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Single-Step Six-Dimensional Movable Antenna Reconfiguration for High-Mobility IoV: Modeling, Analysis, and Optimization
arXiv:2605.03321v1 [cs.NI] 5 May 2026
Maoxin Ji, Qiong Wu, Senior Member, IEEE, Pingyi Fan, Senior Member, IEEE, Kezhi Wang, Senior Member, IEEE, Wen Chen, Senior Member, IEEE, Cui Zhang, and Khaled B. Letaief, Fellow, IEEE
Abstract—The Six-Dimensional Movable Antenna (6DMA) system has emerged as a promising technology to enhance wireless capacity by fully exploiting spatial degrees of freedom. However, applying 6DMA to high-mobility Internet of Vehicles (IoV) scenarios faces significant challenges, primarily due to the difficulty of acquiring instantaneous Channel State Information (CSI) and the risk of service interruptions caused by mechanical reconfiguration delays. To address these issues, this paper proposes a low-complexity, CSI-free singlestep reconfiguration framework. First, we design a deterministic discrete position generation scheme based on a latitudelongitude grid with inherent topological structures. Leveraging graph theory, we explicitly model and theoretically derive the lower bounds of movement and time costs for antenna reconfiguration. Subsequently, utilizing the directional sparsity of 6DMA channels, we develop an adaptive optimization strategy that fuses offline environmental priors with online historical feedback. Furthermore, a periodic reconfiguration mechanism based on predicted cumulative vehicle distributions is introduced. By strictly restricting antenna adjustments to the first-order spatial neighborhood, the proposed single-step method effectively eliminates service interruptions. Simulation results demonstrate that the proposed scheme significantly outperforms traditional fixed and global-search-based benchmarks in terms of uplink sum rate, while incurring negligible mechanical overhead and latency, thereby validating its feasibility and robustness in highly dynamic vehicular networks. Index Terms—6DMA, Internet-of-Vehicles, user distribution.
I. I NTRODUCTION
T
HE evolution of 6G communication technologies is significantly driving the transformation of the Internet of Vehicles (IoV) [1]–[9]. IoV not only provides vehicle users with Part of this work has been submitted to IEEE International Conference on Communications (ICC), 24–28 May 2026, Glasgow, Scotland, UK. Maoxin Ji and Qiong Wu are with the School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China (e-mail: [email protected], [email protected]). Pingyi Fan is with the Department of Electronic Engineering, State Key laboratory of Space Network and Communications, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). Kezhi Wang is with the Department of Computer Science, Brunel University, London, Middlesex UB8 3PH, U.K (e-mail: [email protected]). Wen Chen is with the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: [email protected]). Cui Zhang is with the School of Internet of Things Engineering, Wuxi Institute of Technology, wuxi, 214121, China (e-mail: [email protected]). Khaled B. Letaief is with the Department of Electrical and Computer Engineering, the Hong Kong University of Science and Technology, Hong Kong (email: [email protected]).
intelligent, convenient, and diversified travel experiences but also triggers an explosive growth in data transmission demands [10]–[19], posing severe challenges to the resource efficiency and deployment strategies of wireless networks [20], [21]. To address this demand, Multiple-Input Multiple-Output (MIMO) [22], [23] and massive MIMO [24], [25] technologies have been successively introduced into the IoV domain. However, although increasing the number of antennas can significantly enhance array gain, the associated high hardware costs and radio frequency (RF) link power consumption restrict their large-scale application [26]–[30]. Therefore, exploring spatial degrees of freedom to improve system efficiency under the premise of a limited antenna scale has become a critical issue to be resolved. In recent years, Movable Antenna (MA) technology has received widespread attention as an emerging paradigm [31], [32], [33]. Its core idea is to reconstruct the channel by adjusting antenna positions, thereby suppressing interference and enhancing signal power [34]. Fluid Antenna [35] and TwoDimensional Movable Antenna (2DMA) [36], [37] technologies have been proposed to enhance system performance by adjusting individual antenna positions to capture small-scale Channel State Information (CSI) variations. However, fluid antennas typically require rapid switching of individual antennas along a one-dimensional space to suppress interference, necessitating frequent position changes, which is difficult to apply in IoV networks with rapidly changing instantaneous channel information. While 2DMA technology allows antennas to move within a given two-dimensional plane, granting certain spatial degrees of freedom, it also faces the issue of frequent movement. In particular, using a single antenna as the movement unit results in high movement frequency and mechanical overhead. Building on this, Shao et al. proposed a novel SixDimensional Movable Antenna (6DMA) technology [38]. In this architecture, all antennas are divided into multiple surfaces deploying rectangular antenna arrays, connected to a central processing unit (CPU) via extendable and rotatable rods, with flexible wires inside the rods for power supply and signal exchange [39]. Each surface can move in three-dimensional (3D) space, and its orientation can be rotated in 3D space, hence the name 6DMA. The 6DMA system possesses extremely high spatial flexibility. By adjusting the position and orientation of antenna surfaces to capture the spatial distribution of
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users, frequent adjustments are not required for scenarios with slowly varying spatial distributions [40]. Moreover, moving rectangular antenna arrays as units rather than single antennas significantly reduces movement costs. Existing studies indicate that 6DMA significantly outperforms traditional Fixed Position Antennas (FPAs) and other mobile antenna schemes. In [38], it shows that in scenarios with clustered user distributions, the spectral efficiency of 6DMA is improved by approximately 497% compared to FPA and 268% compared to fluid antennas or 2DMA schemes. However, the ideal 6DMA supporting continuous spatial movement poses significant challenges in hardware implementation. To address this, in [41], it proposed a 6DMA model based on discrete positions and rotational states, utilizing a Fibonacci sphere method to generate a set of discrete positions satisfying physical constraints. Furthermore, in [42], it revealed the directional sparsity of 6DMA channels for the first time, i.e., an antenna surface with a specific configuration provides high gain only to users in specific spatial regions. This characteristic is determined jointly by the distribution of environmental scatterers and the antenna radiation pattern. In [43], it proposed a hierarchical movement scheme to reduce the reconfiguration cost of 6DMA. These works have laid a solid theoretical foundation for the development of 6DMA. Despite the immense potential of 6DMA, its practical deployment faces severe challenges, particularly in the acquisition of CSI. Due to the flexible and variable antenna positions, traditional channel estimation methods are difficult to apply [44]. Existing optimization schemes mostly rely on statistical CSI obtained via Monte Carlo sampling or heuristic methods that collect large amounts of measurement data [45]. For instance, in [38], it estimated the average channel capacity via the Monte Carlo method and designed an alternating optimization scheme for antenna positioning. In [46], it designed a low-complexity 6DMA optimization algorithm based on statistical channel information. In [41], it adopted the Conditional Sample Mean (CSM) method to evaluate the benefit of 6DMA antenna positions without CSI and selected positions based on a greedy algorithm. However, this method requires sampling multiple antenna configurations to collect data under a fixed user distribution before updating, making it difficult to adapt to dynamic scenarios. Applying 6DMA to IoV scenarios faces two primary difficulties. First, the high-speed mobility of vehicles causes drastic temporal variations in user distribution and instantaneous CSI, necessitating frequent antenna reconfiguration. Second, IoV services have strict requirements for high reliability and low latency, while the delay caused by mechanical antenna reconfiguration may lead to intermittent service interruptions. In addition, although existing reference has provided in-depth analyses of the spatial characteristics of 6DMA, there is a lack of explicit modeling and quantitative analysis regarding the feasibility of antenna movement, movement cost (energy consumption), and time cost (latency). To address the aforementioned challenges, this paper proposes a low-complexity 6DMA single-step reconfiguration
framework suitable for IoV1 . We first design a discrete position generation method with a natural topological structure and quantify the reconfiguration cost based on graph theory. Subsequently, utilizing prediction information of vehicle distribution, we propose a strategy to rapidly optimize antenna positions within the neighborhood, achieving continuous coverage of dynamic traffic flow with extremely low mechanical overhead. The main contributions of this paper are summarized as follows: 1) We introduce 6DMA technology into high-dynamic IoV scenarios for the first time and establish a channel model based on multipath characteristics. A deterministic discrete position and rotation set construction scheme based on a latitude-longitude grid is proposed, which naturally possesses a clear neighbor topological relationship. Based on graph theory, utilizing Breadth-First Search (BFS) and a modified Hungarian algorithm, we define and theoretically derive the lower bounds of movement cost and time cost required for antenna configuration transitions. The analysis shows that, benefiting from the high connectivity of the discrete grid and the sparse distribution of antenna surfaces, these bounds are compact and achievable. 2) To cope with the rapid fluctuations in user distribution caused by high-speed vehicle movement, an optimization perspective based on predicted cumulative distribution rather than instantaneous distribution is proposed. By extending the prediction time window, the cumulative user distribution captures the relatively stable distribution trends in the environment, thereby significantly reducing the frequency of antenna reconfiguration and the physical overhead of each reconfiguration, enhancing system robustness. 3) Addressing the difficulty of acquiring instantaneous CSI and the high sampling overhead of traditional CSM methods, we propose an adaptive position optimization scheme fusing offline priors with online historical feedback. By exploiting the directional sparsity of 6DMA, an offline mapping library is established to link joint position-rotation states to effective coverage areas. During the online phase, historical service rates are used to dynamically correct mapping errors arising from environmental scattering changes, achieving efficient evaluation similar to CSM. 4) To solve the problem of intermittent service interruptions caused by multi-step mechanical movements, the reconfiguration action space of antenna surfaces is strictly restricted to the first-order physical neighborhood. This mechanism ensures that each antenna surface requires at most one step of movement to complete the configuration in each decision cycle, fundamentally eliminating the risk of service interruption. Given that vehicle movement exhibits certain spatiotemporal regularities, it is feasible to substitute the low-frequency global 1 The source code is available at: https://github.com/qiongwu86/SingleStep-6DMA-Reconfiguration-for-High-Mobility-IoV-Modeling-Analysis-andOptimization.
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complete set of all feasible configurations, where M and J represent the total numbers of discrete positions and rotational states, respectively. Specifically, qi = [xi , yi , zi ]⊤ ∈ R3 denotes the center coordinates of the i-th candidate position, and rj = [αj , βj , γj ]⊤ is the Euler angle vector describing the rotation from the reference attitude (with the normal vector pointing towards ex = [1, 0, 0]⊤ ) to the current attitude. For any rotational state j, the corresponding unit outward normal vector nj can be derived from the rotation matrix as: cos βj cos γj (1) nj = sin αj sin βj cos γj − cos αj sin γj . cos αj sin βj cos γj + sin αj sin γj Fig. 1. System Model
reconfiguration strategy used in static environments with a high-frequency fine-tuning neighborhood movement strategy. Simulation results demonstrate the effectiveness of the proposed method. The rest of this paper is organized as follows. Section II presents the system model, detailing the discretized 6DMA architecture, physical constraints, and the channel model tailored for high-mobility IoV scenarios, and formulates a predictiondistribution-based periodic optimization problem under singlestep constraints. Section III establishes a deterministic position generation scheme based on a latitude–longitude grid and analyzes the reconfiguration cost using graph theory. Section IV proposes an adaptive position optimization framework that integrates offline environmental priors with online historical feedback to enable CSI-free decision-making. Section V presents the simulation results and performance analysis. Finally, Section VI concludes the paper. II. S YSTEM M ODEL This paper considers an uplink communication scenario at a typical urban intersection, as illustrated in Fig. 1. Vehicle users are randomly distributed along two cross orthogonal roads and are served by a base station (BS) deployed at the center of the intersection. The network consists of a single BS and K vehicles, with the set of vehicles denoted by K = {1, 2, . . . , K}. Each vehicle is equipped with a FPA, whereas the BS employs a receiving system based on 6DMAs. The time domain is modeled using a discrete time-slot mechanism with a duration of ∆t. We assume that the vehicle mobility exhibits quasi-static characteristics, i.e., the position pk remains constant within a single time slot and is updated only at the slot boundaries based on velocities sampled from a truncated Gaussian distribution. A. Discretized 6DMA Architecture and Constraints The 6DMA system comprises U movable antenna surfaces connected to a CPU via extendable mechanical arms. Each surface is capable of independently adjusting its 3D spatial position and 3D rotational attitude. Constrained by mechanical precision and control complexity, the state space of the antenna surfaces is restricted to a discrete domain. Let P = {(qi , rj ) | i = 1, . . . , M ; j = 1, . . . , J} denote the
To describe the deployment state of the system, we introduce a binary decision matrix Z ∈ {0, 1}M ×J . Specifically, [Z]i,j = 1 indicates that an antenna surface is activated at position i with rotational state j. The system activates a total of U antenna PMsurfaces PJ (with U ≤ M ), subject to the capacity constraint i=1 j=1 [Z]i,j = U . Furthermore, a physically realizable deployment scheme must simultaneously satisfy the following geometric and hardware constraints: 1) Mutual Non-blocking Constraint: To prevent signal blockage or reflection interference between antenna surfaces, for any two activated surfaces (i, j) and (i′ , j ′ ) (i.e., [Z]i,j = [Z]i′ ,j ′ = 1 and (i, j) ̸= (i′ , j ′ )), the normal vector of surface (i, j) must not point towards the location of surface (i′ , j ′ ): n⊤ j (qi′ − qi ) ≤ 0.
(2)
2) CPU Visibility Constraint: The radiation directions of all antenna surfaces must face away from the CPU holder located at the origin to avoid line-of-sight obstruction: n⊤ j qi ≥ 0,
∀(i, j) ∈ supp(Z).
(3)
3) Minimum Separation Constraint: The Euclidean distance between any two activated positions must exceed a safety threshold dmin to prevent mechanical collision: ∥qi − qi′ ∥2 ≥ dmin ,
∀i ̸= i′ .
(4)
4) Single Occupancy Constraint: At most one antenna surface can be deployed at each discrete position: J X
[Z]i,j ≤ 1,
∀i = 1, . . . , M.
(5)
j=1
B. Hybrid-Field Channel Modeling Consider the uplink transmission from vehicle k to the BS. Each 6DMA surface integrates an FPA consisting of Q elements, resulting in a total number of receiving elements Ntotal = U × Q. Given the large-aperture characteristic of the 6DMA, we adopt a hybrid near-field/far-field channel model [47]. Specifically, signal propagation between surfaces is treated as far-field, while the phase differences among elements within a single surface retain near-field spherical wave characteristics. First, a local coordinate system is established to describe the direction of arrival (DoA). Let pk denote the coordinates of
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vehicle k. The unit line-of-sight (LoS) vector pointing towards antenna surface (i, j) is given by d̂k,i,j = (pk −qi )/∥pk −qi ∥. Based on the reference axis eref = [0, 0, 1]⊤ , we construct the tangent plane orthogonal basis vectors ui,j = (nj ×eref )/∥nj × eref ∥ and vi,j = nj × ui,j . The incident direction is projected onto the tangent plane as: d̂k,i,j − (n⊤ j d̂k,i,j )nj ∥ . d̂k,i,j = ∥d̂k,i,j − (n⊤ j d̂k,i,j )nj ∥
(6)
Consequently, the local elevation angle θ̃k,i,j and azimuth angle ϕ̃k,i,j are resolved as: θ̃k,i,j = arccos(n⊤ d̂k,i,j ), j ∥⊤ ∥⊤ ϕ̃k,i,j = atan2 d̂k,i,j vi,j , d̂k,i,j ui,j .
(7) (8)
The antenna gain follows the 3GPP radiation pattern standard [48]. The attenuation in the horizontal and vertical directions is defined as AH (ϕ̃) = − min(12(ϕ̃/ϕ3dB )2 , Am ) and AV (θ̃) = − min(12(θ̃/θ3dB )2 , Am ), respectively. The combined linear gain coefficient is expressed as: (lin) Gk,i,j = 10(Gmax −min(−(AH +AV ),Am ))/10 ,
(9)
where ϕ3dB and θ3dB represent the half-power beamwidths, Am denotes the sidelobe suppression ratio, and Gmax is the peak gain. The path loss model adopts the 3GPP UMi standard [48]. For a path distance dk,i = ∥pk − qi ∥, the LoS probability pLoS (dk,i ) is given by a piecewise exponential function (with parameters set to d1 = 18 and d2 = 36): d1 , 1 (1−e−dk,i /d2 )+e−dk,i /d2 , (10) pLoS (dk,i ) = min dk,i where the propagation state is determined via Monte Carlo sampling. In the LoS state, the path loss PLk,i,j,l depends only on the distance and the carrier frequency fc , which can be expressed as: PLk,i,j,l = 32.4 + 21 log10 dk,i + 20 log10 fc .
(11)
In the non-LoS (NLoS) state, a log-normal shadow fading χl with a standard deviation of σSF = 7.82 dB is superimposed, expressed as: PLk,i,j,l = 35.3 log10 dk,i + 22.4 + 21.3 log10 fc + χl . (12) (LS)
The corresponding large-scale channel gain is ηk,i,j,l = 10−PLk,i,j,l /10 . At the microscopic level, consider the m-th element on surface (i, j), whose global coordinates are ci,j,m = qi + um ui,j + vm vi,j , where um and vm represent the relative displacements within the array. The near-field phase shift received by this element is ϕk,i,j,m,l = − 2π λ ∥pk − ci,j,m ∥. Assuming the channel consists of a multipath set Dk,i,j , where each path undergoes independent Rayleigh fading ξ ∼ CN (0, 1), the composite channel coefficient for this element is modeled as: X q (LS) (lin) hk,i,j,m = ηk,i,j,l Gk,i,j,l ejϕk,i,j,m,l ξk,i,j,l . (13) l∈Dk,i,j
This model accurately decouples the effects of array gain, large-scale fading, near-field phase, and small-scale fading. To derive the aggregate channel vector, we first define the array response vector for a specific active surface (i, j) satisfying [Z]i,j = 1 as: gk,i,j = [hk,i,j,1 , . . . , hk,i,j,Q ]⊤ ∈ CQ .
(14)
By vertically concatenating the response vectors corresponding to all U activated entries in Z (sorted by position index i and rotation index j), the total channel vector hk ∈ CNtotal for user k is constructed. Consequently, the multi-user channel matrix is given by H = [h1 , . . . , hK ]. At this point, the channel matrix H(t) can be regarded as a nonlinear mapping function of the vehicle position distribution and the 6DMA configuration Z(t), concisely expressed as: H(t) = H({pk (t)}K k=1 , Z(t)).
(15)
Based on a matched filter receiver, the received signal-tointerference-plus-noise ratio (SINR) for user k is given by: Γk (H) = P
Pk ∥hk ∥2 |hH h |2
,
(16)
k n 2 n̸=k Pn ∥hk ∥2 +ε + σ
where n ∈ K represents the index of the interfering vehicle, and ε is a regularization factor introduced for numerical stability. Finally, the total PK uplink sum rate of the system is calculated as Rsum = k=1 B log2 (1 + Γk (H)).
C. Dynamic Prediction and Optimization Problem Formulation Due to the high mobility of vehicles in IoV scenarios, the user spatial distribution exhibits rapid time-varying characteristics. Although the 6DMA system can adapt to such changes by flexibly adjusting the antenna configuration, realtime reconfiguration in every time slot is impractical due to the limited response speed of the mechanical servo system and computational resources. Therefore, this paper proposes a periodic single-step reconfiguration strategy based on motion prediction. 1) Vehicle Kinematic Model: Time is discretized into time slots of duration ∆t. The position of vehicle k in slot t, denoted by pk (t) ∈ R3 , follows a linear kinematic model: pk (t + 1) = pk (t) + vk (t)ak (t)∆t,
(17)
where vk (t) ≥ 0 is the instantaneous speed, and ak (t) ∈ R3 is the unit direction vector satisfying ∥ak (t)∥ = 1. 2) Periodic Reconfiguration and State Prediction: To balance system adaptability and implementation complexity, we set the antenna configuration Z to be updated every N time slots. Define the set of time slots covered by the l-th reconfiguration period as Tl = {tl , . . . , tl + N − 1}, where the start time is tl ≜ (l − 1)N + 1. During this period, the antenna configuration remains fixed, i.e., Z(t) = Zl , ∀t ∈ Tl . Leveraging the spatiotemporal correlation of traffic flow, we employ a prediction mechanism PKbased on the instantaneous 1 average velocity v̄(t) = K k=1 vk (t) to estimate future
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trajectories. The predicted position p̂k is calculated recursively as: p̂k (t + 1) = p̂k (t) + ak (t)v̄(t)∆t, (18) with the initial condition set to the current observation p̂k (tl ) = pk (tl ). Based on this predicted trajectory, the average sum rate for the l-th period is defined as: K
1 XX B log2 (1 + Γk (H({p̂k (t)}, Zl ))) . N t∈Tl k=1 (19) 3) Single-Step Reconfiguration Constraint and Problem Formalization: Although prediction-based reconfiguration improves long-term average performance, allowing antennas to jump arbitrarily within the global discrete space may result in significant mechanical displacement delays. Particularly in a discretized grid, cross-region adjustments often require multistep mechanical actions, causing severe service interruptions. To address this, we propose a single-step reconfiguration mechanism. Let Il−1 = {pos1 , pos2 , . . . , posU } denote the set of position indices activated during the previous period, where posu ∈ {1, . . . , M } represents the index of the spatial position occupied by the u-th antenna surface within the global discrete position set. To resolve the ambiguity of antenna correspondence and prevent infeasible long-distance swapping, we distinguish the U antenna surfaces and track their individual trajectories. For the u-th antenna, its feasible search space for the current period is restricted to its closed neighborhood: Cavg (Zl ) ≜
N̄posu = Nposu ∪ {posu },
u = 1, . . . , U,
(20)
where Nposu represents the set of physical neighbors of position posu in the discrete grid. The definition of neighbors will be provided in a later section. This definition ensures that each antenna moves at most one step or remains stationary. Consequently, we formulate the optimization problem by introducing specific decision variables for each antenna to ensure their staying within their respective local neighborhoods. The problem is modeled as: ! U X (u) max Cavg Zl (21a) (u) U }u=1
{Zl
s.t.
u=1 J X
(u)
[Zl ]i,j ∈ {0, 1},
∀i, u,
(21b)
∀u,
(21c)
j=1 M X J X
(u)
[Zl ]i,j = 1,
i=1 j=1 (u)
[Zl ]i,j = 0, U X J X
(u)
∀i ∈ / N̄posu , ∀u,
[Zl ]i,j ≤ 1,
∀i,
(21d) (21e)
u=1 j=1
Physical Constraints (2), (3), (4), (u)
(21f)
where Zl ∈ {0, 1}M ×J represents the configuration matrix specifically for the u-th antenna. Constraint (21c) ensures each antenna selects exactly one position-rotation state. Constraint (21d) strictly limits the u-th antenna to its local neighborhood
Su , effectively eliminating the risk of logical teleportation between disjoint regions. Constraint (21e) prevents collisions by ensuring that no two antennas occupy the same position, even if their neighborhoods overlap. Finally, the aggregate PU (u) configuration Zl = u=1 Zl is used to evaluate the physical constraints and system capacity. Although the above problem is formally closed, the precise acquisition of H requires enormous pilot overhead due to the complexity of 6DMA channels. Furthermore, the objective function exhibits high non-convexity and non-linearity, making direct numerical solutions infeasible in millisecond-level IoV scenarios. To tackle this challenge, in the following sections, we exploit the beam direction sparsity of 6DMA to propose a fast heuristic algorithm that does not require instantaneous CSI. III. D ISCRETE P OSITION G ENERATION AND C OST M ODELING FOR M OVEMENT AND T IME A. Discrete Position Generation Based on Latitude-Longitude Grid To generate a set of discrete positions satisfying the aforementioned constraints on a spherical surface, a Fibonacci sphere-based method was proposed in [41]. However, such automatically generated positions lack natural topological relationships, requiring the calculation of pairwise distances to manually construct connections, which complicates the indepth analysis of antenna movement and time costs. To address this issue, we propose a deterministic discretization scheme based on a latitude-longitude grid. Assume the BS is located at the origin, and the 6DMA antenna surfaces are deployed on a sphere of radius r0 centered at the BS. The sphere is divided into F equally spaced meridians, with the set of −1 azimuth angles denoted by Φ = {ϕf = 2πf /F }F f =0 . To satisfy the minimum inter-antenna spacing constraint dmin , we first determine the first valid latitude circle closest to the pole. This latitude must satisfy two conditions simultaneously. First, the chord length between adjacent points on the latitude (with an azimuthal interval of 2π/F ) must not be less than dmin , leading to the constraint on the cylindrical radius of the latitude circle: dmin . (22) rfirst = 2 sin(π/F ) Second, the chord length from the pole to any point on this latitude must be at least dmin . Based on the chord length formula s = 2r0 sin(θ/2), the corresponding polar distance (the polar angle between the pole and the latitude) must satisfy: 2r0 sin(θfirst /2) ≥ dmin ,
(23)
combining the above two conditions, we set: dmin dmin θfirst = max arcsin , 2 arcsin . 2r0 sin(π/F ) 2r0 (24) The corresponding axial distance from the pole is given by: dpole = r0 (1 − cos θfirst ).
(25)
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Fig. 2. Illustration of the 8-neighbor topology and normal vector generation for general positions.
Fig. 3. Neighbor definition and discrete orientation generation for the polar positions.
To ensure that the axial distance between the first northern latitude and the first southern latitude is no less than dmin , we must verify: 2r0 cos θfirst ≥ dmin , (26) otherwise, the configuration is infeasible. The remaining axial length available for dividing intermediate latitudes is: D = 2r0 cos θfirst .
(27)
By fixing the axial spacing between adjacent latitude circles to dmin , the number of intermediate latitudes is determined as: D L= , (28) dmin where ⌊·⌋ denotes the floor function. Since the chord length between two points on a sphere is strictly greater than the difference in their z-coordinates, and the z-difference here is defined as dmin , the distance between any points on adjacent latitude circles exceeds dmin , thereby satisfying constraint (4). The total number of latitude circles includes the first northern latitude, the first southern latitude, and the L intermediate latitudes, totaling L + 2. Including the North and South Poles, the total number of discrete positions is: M = F · (L + 2) + 2.
(29)
Each non-pole position is represented in spherical coordinates as (r0 , θg , ϕf ), where θg denotes the polar angle of the g-th latitude circle, with g = 0 corresponding to the first northern latitude and g = L + 1 corresponding to the first southern latitude. As shown in Fig. 2, to define the neighborhood relationship, an 8-neighbor structure is established for each non-pole position and its adjacent polar positions, covering upper/lower neighbors on the same meridian, left/right neighbors on the same latitude, and four diagonal neighbors. For any current point qi and its two neighbors qi1 , qi2 forming a triangle, the unit normal vector is calculated as: (qi1 − qi ) × (qi2 − qi ) (m) , m = 1, . . . , 8. (30) ni = ∥(qi1 − qi ) × (qi2 − qi )∥ In addition, each position includes a radial outward normal
vector:
Fig. 4. Topological structure and orientation definition for positions on the first latitude circle.
(0)
ni
=
qi , ∥qi ∥
(31)
resulting in a total of J = 9 discrete orientations for each position. Fig. 3 illustrates the neighbor definition for the poles, where all points on the first latitude circle serve as neighbors, yielding J = F + 1 discrete orientations. Fig. 4 defines the neighbors for the first latitude circle, which includes the pole, left/right neighbors on the same latitude, and three points on the adjacent latitude (on the same and adjacent meridians), resulting in J = 7 discrete orientations. The generation of discrete orientations follows a similar method to that of intermediate positions, determining rotation directions via triangular facets formed with neighbors, and including the radial direction. Based on this, we can generate a graph according to the topological relationships between discrete positions and further analyze the movement patterns and costs of the antennas using graph theory. Let the set of discrete positions be Q = {qi }M i=1 , corresponding to an undirected adjacency graph G = (Q, E), where an edge (i, j) ∈ E exists if and only if qj ∈ Ni , i.e., position j is a neighbor of position i. B. Definition and Proof of Lower Bounds on Movement Cost and Time Cost Given the current antenna configuration set Z(t) and the next configuration set Z(t + 1), since the antennas are indistinguishable, the transition from Z(t) to Z(t+1) can be viewed as an unlabeled Multi-Agent Path Finding (MAPF) problem [49], [50]. Since the number of discrete positions is typically much larger than the number of configured antenna surfaces, the probability of mutual blocking during movement is low. Thus, the specific movement pattern is not difficult to solve. To define the movement and time costs of the configuration transition, we assume that the unit energy consumption for a single antenna surface to move to an adjacent discrete position is ∆E, and the unit time duration is ∆tstep . The rotational transformation of the antenna surface can be completed simultaneously with the positional movement and is therefore not considered separately. The lower bounds of the movement cost and time cost from configuration Z(t) to Z(t + 1) can
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be exactly solved using the BFS algorithm and the Hungarian algorithm. The shortest path for any antenna surface from an initial position qiu belonging to Z(t) to a target position qjv belonging to Z(t + 1) can be determined via BFS on graph G. The path length (in steps) is defined as: du,v = BFS(qiu , qjv ) ∈ N.
(32)
By running BFS for every pair of initial and target positions (iu , jv ), we obtain the distance matrix D = [du,v ] ∈ NU ×U . The total number of steps required for movement can be calculated using the Hungarian algorithm. Due to the high connectivity of the graph, there may exist multiple assignment schemes with the minimum total steps for the transition from Z(t) to Z(t + 1). To simultaneously ensure the minimum time cost, we slightly modify the Hungarian algorithm. We define a cost matrix with a penalty term: Cu,v = du,v + κd2u,v ,
(33)
where κ > 0 is a penalty coefficient. By incorporating the quadratic term d2u,v , we aim to construct a lexicographical optimization mechanism: the primary objective is to minimize the total movement steps (energy cost), while the secondary objective is to minimize the variance of the movement steps, which in turn minimizes the maximum displacement of any single antenna and thereby minimizes the time cost. The validity of this cost function is rigorously established through the following propositions. Proposition 1 (Priority of Total Energy Efficiency): To ensure that the algorithm strictly prioritizes the minimization of total movement steps Emin over the penalty term, the coefficient κ is required to satisfy the condition: κ<
1 , U · d2max
(34)
where dmax represents the diameter of the graph G (the maximum possible distance between any two nodes). Proof: Let XA and XB be P two distinct valid matching schemes. Let SA = = (u,v)∈XA du,v and PA P 2 d denote the total steps and the penalty sum (u,v)∈XA u,v for scheme A, respectively (similarly for scheme B). Assume that scheme A is superior in terms of energy efficiency, i.e., SA < SB . Since the steps are integers, the minimum difference is SB ≥ SA + 1. To guarantee that the modified Hungarian algorithm selects scheme A, the total cost JA needs to be strictly less than JB : SA + κPA < SB + κPB .
(35)
Considering the worst-case scenario where SB = SA + 1 and the penalty difference is maximized (i.e., PA approaches its theoretical maximum Pmax while PB → 0), the condition becomes: 1 . (36) SA + κPmax < SA + 1 + 0 =⇒ κ < Pmax The theoretical maximum penalty occurs when all U antennas move the maximum distance dmax , yielding Pmax = U · d2max . Thus, setting κ < (U · d2max )−1 ensures that the weighted
penalty term never exceeds the cost of a single movement step, thereby preserving the optimality of the total energy consumption. ■ Proposition 2 (Optimization of Time Cost via Load Balancing): For any two schemes with the same total movement steps (i.e., SA = SB ), the cost function with a quadratic penalty (n = 2) ensures that the solution with a more balanced step distribution (smaller maximum step) yields a lower total cost. Proof: This property is derived from Majorization Theory. Let the movement step vectors of two schemes be sorted in deA B B scending order: dA = (dA 1 , . . . , dU ) and dB = (d1 , . . . , dU ). If scheme A has a more uneven distribution (e.g., a larger maximum step) than scheme B while maintaining the same sum, vector dA is said to majorize dB , denoted as dA ≻ dB . According to the Hardy-Littlewood-Pólya inequality, for any strictly convex function f (·), if dA ≻ dB , then: U X
f (dA u) >
U X
f (dB u ).
(37)
u=1
u=1
In our cost function, the penalty term f (d) = κd2 has a second derivative f ′′ (d) = 2κ > 0, confirming that it is strictly convex. Therefore, the scheme with the more balanced distribution (scheme B) will result in a lower total penalty sum. Consequently, the modified Hungarian algorithm will automatically prefer the matching scheme that suppresses outliers, thereby minimizing the maximum single-antenna movement steps dmax and reducing the time cost Tmin . ■ The matching variable is defined as: ( 1, if antenna moves from qiu → qjv , xu,v = 0, otherwise.
(38)
The optimal matching is obtained by solving the following linear assignment problem: min
{xu,v }
s.t.
U U X X
Cu,v xu,v
u=1 v=1 U X v=1 U X
xu,v = 1,
∀u,
xu,v = 1,
∀v,
(39)
u=1
xu,v ∈ {0, 1}. Using the Hungarian algorithm, the optimal matching X̂ = [x̂u,v ] can be found in polynomial time. Let the corresponding distance matrix after matching be: Dassigned = D ⊙ X̂,
(40)
where ⊙ denotes the element-wise product, representing the distances of the selected pairs. The total movement steps (lower bound on energy cost) is defined as: Emin = ∆E
U X U X u=1 v=1
x̂u,v du,v ,
(41)
8
service data to adapt to the mobility characteristics of vehicle users.
Algorithm 1: Adaptive Single-Step Reconfiguration with Historical Feedback Input: Offline mapping library {Cg }, update interval N , initial warmup periods Linit , history weight factor ω, max simulation time Tmax . Output: Dynamic antenna configuration Z(t). 1 Initialize: Current configuration Z ← Default, History library H ← ∅, Period index l ← 0; 2 for t ← 1 to Tmax do 3 Update positions of all vehicles pk (t) based on kinematic model; 4 if (t − 1) (mod N ) == 0 then 5 l ← l + 1; 6 Predict vehicle trajectories for the upcoming period Tl ; S 7 Identify candidate search space U u=1 N̄posu based on Z and neighbors; 8 if l ≤ Linit then 9 Set current weight ωcurr ← 0 (Use offline prior only); 10 else 11 Set current weight ωcurr ← ω (Enable historical feedback); 12 end S 13 foreach position i ∈ U u=1 N̄posu do 14 Calculate offline prediction score Sipre based on active grids; 15 Retrieve historical rate R̄i from H to compute Sihist ; 16 Compute composite score Si via Eq. (47) using ωcurr ; 17 end 18 Select U positions with highest scores to form Inew ; 19 Determine optimal rotation j ∗ using offline stats; 20 Update antenna configuration Z ← Znew ; 21 end 22 Execute uplink transmission and measure sum rate; 23 if t (mod N ) == 0 then 24 Calculate average rate Rl for current period; 25 Update history library H ← H ∪ {(Inew , Rl )}; 26 end 27 end
A. Offline Environment Profiling and Space-Configuration Mapping Modeling
which is the sum of movement steps of all antennas multiplied by the unit energy consumption. The maximum single-antenna movement steps can be calculated as: dmax = max
u=1,...,U
U X
x̂u,v du,v ,
(42)
v=1
corresponding to the steps required by the slowest moving antenna. Therefore, the lower bound on time cost is defined as: Tmin = ∆tstep × dmax . (43) Here, it is assumed that all antennas start moving simultaneously, and the overall time is determined by the longest path. IV. CSI-F REE 6DMA R ECONFIGURATION M ETHOD In this section, we propose a fast, CSI-free antenna configuration method. This approach utilizes offline collected data to determine the initial antenna positions and dynamically adjusts the configuration based on both offline data and historical
Given the directional sparsity characteristic of 6DMA systems in complex scattering environments, users located in a specific physical space can typically achieve high-gain service only through a limited set of position-angle combinations. By exploiting the relatively static nature of macroscopic scatterers like buildings in urban environments, we can pre-construct a static mapping library that links each spatial grid to a preferred antenna configuration, serving as prior knowledge for online decision-making. First, the ground service area Ω = [0, X] × [0, Y ] is discretized into uniform grids with a side length of W . The total number of grids is denoted by Ngrid = ⌈X/W ⌉ · ⌈Y /W ⌉. For a grid with index g = (gx , gy ), its geometric center coordinates are set to cg = [(gx − 0.5)W, (gy − 0.5)W, zveh ]⊤ , where zveh represents the typical antenna height of a vehicle. To quantify the configuration gain, S typical user positions (s) {pg }Ss=1 are uniformly sampled within each grid g. For each tuple (qi , rj ) in the global discrete configuration set P, the average theoretical spectral efficiency within the grid is calculated as: S 1X S B log2 1 + Γk H({p(s) , r̄g (i, j) = g }s=1 ), (qi , rj ) S s=1 (44) where the Γk is calculated according to (16) based on static large-scale channel parameters. Theoretically, traversing all grids and feasible configurations allows for the establishment of a complete prior map. However, due to the massive number of combinations involving discrete positions M and rotational states J, an exhaustive search over the entire domain faces prohibitively high computational complexity. To address this issue, we propose a geometric pruning and hierarchical search strategy based on the geometric properties of 6DMAs to dynamically constrain the search space: 1) Geometric Hemispherical Pruning: Utilizing the LoS relationship between the BS and the target grid, obvious back-facing invalid positions are eliminated. The antenna positions are restricted to the grid-facing hemisphere, constructing a valid position subset Qhg : Qhg = qi ∈ Q | n⊤ (45) i (cg − qBS ) ≥ 0 , where qBS denotes the BS coordinates, and ni is the reference normal vector at position qi . This constraint ensures that the angle between the antenna position and the grid center does not exceed 90◦ . 2) Two-Stage Hierarchical Sampling: Based on Qhg , the candidate scale is further reduced. • Coarse-Grained Screening: Using the K-means clustering algorithm, Y representative anchor positions are uniformly selected within Qhg . The average rates of these positions under the default radial orientation are calculated to quickly evaluate their
9
coverage potential, from which the top Nseed seed positions with the highest rates are screened out. • Fine-Grained Expansion: Centered on these Nseed seed positions, an expanded search is conducted within their first-order physical neighborhood (which is still required to satisfy the hemispherical constraint) to discover local optimal positions. 3) Rotation Refinement: For the high-potential positions identified through the two-stage screening, all feasible rotational states j ∈ {1, . . . , J} are traversed to finally determine the optimal position-rotation combination. Through the above three-level search strategy, the directional sparsity of the 6DMA is fully utilized. While ensuring that the candidate set covers high-performance configurations, the search space is compressed by several orders of magnitude. Finally, for each grid g, the top H configurations with the highest rates are retained to form the offline preferred candidate set: Cg = {(qi , rj ) ∈ P | r̄g (i, j) ranks Top-H} . (46) This prior library Cg accurately captures the directional response characteristics under stable scattering environments and macroscopic geometry, providing a high-quality and compact decision-making basis for subsequent online antenna scheduling. B. Online Adaptive Optimization Based on Historical Rates Although the offline mapping library provides optimal solution suggestions for static environments, instantaneous channel perturbations caused by vehicle movement and prediction errors may lead to deviations between actual performance and prior estimates. To enhance the system robustness in dynamic environments, this paper proposes an adaptive configuration scheme fusing offline prior and online feedback. This scheme relies not only on the current predicted distribution but also makes full use of historical periodic measured data. By accumulatively learning from historical configuration performance, the evaluation of channel quality for each candidate position is continuously corrected, thereby guiding the antenna position and rotation decisions for the (l)-th period. 1) Multi-Dimensional Hybrid Scoring Mechanism: Recalling the problem formulation in Section II-C3, the feasible search space for the u-th antenna is restricted to its closed neighborhood N̄posu . To determine the optimal configuration, we first construct a comprehensive scoring function Si for every unique candidate position i contained within the union SU of these neighborhoods (i.e., i ∈ u=1 N̄posu ). This score is a weighted sum of the offline prediction score Sipre , the historical accumulated measured score Sihist , and the stability reward Bistab : Si = (1 − ω)Sipre + ωSihist + Bistab ,
(47)
where ω ∈ [0, 1] is a balancing factor used to adjust the weights of the offline prior and online historical feedback. a) Offline Prediction Score: This term aims to index the offline library using the predicted vehicle distribution. Let Gactive denote the set of active grids covered by the predicted
trajectory for the (l)-th period, where the predicted demand density of grid g is ρg and the maximum density is ρmax . We evaluate the hit status of position i in the preferred sets Cg of these grids: X ρg · [β0 + β1 (νg,i − 1)] · I(i ∈ Cg ), (48) Sipre = ρmax g∈Gactive
where I(·) is the indicator function, indicating whether position i exists in Cg , and νg,i represents the number of distinct rotational states associated with position i in Cg . Here, β1 > 0 is a multi-modal reward coefficient, which tends to favor robust positions that perform excellently under multiple rotations. b) Historical Accumulated Rate Score: This term utilizes historical data to correct prior biases. A constantly growing historical record library Hl−1 = {(Ik , Rk ) | k = 1, . . . , l − 1} is maintained, where Rk is the measured system average sum rate in the k-th period. For any candidate position i, its score depends on the average performance when activated in all past periods. The historical average contribution rate R̄i is calculated as: Pl−1 Pl−1 P k=1 I(i∈Ik )Rk , if l−1 k=1 I(i ∈ Ik ) > 0, (49) R̄i = k=1 I(i∈Ik ) R̄ otherwise, global , where the denominator counts the total number of times position i has been selected in history, and the numerator is the corresponding accumulated rate. If position i has never been selected (i.e., a cold-start position), it is filled with current Pthe l−1 1 global historical average rate R̄global = l−1 k=1 Rk to provide an unbiased initial estimate. The normalized historical score is given by Sihist = R̄i /Rnorm , where Rnorm is the historical peak rate. c) Stability Reward: To suppress frequent mechanical switching caused by marginal performance gains (the pingpong effect), an inertia reward is granted to positions activated in the current period: ( µ, if i ∈ Il−1 , stab Bi = (50) 0, otherwise, where µ is the stability threshold. 2) Greedy Position Assignment and Decoupled Rotation Decision: Based on the comprehensive score Si , we employ a position-rotation decoupling strategy to generate the new configuration Zl and approximate the optimal solution with minimal computational complexity. We first perform position selection using a conflict-aware greedy algorithm that respects the individual movement constraints. Specifically, for each antenna surface u (u = 1, . . . , U ) activated at position posu during the previous (l − 1)-th period, we traverse all candidate positions i belonging to its specific closed neighborhood N̄posu . We then identify the candidate i∗ that yields the maximum score Si within this local subset (i.e., i∗ = arg maxi∈N̄posu Si ) as the intended target for antenna u. To resolve potential conflicts where neighborhoods overlap, we prioritize the antenna-position assignments with higher scores to form the final non-conflicting position set Il . Following this, the rotation decision involves tallying the occurrence of rotation states in the currently active grids for
10
each position i ∈ Il via the offline library: X mi,j = I ((qi , rj ) ∈ Cg ) .
(51)
g∈Gactive
The rotation direction j ∗ = arg maxj mi,j with the highest accumulated frequency is selected as the optimal solution. If no prior match exists where mi,j = 0, the system defaults to the radial direction pointing toward the BS, specifically the j that minimizes n⊤ j qi . We then finalize the update by setting [Zl ]i,j ∗ = 1. The detailed procedure is outlined in Alg. 1. At the initialization stage, offline mapping solely determines the initial antenna positions. The quality of this initial solution is of critical importance to the proposed single-step 6DMA system. Upon accumulating sufficient online data, the weighting factor for historical feedback is restored to its nominal level. Additionally, the antenna reconfiguration interval N defines the prediction horizon for the cumulative vehicle distribution.
TABLE I VALUES OF PARAMETERS Parameter K U B dmin X ×Y F ϕ3dB Gmax
Value 30/35/40/45/50 16 20 MHz 0.1 m 300 m × 300 m 12 65◦ 8.0 dBi
Parameter v Q N r0 W S θ3dB
Value 10–20 m/s 4 (2 × 2) 20/10/1 0.5 m 15 m 20 25◦
V. S IMULATION R ESULTS In this section, we evaluate the performance of the proposed 6DMA system in IoV scenarios through numerical simulations implemented in Python 3.8. We consider a typical urban intersection scenario where roadside buildings serve as the primary reflectors. It is worth emphasizing that while the antenna configuration is optimized based on the predicted vehicle trajectories, the simulation performance metrics are evaluated using the actual vehicle positions. This approach validates the robustness of the proposed scheme against prediction errors. Detailed simulation parameters are summarized in Table I. To validate the superiority of the proposed method, we compare the following five schemes: 1) Fixed Position Antenna: A static deployment scheme serving as a benchmark. This scheme consists of four 90◦ sectors, each equipped with a fixed rectangular antenna array and a uniform 15◦ downtilt. The total number of antenna elements is the same as that of the 6DMA system. 2) Circular Position 6DMA: Four sectorized surfaces move along a fixed circular track parallel to the ground, with a downtilt of 15◦ . 3) Discrete-Rotation-Only 6DMA: The positions of the four surfaces are fixed, but their orientations can be adjusted at discrete intervals within a predefined angular range.
Fig. 5. Grids Performance Heatmap
4) Full Reconfiguration 6DMA: A global search baseline scheme. This scheme includes 16 movable surfaces (each being an array with the same total number of elements as the FPA). At each reconfiguration instance, the next position for every surface is searched from the entire discrete space. 5) Proposed Single-Step 6DMA: The scheme proposed in this paper. Its hardware parameters are identical to the Full Reconfiguration scheme, but at each update, the search is restricted to the current position and its onehop neighborhood, as defined in (21d). Fig. 5 illustrates the mapping from the user grid to the antenna configuration, established based on directional sparsity. Each square represents a physical location in the scenario, and the shade of the color represents the average rate achievable by a single antenna surface that provides the best coverage for that square. Users located directly beneath the BS suffer from relatively low rates due to excessive incident angles and lower antenna gains. The annular region surrounding the BS yields the highest rates due to low path loss and favorable incident angles. Conversely, cell-edge users exhibit the poorest performance due to severe path loss and the lack of LoS links. Fig. 6 presents the variation of the system sum rate with transmit power for a scenario with 30 vehicles. The proposed 6DMA scheme significantly outperforms the traditional FPA, indicating that the high spatial flexibility of the 6DMA can effectively adapt to user distributions and capture large-scale channel variations. Although the Circular-Track and DiscreteRotation-Only 6DMA schemes perform better than the FPA, their gains are constrained by limited spatial degrees of freedom. It is noteworthy that the optimization method based on single-step movement achieves a higher rate than the full reconfiguration method. This is attributed to the fact that the single-step method has a smaller action space, making it easier to find a near-optimal solution, whereas the full reconfiguration method involves a vast action space where heuristic approaches often fail to fully exploit its potential. Fig. 7 illustrates the trend of the system sum rate with respect to the number of users under a fixed transmit power. As the number of vehicles increases, the sum rate rises rapidly but
11
Fig. 6. Comparison of uplink sum rates versus transmit power for different antenna schemes.
Fig. 8. Impact of reconfiguration interval N on sum rate under different transmit powers.
Fig. 7. System sum rate versus number of vehicle users under fixed transmit power.
Fig. 9. Impact of reconfiguration interval N on sum rate under different vehicle densities.
eventually saturates due to intensified inter-user interference. The proposed 6DMA framework consistently demonstrates the best performance among all baselines. This is because vehicle distributions in road environments are typically dispersed. The 6DMA system can leverage its spatial flexibility to dynamically concentrate antenna resources on relatively clustered areas, whereas physically constrained baseline schemes fail to provide such targeted services. Fig. 8 analyzes the system performance under different transmit powers with a fixed number of 30 vehicle users, varying the antenna update interval N . It can be observed that the proposed single-step movement scheme comprehensively outperforms the heuristic global reconfiguration scheme. Notably, the achievable rate at N = 1 is lower than that at N = 10 and N = 20. This is because, at N = 1, the optimization relies on the instantaneous sparse distribution of a few vehicles, resulting in a low-density grid map where it is difficult for the algorithm to discriminate between superior antenna positions. In contrast, for N = 10 and 20, the input is the cumulative predicted distribution over future time slots. This aggregation provides a statistically more robust heatmap of user hotspots, offering a better basis for decision-
making even in the presence of minor prediction errors. This further demonstrates the feasibility of antenna configuration based on predicted distributions, which not only reduces the reconfiguration frequency but also enhances performance. Fig. 9 analyzes the system performance under different vehicle user counts with a fixed transmit power of 23 dBm, varying the antenna update interval N . The experiment employed 10 random seeds, with fifty simulations conducted for each seed, and the global mean was taken. The results indicate that while the value of N has some impact on system performance, it is not significant, and a higher N value is slightly superior to N = 1 when the number of users is small. As user density increases, a smaller reconfiguration interval begins to show a slight advantage, as it can better track fast-changing microscopic dynamics. However, from a practical implementation perspective, a larger N can significantly reduce physical overhead with negligible performance loss. The singlestep method consistently outperforms the full reconfiguration scheme, demonstrating excellent local adaptability. Fig. 10 analyzes the theoretical lower bound of the average movement cost required for each position update for both the single-step movement method and the full reconfiguration
12
values less than 1 appearing in the single-step movement method imply that for some reconfigurations, no changes in antenna positions occurred. This reflects that the variation in the predicted cumulative vehicle user distribution is limited, as the macroscopic distribution remains approximately static within the prediction window. By capturing long-term patterns rather than chasing instantaneous fluctuations, the system avoids unnecessary mechanical adjustments, demonstrating high implementability. VI. C ONCLUSION
Fig. 10. Average movement cost versus reconfiguration interval N .
In this paper, we introduced 6DMA antenna technology into IoV to improve the achievable rate. Based on graph theory, we modeled the movement cost and latency cost of 6DMA for the first time. To address the challenges of fast-varying channels, we proposed a low-complexity, CSI-free optimization framework. This framework leverages predicted vehicle distribution information to enable rapid antenna deployment by restricting the search space to a single-step spatial neighborhood. Simulation results demonstrate that the proposed scheme significantly outperforms traditional baseline schemes. Furthermore, the analysis indicates that the prediction-based method typically requires moving only a small number of antennas, or even none, during reconfiguration, thereby demonstrating its robustness, low mechanical overhead, and good practical feasibility in highly dynamic wireless networks. R EFERENCES
Fig. 11. Average time cost versus reconfiguration interval N .
method. According to the modeling in Section III, moving each antenna to a neighbor position incurs one unit of cost. When N is low, the adjustment of the antenna configuration is based on the instantaneous actual vehicle user distribution. Due to the high mobility of vehicles, the grids containing users may change significantly between adjacent decision intervals, thus requiring substantial adjustments to antenna positions, leading to high movement costs and frequent reconfiguration. As N increases, the cumulative user distribution exhibits stable macroscopic patterns, resulting in minimal distribution changes between adjacent decision moments, and consequently, lower antenna movement amplitudes. The average movement cost of the antenna configuration method based on single-step movement is in the single digits, implying that adapting to a new distribution requires moving only a few antennas. This provides strong theoretical support for the practical deployment of 6DMA. Fig. 11 analyzes the theoretical lower bound of the time cost required for each antenna reconfiguration for the two methods. The time cost is defined as the number of steps required by the antenna with the longest moving path during reconfiguration. Similar to the movement cost, the time cost shows a significant downward trend as N increases. The minimum value for the time cost of a single reconfiguration should be 1. However,
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