source: F. Relation-Aware Graph Transformer · p. 10, E. Cross-Band Graph Representation · p. 10
G. Assignment and MA-Configuration Decoding
The decoder selects one candidate band per UE and projects its predicted common MA configuration onto a feasible set. CBGT is trained offline from multi-start CAGO solutions and uses online candidate checks and refinement.
G. Assignment and MA-Configuration Decoding
- Assignment probabilities are normalized over each UE’s candidate bands, while analytical screening excludes pairs that cannot meet the required SINR.The global-node representation predicts the common MA configuration relative to a uniformly spaced feasible reference, followed by a feasibility-constrained projection.Source: G. Assignment and MA-Configuration… · p. 10
H. Training and Online Refinement
- CBGT is trained offline on multi-start CAGO solutions using assignment and MA-configuration losses plus a differentiable surrogate sum-rate term.The assignment and configuration losses guide predictions toward CAGO solutions, while the surrogate term promotes the original sum-rate objective.Source: H. Training and Online Refinement · pp. 10–11
- Online refinement checks high-probability assignments for feasibility, evaluates feasible candidates with WMMSE updates, then jointly refines precoders and MA positions.The final solution satisfies the original assignment, SINR, power, aperture, and spacing constraints; the graph prediction initializes the optimization.Source: H. Training and Online Refinement · p. 11
V. Numerical Results
The numerical results validate the cross-band spatial analysis and show that CAGO performs close to the idealized independent-MA benchmark, while CBGT with online refinement approaches CAGO with lower online computational cost. The conclusion presents these findings as an approach to exploiting MA spatial reconfiguration in multi-band systems.
V. Numerical Results
- The normalized channel-power patterns match under frequency-dependent coordinate scaling when normalized MPC powers and pairwise phase differences are identical across bands.With band-dependent MPC powers and reference phases, the patterns have different spatial structures and cannot be related through simple coordinate scaling.Source: §V · p. 11, Figure 2 · p. 11, Figure 4 · p. 12
- CBGT’s normalized training and validation losses decrease and converge, reaching approximately 0.11 and 0.16, respectively.Training loss is nearly stable after about 300 epochs, while validation loss follows a similar trend with moderate fluctuations.Source: §V · p. 12, Figure 3 · p. 12
- CAGO consistently outperforms the considered practical benchmarks while remaining close to independent-MA; CBGT with online refinement achieves sum rates close to CAGO.These comparisons hold across the reported variations in UE count, MA count, and multipath richness.Source: Figure 5 · p. 12, §V · pp. 12–13, §VI · p. 13
- As UE count increases, CAGO, CBGT, and independent-MA sum rates generally rise, while wideband and fixed-antenna rates gradually saturate.For the narrowband scheme, sum rate declines at K = 5 and no feasible solution is obtained for K ≥6 under the considered constraints.Source: Figure 5 · p. 12
- For K = 6, feasible schemes generally gain sum rate as M increases to around 8, after which gains diminish and a slight decrease appears for M > 8.The decline does not establish an intrinsically optimal MA count.Source: §V · p. 12
- As MPC count L grows, feasible schemes generally gain sum rate with diminishing gains; CAGO remains near independent-MA and refined CBGT near CAGO.Wideband and fixed-antenna schemes saturate more for large L, and narrowband remains infeasible throughout the considered range.Source: §V · p. 13, Figure 6 · p. 13
- CBGT consumes less than one tenth of CAGO’s CPU cycles at K = 10 and has the lowest computational cost among feasible schemes for K ≥5.The independent-MA scheme has the highest cost because it optimizes MA positions separately across communication bands.Source: §V · p. 13, Figure 7 · p. 13