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AP Association for RHS-Enabled Cell-Free Uplink MIMO in Industrial Indoor UAV Networks

2026 · arxiv_cs

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AP Association for RHS-Enabled Cell-Free Uplink MIMO in Industrial Indoor UAV Networks

arXiv:2608.03752v1 [cs.NI] 4 Aug 2026

Liangshun Wu, Wen Chen*, Zhendong Li, Qiong Wu and Ying Wang

Abstract—Indoor industrial UAV uplink networks face serious blockage and shadowing from shelves, metal equipment, and production facilities. UAVs are also often clustered and fly along similar straight inspection routes at fixed heights. These features make traditional small-cell deployment less suitable, especially when high reliability, continuous coverage, and good service for weak UAVs are required. Cell-free networks can improve robustness through distributed access points (APs) and UAVcentric communications. Reconfigurable holographic surface (RHS)-enabled APs provide programmable analog receive beams and generate scalar post-RHS observations, which are jointly processed at the CPU for distributed uplink MIMO detection at relatively low hardware cost. Conventional AP association relies on distance, large-scale fading, or post-combining SINR obtained with user-specific digital combiners. Here, however, all UAVs served by a single-feed RHS AP share one amplitudeconstrained receive pattern and one scalar AP output. We therefore derive an SINR-like score from this physical output and, under weak inter-AP disturbance correlation, approximate the CPU-side log-det objective by an additive per-AP surrogate, yielding a low-complexity ranking rule. The results show that the nearest AP is not always the best choice, the AP-UAV height difference may have an optimal value, and larger serving clusters bring diminishing returns. Simulations show that the proposed method improves the minimum UAV data rate, average spectral efficiency, fairness, and energy efficiency compared with benchmark schemes. Index Terms—Indoor industrial UAV communications, cellfree, holographic MIMO, AP association, user-centric

I. I NTRODUCTION

NDOOR industrial UAV communication networks are expected to support emerging applications such as warehouse inspection, facility monitoring, inventory sensing, and production-line inspection. In such scenarios, UAVs usually operate inside workshops or warehouses filled with shelves, metal equipment, rails, robots, and conveyor systems, which lead to link-dependent shadowing, occasional blockage, and highly non-uniform large-scale propagation conditions. Moreover, inspection UAVs are often deployed in localized task regions and may move along similar straight-line paths at approximately fixed altitudes, rather than being uniformly distributed over the entire hall. Meanwhile, industrial uplink * Corresponding author: Wen Chen. Liangshun Wu and Wen Chen are with the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China (e-mail: wuliangshun@sjtu.edu.cn; wenchen@sjtu.edu.cn). Zhendong Li is with the School of Information and Communication Engineering, Xi’an Jiaotong University, Xi’an, China (e-mail: lizhendong@xjtu.edu.cn). Qiong Wu is with the School of Internet of Things Engineering, Jiangnan University, Wuxi, China (e-mail: qiongwu@jiangnan.edu.cn). Ying Wang is with the State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China (e-mail: wangying@bupt.edu.cn).

services typically place stronger emphasis on reliability, coverage continuity, link stability, and weak-UAV performance than on hotspot peak throughput. These features make conventional small-cell architectures less suitable for indoor industrial UAV communications. Cell-free architectures are promising for such scenarios because distributed access points (APs) connected to a central processing unit (CPU) can jointly receive uplink signals from UAVs and thereby improve service robustness [1]–[9]. Since the seminal work on cell-free massive MIMO [1], subsequent studies have shown the importance of centralized processing, scalable implementation, and user-centric reception for improving performance and complexity tradeoffs [2], [4], [5]. For indoor industrial UAV uplink transmission, UAV-centric reception is particularly attractive because it can alleviate the cell-edge effect, improve macro-diversity, and provide stable connectivity under blockage and uneven UAV distributions [6]–[8], [10]. However, the performance of a cell-free system depends critically on AP association, since each UAV must determine an appropriate serving AP set before CPU-side combining is performed. Existing AP association methods are still largely based on distance, large-scale fading, received power, threshold rules, heuristic matching, mixed-integer optimization, or learningbased policies [6]–[8], [10]–[22]. These methods are useful for conventional cell-free and distributed MIMO systems, and prior studies on factory automation and indoor industrial networks have demonstrated the importance of vertical geometry, centralized processing, and user-centric AP selection [6]–[8], [10]. Nevertheless, many low-complexity rules among them assume conventional phased-array (PA)-based AP transceivers and implicitly regard average link strength as the dominant indicator of AP quality. This assumption becomes less accurate in indoor industrial UAV scenarios. First, UAVs may appear in clustered regions, which increases the probability of strong spatial overlap and localized interference. Second, UAVs following nearby inspection paths at similar heights may be difficult to separate from the viewpoint of a given AP, even when their large-scale fading values are favorable [23], [24]. Therefore, a nearer AP or an AP with stronger average received power is not necessarily the best serving AP. Reconfigurable holographic surfaces (RHSs), which are closely related to large intelligent surfaces, holographic MIMO, and dynamic metasurface antennas, provide densely spaced programmable elements, amplitude-only control, and flexible directional responses with relatively low hardware complexity [25]–[33]. Existing RHS-related studies have mainly focused on hardware architectures, holographic beam-

forming, multi-UAV access, and holographic radio [28]–[33]. These features make RHSs attractive as AP front ends for indoor industrial UAV cell-free networks, since they can offer both large effective apertures and fine-grained directional selectivity for uplink MIMO reception. Both single- and multi-feed RHS architectures have been investigated, while the single-feed leaky-wave RHS represents a low-complexity implementation with experimentally demonstrated feasibility [32], [33]. Accordingly, this work focuses on a single-feed, single-RF-chain RHS receiver, which produces one scalar output per AP. At the same time, the considered single-feed RHSenabled reception further exposes the limitations of conventional AP association rules. In particular, the service capability of a candidate AP depends not only on large-scale fading, but also on the effective channel gain produced by the RHS response, the overlap between different UAV channels, and the post-combining disturbance covariance, because all UAVs associated with an AP share the same amplitude-constrained receive pattern. Therefore, AP association for uplink RHSenabled MIMO indoor industrial cell-free networks remains insufficiently explored. Motivated by these observations, this paper studies AP association for uplink RHS-enabled MIMO transmission in indoor industrial UAV cell-free networks. An uplink signal model is developed for RHS-enabled MIMO indoor industrial UAV cell-free networks, where multi-antenna UAVs transmit to distributed RHS-enabled APs and the AP-side analog-combined scalar outputs are forwarded to the CPU for combining. The goal is to develop an association metric that captures the actual service capability of each AP for a given UAV while remaining interpretable and suitable for low-complexity ranking-based association. Building on the effective desired gain, interUAV overlap, and disturbance covariance after AP-side RHS combining, we formulate the AP association problem and derive a score-based rule. This relation between the proposed design and the indoor industrial UAV communication scenario deserves emphasis. Conventional distance- or fading-based association fails here for two reasons: clustered UAVs on similar paths present nearly identical LSF and ranges to a given AP, so scalar ranking cannot distinguish APs with severe inter-UAV overlap, a limitation that the proposed score overcomes by directly sensing this interference in its denominator; and dense blockages create strong but angularly mismatched links whose multipath energy the RHS receive pattern cannot effectively combine, so evaluating the post-RHS signal quality naturally deprioritizes such APs. Moreover, the system model embeds the scenario geometry and operation: the three-dimensional AP-UAV geometry underpins the height-angle tradeoff, which exists only with ceiling-mounted APs and constant-altitude UAVs; the deterministic straight-line motion model matches aisle inspection and enables trajectory-predictable association updates; and the large shadowing variance captures the severe indoor environment and produces the distance-order reversal probability. This paper provides two main contributions: 1) a low-complexity AP association method is proposed for RHS-enabled UAV-centric cell-free reception. Unlike distance-, LSF-, and received-power-based meth-

ods [12]–[14], and coverage-, load-, or pilot- schemes whose AP metrics remain largely LSF-based [15], [17], the proposed score captures the post-RHS desired gain, residual inter-UAV leakage, and filtered noise. In contrast to conventional SINR-based association with user-specific digital combiners, each single-feed, single-RF-chain RHS AP produces one scalar output, so its associated UAVs share one amplitude-constrained receive pattern. Compared with joint MINLP-, learning-, SIM-, DMA-, and mmWave-based designs [18]–[22], the proposed method retains a one-shot ranking implementation without repeatedly solving the joint association–RHS optimization problem. Under fixed probing weights and weak cross-AP disturbance correlation, it provides a lower-bound surrogate of the probing-stage logdet rate, for which the Top-Jk rule is optimal. 2) Three interpretable conclusions are obtained. First, a nearer AP is not necessarily better than a farther AP. Second, the AP-UAV relative height difference introduces a heightangle tradeoff, which implies the existence of an interior optimum under suitable conditions. Third, enlarging the serving cluster leads to diminishing marginal gains. The rest of this paper is organized as follows. Section II presents the system model. Section III develops the AP association method. Section IV compares with existing methods, Section V provides analytical findings and design guidelines. Section VI presents simulation results. Section VII concludes the paper. II. S YSTEM M ODEL A. Industrial indoor UAV communication scenario

Fig. 1: Illustration of a cell-free industrial indoor UAV communication scenario. Consider an industrial indoor UAV communication scenario in a workshop or warehouse of size Dxhall × Dyhall × Dzhall , as illustrated in Fig. 1, where L APs are connected to a CPU through wired links and jointly serve K UAV users performing inspection and monitoring tasks. Each RHS-enabled AP has

a single RF chain and produces one analog-combined scalar observation per resource block. The MIMO dimension is formed by the multi-antenna UAV streams and the stacked scalar observations from multiple distributed APs at the CPU. Each UAV follows a straight-line inspection trajectory inside the hall at an approximately constant altitude, which is consistent with aisle inspection in warehouses or facility inspection along shelves, beams, or production lines. UAV user k is equipped with Mk antennas, while AP l is equipped with an RHS consisting of Nl controllable radiating elements. Let ql = [ql,x , ql,y , ql,z ]⊤ ∈ R3 denote the position of AP l, and let Qk = [qk,1 , . . . , qk,Mk ] ∈ R3×Mk collect the antenna positions of UAV user k, where qk,m ∈ R3 is the position of the m-th UAV antenna. For the RHS of AP l, let Nl = {1, . . . , Nl } denote the element index set. The n-th RHS element is characterized by its local surface coordinate ul,n ∈ R2 and physical position rl,n ∈ R3 . Define the element-position matrix Rl = [rl,1 , . . . , rl,Nl ] ∈ R3×Nl . The local coordinate ul,n ∈ R2 describes the position of the n-th RHS element on the two-dimensional surface, whereas rl,n ∈ R3 denotes its physical position in " the global # coordinate (x) ul,n system. For a planar RHS, ul,n = is the two(y) ul,n dimensional local coordinate of the n-th RHS element on the surface, if the RHS is horizontallymounted  and aligned (x) u  l,n  with the global x-y plane, then ql +  u(y)  Within one l,n 0 channel coherence block, each UAV is assumed to be quasistatic, so that its position and body orientation can be treated as approximately constant. The effects of residual UAV attitude variation and antenna misalignment are absorbed into the effective steering vectors and channel matrices defined below. PMk qk,m (t) denote For UAV user k, let q̄k (t) = M1k m=1 the UAV-center position at time t. Since UAV k performs inspection along a straight-line trajectory at a constant altitude, its center position is modeled as q̄k (t) = qk,0 + vk t dk ,

Fig. 2: Geometry of UAV-AP communications.

aerial UAVs, the LSF is expressed as βlk = C̄ d−α lk χlk ,

(2)

where α is the path-loss exponent, χlk is the shadow fading factor, and C̄ denotes the power gain at a reference channel 2

λ , d0 = 1 m. This model is distance of 1 m, C̄ = 4πd 0 used to capture the dominant distance-dependent attenuation for indoor UAV links, while the effects of UAV height, local blockage, and propagation heterogeneity are reflected through the three-dimensional geometry and the shadowing term. For notational simplicity, the explicit time index t is omitted, and all quantities are understood as being evaluated at an instantaneous point on the UAV inspection trajectory. Then, the above notations will be rl,k , θl,k , dl,k .

B. RHS receive model

(1)

where qk,0 ∈ R3 is the initial UAV-center position, vk is the UAV speed, and dk = [dk,x , dk,y , 0]⊤ ∈ R3 is a constant unit-direction vector satisfying ∥dk ∥2 = 1. Hence, the UAV flies at a fixed altitude along its inspection path. For AP l and UAV user k, define the relative position vector as δlk (t) = ⊤ ql − q̄k (t) = [δlk,x (t), δlk,y (t), δlk,z (t)] . Accordingly, the horizontal distance, the vertical height difference, and the three-dimensional distance q between AP l and UAV user k 2 (t) + δ 2 (t), z are defined as rlk (t) = δlk,x lk = |δlk,z (t)|, lk,y p 2 2 dlk (t) = ∥δlk (t)∥2 = rlk (t) + zlk . Since the UAV altitude is fixed and AP l is stationary, the vertical height difference zlk remains constant along the trajectory, whereas the horizontal distance rlk (t) and the three-dimensional distance dlk (t) vary with time. If the RHS normal points vertically downward, the zlk incidence angle θlk (t) satisfies cos θlk (t) = dlk (t) . The geometry of the above UAV-AP pair is shown in Fig. 2. Following a three-dimensional indoor propagation model for

Fig. 3: RHS-based uplink receiving. The incident wave is spatially sampled by the RHS elements, each of which applies an amplitude weight before coupling to the common feeder. In transmit mode, the RHS functions as a holographic beamformer where a reference wave on the surface launched from the feed is shaped by pre-designed real-valued amplitude weights that encode the interference between the reference wave and the desired spatial object wave, and the resulting diffraction reconstructs the target beam in space. In receive mode, the same RHS operates as a passive amplitude-only weighted array with no reference wave present; incident waves are sampled at each element, multiplied by the same amplitude coefficients, and then passively combined through a fixed feeder network into a single RF chain. The receive process merely reuses the pre-computed transmit holographic pattern,

exploiting channel reciprocity because the phase compensation that produces a directional beam in transmission also provides maximum-ratio combining for signals arriving from that same direction. Consider the uplink transmission from UAV k to AP l, where the RHS is used as a receive antenna. UAV k transmits xk = [xk,1 , . . . , xk,Mk ]⊤ ∈ CMk ×1 . The covariance of xk is E{xk xH (3) k } = Pk , and for equal-power transmission, Pk = pk IMk . The RHS surface consists of Nl elements. Each element independently receives the incident signals from all UAVs in space. Each element applies a real-valued amplitude control. All elements are combined through a fixed feeder network to a single RF chain, producing a scalar output zl . 1) Step 1: Element-level received signal: The signal [yl,k ]n received by the n-th element of the RHS mounted on AP l from UAV k is the spatial sample of the incident waves: yl,k = Hl,k xk + nl ∈ CNl ×1 ,

(4)

with p Hl,k = βlk cos θlk  2π (0) ⊤ ejκl,k,1 ul,1 e−j λ dl,k,1  2π (0)  ejκ⊤ l,k,1 ul,2 e−j λ dl,k,1   ..  .  (0)

2π jκ⊤ l,k,1 ul,Nl −j λ dl,k,1

⊤

···

ejκl,k,Mk ul,1 e

··· .. .

ejκl,k,Mk ul,2 e .. .

⊤

(0)

−j 2π λ dl,k,M

 k

(0)

−j 2π λ dl,k,M

(0)

···

2π jκ⊤ l,k,M ul,Nl −j λ dl,k,M k

     

(5) ∈ CNl ×Mk , where jκ⊤ u • e l,k,m l,n is the spatial phase sample of the incident wave at this element; (0) −j 2π λ dl,k,m is the absolute propagation phase correction; • e and nl ∼ CN (0, σl2 INl ). Let κl,k,m ∈ R2 denote the equivalent transverse wavevector associated with the uplink wave emitted by the m-th antenna of UAV k and arriving at AP l. Since the RHS is horizontally mounted and aligned with the global x-y plane, κl,k,m is obtained by projecting the propagation direction from qk,m to ql onto the local RHS plane. Under the plane-wave approximation across the RHS surface, we have  q −q  l,x k,m,x 2π  ∥ql − qk,m ∥2  κl,k,m = − (6)  ql,y − qk,m,y  , λ ∥ql − qk,m ∥2

from uplink pilots and report the required large-scale or post-RHS quality information to the CPU. Based on these quantities, the CPU determines the UAV-centric serving AP sets {Sk }K k=1 . Then, for each AP l, the set of UAVs served by this AP is defined as Ul = {k | l ∈ Sk }. The signal sampled across the RHS elements yl = √ P P of AP PMl kbecomes βlk cos θlk · k∈Ul Hl,k xk + nl , i.e., [yl ]n = k∈Ul m=1 ⊤

2π

(0)

ejκl,k,m ul,n e−j λ dl,k,m xk,m + nl,n , with [Hl,k ]n =

Mk X p 2π (0) ⊤ βlk cos θlk · ejκl,k,m ul,n e−j λ dl,k,m ,

(8)

m=1

where xk,m is the symbol transmitted from the m-th antenna of UAV k; nl,n is the thermal noise at this element. 2) Step 2: Amplitude weighting: Each element applies its real-valued amplitude gain bl,n to the received signal before coupling to the feeder: [ỹl ]n = bl,n · [yl ]n . by tuning a local impedance (e.g., via a varactor). Fig. 3 illustrates the control process. The amplitude patP PMcomposite k tern is then bl,n = k∈Ul m=1 al,k,m b̄l,k,m,n , denote {a : k ∈ Ul , m = 1, . . . , Mk } as Al , al,k,m ≥ 0, and Pl,k,m PMk k∈Ul m=1 al,k,m = 1. Since each basis pattern satisfies 0 ≤ b̄l,k,m,n ≤ 1, the convex combination also satisfies 1+cos(κ⊤ l,k,m ul,n −βs ρl,n ) = 0 ≤ bl,n ≤ 1; and b̄l,k,m,n = 2 1+ℜ e

jκ⊤ l,k,m ul,n e−jβs ρl,n

. which maximizes the received 2 power from the direction of κl,k,m when applied alone. ρl,n is the propagation distance along the feeding structure, r 2 2 (x) (x) (y) (y) ρl,n = ∥ul,n − ul,0 ∥2 = ul,n − ul,0 + ul,n − ul,0 , and βs is the guided-mode propagation constant. Any other pattern that concentrates gain toward the desired angular direction can be used without affecting the subsequent association algorithm. 3) Step 3: Feeder combining: The weighted signals are combined through a fixed feeder network toward the RF chain. The feeder introduces a fixed transmission coefficient from the √ n-th element to the RF chain: gl,n = √1N ηl,n · e−αs ρl,n · l e−jβs ρl,n which is the internal feed response from the n-th RHS element to the single RF port, where ηl,n is the elementto-feed coupling efficiency, αs is the guided-mode attenuation coefficient.

where λ is the carrier wavelength. The negative sign follows the receive-phase convention in which the baseband phase of the received wave is proportional to the negative propagation distance. If the opposite phase convention is used, the sign of κl,k,m should be changed consistently in both the channel model and the holographic pattern construction. (0)

dl,k,m = ∥ql − qk,m ∥2

(7)

denotes the distance of the m-the antenna of UAV k to AP l. Note that before data transmission, the network operates in a pilot association phase. During this phase, all APs estimate the spatial directions or effective channels of candidate UAVs

Fig. 4: Composite receive amplitude pattern construction under a single-feed RHS architecture.

wlH yl | {z }

zl =

wlH Hl,k xk

k∈Ul

Scalar RF-chain output for AP l

}

AP l received from served UAVs ! Nl X p 2π (0) d −j ∗ jκ⊤ u βlk cos θlk [wl ]n e l,k,m l,n e λ l,k,m xk,m + n=1

Mk X X k∈Ul m=1

| N

Filtered noise

+ wlH nl | {z }

l 1 X =√ Nl n=1

Effective post-RHS channel from stream m of UAV k to AP l Mk X X

√ ηl,n | {z }

}

Nl X

n=1

⊤

Mi XX p βli cos θli | {z } m=1

i∈Ul

jκ⊤ l,i,m ul,n

}

Signal received at element n from all served UAVs

4) Step 4: Scalar RF-chain output: As shown in Fig. 4, define the physical feed-combining vector vl ∈ CNl ×1 with entries 1 √ [vl ]n = gl,n bl,n = √ ηl,n bl,n e−αs ρl,n e−jβs ρl,n . Nl

(9)

# } xi,m +

Element thermal noise

where Gk,k (Sk )xk ∈ C|Sk |×1 and Gk,i (Sk )xi ∈ C|Sk |×1 . The disturbance covariance for detecting UAV k is  " X Ξk (Sk ) =E  Gk,i (Sk )xi + ñ(Sk ) (14) i̸=k

 H # X  Gk,i (Sk )xi + ñ(Sk )

(15)

i̸=k

gl,n bl,n [yl ]n .

(10)

n=1

For consistency with the standard complex-baseband innerproduct notation, we define the receive combining vector as wl ≜ vl∗ . Then the same scalar output can be written as zl = wlH yl . Accordingly, [wl ]∗n = [vl ]n Then the scalar output can be expanded as (11). Denote the noise as ñl = wlH nl = PNl [w ]∗ n , and its variance E{|ñl |2 } = σl2 wlH wl = n=1 PNl l n l,n 2 2 σl n=1 |[wl ]n | . For UAV k, let Sk = {l1 , . . . , l|Sk | } denote the serving AP set whose scalar outputs are used by the CPU to detect xk ∈ CMk ×1 . The CPU stacks the scalar outputs of the selected APs as zSk = [zl1 , . . . , zl|Sk | ]⊤ ∈ C|Sk |×1 . For any UAV i, define the stacked post-RHS effective channel over the serving AP set Sk as   wlH1 Hl1 ,i H  wl2 Hl2 ,i    Gk,i (Sk ) =  (12) ..  ∈ C|Sk |×Mi ,   . wlH|S | Hl|Sk | ,i k

where wl ∈ CNl ×1 and Hl,i ∈ CNl ×Mi . Hence, wlH Hl,i ∈ C1×Mi . The m-th entry of wlH Hl,i is √ PNl 2π (0) ⊤ [wlH Hl,i ]m = βli cos θli n=1 [wl ]∗n ejκl,i,m ul,n e−j λ dl,i,m , m = 1, . . . , Mi . The stacked post-RHS noise vector is ñ(Sk ) = [ñl1 , ñl2 , . . . , ñl|Sk | ]⊤ ∈ C|Sk |×1 . Using (11), the stacked CPU observation for detecting UAV k is X zSk = Gk,k (Sk )xk + Gk,i (Sk )xi + ñ(Sk ), (13) i̸=k

nl,n |{z}

}

The scalar RF-chain output is therefore zl = vl⊤ yl =

s ρl,n e|−jβ {z }

}

(0)

−j 2π λ dl,i,m

Projected LSF Element sampling phase Propagation phase

Nl X

(11) s ρl,n e|−α{z }

Feed attenuation Feed phase shift

Amplitude-controlled receive holographic pattern

}

k∈U m=1 Element radiation efficiency | l

Sum of thermal noises from all RHS elements in AP l

1 + ℜ ejκl,k,m ul,n e−jβs ρl,n al,k,m

[wl ]∗n nl,n

∈ C|Sk |×|Sk | , which is decomposed as X 2 2 Gk,i (Sk )Pi GH k,i (Sk ) + diag . . . , σl|S | ∥wl|Sk | ∥2 k

i̸=k

(16) where Gk,i (Sk ) ∈ C|Sk |×Mi , Pi ∈ CMi ×Mi , and GH k,i (Sk ) ∈ |Sk |×|Sk | CMi ×|Sk | , so that Gk,i (Sk )Pi GH (S ) ∈ C . Since k,i k ñl = wlH nl , if nl ∼ CN 0, σl2 INl , then n o 2 2 H 2 2 E |ñl | = E wlH nl nH l wl = wl σl INl wl = σl ∥wl ∥2 . (17) P N 2 2 lj And, wlj 2 = n=1 wlj n , therefore expand form P N 2 2 lj is σl2j n=1 wlj n = σl2j wlj 2 . Assuming Gaussian signaling and treating inter-UAV overlap as colored noise, the achievable information rate of UAV k is given by (22). 5) Step 5: CPU linear combining: The condition |Sk | ≥ Mk is necessary but not sufficient for separating the Mk streams. A sufficient rank condition is rank (Gk,k (Sk )) = Mk . If this condition is not satisfied, the effective number of reliably separable spatial streams is limited by the rank of the stacked post-RHS channel matrix. The CPU performs linear minimum mean square error (LMMSE) estimation as Mk ×1 x̂k = CH , zSk ∈ C|Sk |×1 , and k zSk , where x̂k ∈ C H Mk ×|Sk | hence Ck ∈ C . The LMMSE combining matrix is −1 H Ck = Gk,k (Sk )Pk Gk,k (Sk ) + Ξk (Sk ) Gk,k (Sk )Pk ∈ C|Sk |×Mk gives the practical LMMSE estimator. Equivalently, H CH = Pk GH k k,k (Sk ) Gk,k (Sk )Pk Gk,k (Sk ) + Ξk (Sk )

−1

1/2 1/2 −1 Rk (Sk ) = log2 det IMk + Pk GH (S )Ξ (S )G (S )P (18) k k k,k k k,k k k    H   wlH1 Hl1 ,k wlH1 Hl1 ,k   H H  wl2 Hl2 ,k   wl2 Hl2 ,k    1/2    1/2  −1  (19) = log2 det IMk + Pk  .. ..  Pk   Ξk (Sk )       . .   wlH|S | Hl|Sk | ,k wlH|S | Hl|Sk | ,k k k   −1  X  1/2 1/2  2 2 2 2   Gk,k (Sk )Pk  = log2 det IMk + Pk GH Gk,i (Sk )Pi GH k,k (Sk ) k,i (Sk ) + diag σl1 ∥wl1 ∥2 , . . . , σl|Sk | ∥wl|Sk | ∥2 i̸=k

(20) −1 wlH1 Hl1 ,i wlH1 Hl1 ,i     wlH2 Hl2 ,i   wlH2 Hl2 ,i   X       1/2 H 2 2 2 2   = log2 det IMk + Pk Gk,k (Sk )  .. ..  + diag σl1 ∥wl1 ∥2 , . . . , σl|S | ∥wl|Sk | ∥2   Pi   k     . .   i̸=k   H H wl|S | Hl|Sk | ,i wl|S | Hl|Sk | ,i 







H



(21) 

wlH1 Hl1 ,k wlH2 Hl2 ,k





     1/2  × ..  Pk  ,    . H wl|S | Hl|Sk | ,k

(22)

1/2

∈ CMk ×|Sk | . Here, Pk ∈ CMk ×Mk , Gk,k (Sk ) ∈ |Sk |×Mk H Mk ×|Sk | C , Gk,k (Sk ) ∈ C , Ξk (Sk ) ∈ C|Sk |×|Sk | , 1/2 H 1/2 −1 Pk Gk,k (Sk )Ξk (Sk )Gk,k (Sk )Pk ∈ CMk ×Mk . The above model can be extended to account for practical hardware impairments and power consumption as follows: −αs ρl,n • Feeder loss: considered by ηl,n and e ; the default values ηl,n = 1 and αs = 0 isolate the association effect. • Mutual coupling: replace the effective channel by Hl,k to Cl Hl,k [34]–[37], with Cl denotes the coupling matrix. • Finite-resolution and pattern errors: use bl,n to Q(bl,n ), where Q(·) maps the designed amplitude to the nearest hardware-supported level, e.g., the ON/OFF states of PIN-diode elements [38]. Fabrication, temperature, and calibration errors can also be included by replacing the ideal feeder coefficient gl,n with its actual value gbl,n . • RF-chain impairments: include signal attenuation and an √ additional distortion term [39], e.g., zbl = εl zl + dl , where εl ∈ [0, 1] is the RF-chain hardware-quality factor and dl is the signal-dependent distortion noise. • Power consumption: a full metric should include AP, RFchain, RHS-control, fronthaul, and CPU power. In this paper, we only consider the power of UAV transmitters. These modify the effective post-RHS gain and disturbance. III. AP A SSOCIATION M ETHOD A. Problem formulation The original AP association problem is to maximize the CPU-side achievable rate in (22), (P0) : max

{Sk }K k=1

K X k=1

s.t.

(24) (25)

B. Pilot association phase Since the associated-user set Ul is unknown before AP association, the data-phase RHS coefficient vector A⋆l cannot be used to rank candidate APs. Therefore, the association (0) stage uses a fixed wl , e.g., a wide-beam or codebook-based probing pattern, which is independent of Ul . The preliminary association score is defined as (0)

(23)

∀k, ∀k.

Here Rk (Sk ), defined in (22), is the log-det achievable rate in the system model per bandwidth, i.e., spectral efficiency (unit: bit/s/Hz). Although (P0) is written in set form, it is equivalent to a binary AP association problem. (P0) is hard to solve directly. For Sk = {l1 , . . . , l|Sk | }, the (p, q)-th element of the disturbance covariance matrix is [Ξk (Sk )]p,q = ( 2 H P σ w lp lp wlp , p = q, H H Thus, w H P H w + l ,i i l p q lp lq ,i i̸=k 0, p ̸= q. different selected APs are coupled inside Ξk (Sk ) and its inverse in the log-det rate. In addition, AP association and RHS configuration are mutually dependent. Specifically, the serving AP sets determine {Sk }K k=1 , then affects Ul = {k : l ∈ Sk }, changes Al and wl (Al ), whereas the receive pattern wl (Al ) is itself required to evaluate the quality of AP l before association. To break this circular dependence while retaining a low-complexity online implementation, we adopt a two-stage strategy, summarized as Algorithm 1.

(0)

Rk (Sk )

Sk ⊆ {1, . . . , L}, Mk ≤ |Sk | ≤ Jk ,

ψl,k =

(0)

(w )H Hl,k Pk HH l,k wl Pl . (0) (0) H + σ2 I (wl )H H P H w l,i i N l i̸=k l,i l l

(26)

We consider the weak cross-AP disturbancecorrelation approximation, under which the offdiagonal entries of Ξk (Sk ) are neglected. The CPUside

rate

becomes

Rk (Sk )

1/2

(0)

≃ 1/2

H HH l,k wl (wl ) Hl,k Pk (0) l∈Sk (w(0) )H (P H +σ 2 I H P H l,i i i̸=k l Nl )wl l,i l

log2 det IMk + !

Proof. Because log2 (1 + x) is monotonically increasing and (0) ψl,k ≥ 0, maximizing Γk (Sk ) is equivalent to selecting the Jk largest scores. ■ C. Data-phase RHS configuration The probing stage determines the serving AP sets {Sk⋆ }K k=1 . Consequently, the associated-UAV set of AP l becomes known as Ul = {k : l ∈ Sk⋆ }. (33)

. (0)

Proposition 1 (Trace-based bounds). Under a fixed wl and the weak cross-AP disturbance-correlation diagonal approximation, the CPU-side rate satisfies Each AP can then configure its shared RHS receive pattern ! ! X (0) 1 X (0) for its selected UAVs. This second stage affects the data-phase log2 1 + ψl,k ≤ Rk (Sk ) ≤ Mk log2 1 + ψl,k transmission . and final rate evaluation, but does not trigger AP Mk l∈Sk l∈Sk re-ranking within the same association interval. (27) For given Al = {al,k,m : k ∈ Ul , m = 1, . . . , Mk }, define the post-RHS signal-to-disturbance ratio of AP l for UAV k: The two bounds coincide when Mk = 1. Proof. Under the diagonal approximation, define Ak (Sk ) = 1/2 (0) (0) H 1/2 P Pk HH l,k wl (wl ) Hl,k Pk Each numerator (0) . l∈Sk (w(0) )H (P H 2 i̸=k Hl,i Pi Hl,i +σl INl )wl l H has the form xx and each denominator is strictly positive due to thermal noise; hence, Ak (Sk ) ⪰ 0. By the linearity and cyclic property of the trace, (0)

γl,k (Al )

(34)

wlH (Al )Hl,k Pk HH l,k wl (Al ) P = H + σ2 I wlH (Al ) H P H wl (Al ) l,i i N l i̸=k l,i l

(35)

Nl X Nl X [wl ]∗n (Al ) Hl,k Pk HH l,k n,r [wl ]r (Al )

(0)

n=1 r=1   (w )H Hl,k Pk HH , = l,k wl N N Pl l l X XX (0) H (0) H 2 2  [wl ]r (Al ) [wl ]∗n (Al )  Hl,i Pi HH l∈Sk (wl ) i̸=k Hl,i Pi Hl,i + σl INl wl l,i + σl INl X (0) n=1 r=1 i̸=k n,r = ψl,k . (28) (36)

tr(Ak (Sk )) =

l∈Sk

Let λ1 , . . . , λMk ≥ 0 denote the eigenvalues of Ak (Sk ). Then Mk Y

det(IMk + Ak (Sk )) =

(1 + λm ) ≥ 1 +

m=1

Mk X

λm , (29)

The lower bound in (27) leads to the following separable surrogate of (P0): X (0) (P0′ ) : max Γk (Sk ) = ψl,k (31) s.t.

m=1

which gives the lower bound after taking log2 (·). Moreover, the arithmetic–geometric mean inequality yields !Mk Mk Mk Y 1 X (1 + λm ) ≤ 1 + λm , (30) Mk m=1 m=1 P which gives the upper bound. Since m λm = tr(Ak (Sk )) = P (0) l∈Sk ψl,k , the result follows. When Mk = 1, the matrix has only one eigenvalue, and both inequalities hold with equality. ■

with components computed as (37). The RHS amplitude optimization problem at AP l is formulated as X (P1) : max γl,k (Al ) (38)

l∈Sk

Mk ≤ |Sk | ≤ Jk .

(32)

Proposition 2 (Optimal solution of (P0′ )). Assume Mk ≤ (0) |Sk | ≤ Jk ≤ L. Since ψl,k ≥ 0, an optimal solution is obtained by selecting the Jk APs with the largest scores: Sk⋆ = {l : ψl,k is among the largest Jk values for UAV k} . P (0) The optimal value is Γ⋆k = l∈S ⋆ ψl,k . If ties occur at the k Jk -th largest score, any tied selection is optimal.

s.t.

k∈Ul

al,k,m ≥ 0, k ∈ Ul , m = 1, . . . , Mk , Mk X X

al,k,m = 1.

(39) (40)

k∈Ul m=1

(P1) is a nonconvex sum-of-ratios problem. Proposition 3 (Projected-gradient update for (P1)). At iteration q, the RHS coefficients are updated by " #+ X ∂γl,k (q+1) (q) (q) al,k,m = al,k,m + µ(q) − νl , ∂al,k,m Al =A(q) k∈Ul l (41) (q) where [x]+ = max{x, 0}, µ(q) > 0 is the step size, and νl P PMk (q+1) is chosen such that k∈Ul m=1 al,k,m = 1. This update is the Euclidean projection of the gradient-ascent point onto the simplex feasible set of (P1). P (q) (q) ∂γl,k Proof. Define ãl,k,m = al,k,m + µ(q) k∈Ul ∂al,k,m . (q) The

Al =Al

projection onto the simplex solves 2 P PMk (q) minAl k∈Ul m=1 al,k,m − ãl,k,m subject to P PMk al,k,m ≥ 0, k∈Ul m=1 al,k,m = 1. The KKT conditions (q) (q) are al,k,m − ãl,k,m + νl − λl,k,m = 0, al,k,m ≥ 0,

Mk X X

1 √ [wl ]n (Al ) = √ ηl,n al,k,m Nl k∈U m=1

n ⊤ o 1 + ℜ ejκl,k,m ul,n e−jβs ρl,n 2

e−αs ρl,n e−jβs ρl,n ,

Mk X Mk X 2π (0) 2π (0) ⊤ ⊤ H Hl,k Pk Hl,k n,r = βlk cos θlk [Pk ]m,t ejκl,k,m ul,n e−jκl,k,t ul,r e−j λ dl,k,m e+j λ dl,k,t ,

  m=1 t=1 ( Mi X Mi X X X 2π (0) 2π (0) ⊤ ⊤ 1, d +j d −j 2 H 2 jκ u −jκ u l,i,t l,r e  λ l,i,m e λ l,i,t + σ Hl,i Pi Hl,i + σl INl  = βli cos θli [Pi ]m,t e l,i,m l,n e l 0, m=1 t=1 i̸=k i̸=k

n = r, n ̸= r,

n,r

(37)

P PMk λl,k,m ≥ 0, λl,k,m al,k,m = 0, k∈U m=1 al,k,m = 1. l h i+ (q+1) (q) (q) Thus, al,k,m = ãl,k,m − νl , which gives (41). ■ ∂γ

l,k is computed as Specifically, ∂al,k,m H ∂wl H Hl,k Pk Hl,k wl 2ℜ ∂al,k,m ∂γl,k P − = ∂al,k,m H 2 wlH i̸=k Hl,i Pi Hl,i + σl INl wl

wlH Hl,k Pk HH l,k wl h P i2 × H + σ2 I wlH H P H l,i i l,i i̸=k l N l wl      ∂w H X  l 2   wl . 2ℜ Hl,i Pi HH l,i + σl INl  ∂al,k,m  i̸=k

(42) The above procedure is summarized in Algorithm 1 and is executed over association rounds. Within each interval, UAV positions and channels are regarded as quasi-static or predictable from recent pilots, and the obtained Sk , Ul , and wl are used for the corresponding data-transmission phase. When UAVs move, the scores are updated and the AP association is recomputed. To avoid circular dependence between AP association and RHS optimization, the CPU first determines {Sk }K k=1 and Ul = {k : l ∈ Sk } from the preliminary scores (0) ψl,k . Then, Al and wl are optimized for the selected users and used only for final rate evaluation, not for AP re-ranking. The implementation analysis and computational-complexity assessment of Algorithm 1 are provided as follows. After estimating the post-RHS effective channels, AP l computes its K scores locally and reports only these real-valued scores to the CPU. Thus, the CPU stores LK scores. Sorting the L candidate APs for each UAV requires O(KL log L) operations, which can be reduced to O(KL) by partial TopJk selection. The subsequent RHS configurations are independently optimized at different APs. In contrast, one-swap refinement evaluates up to KJk (L − Jk ) candidate exchanges K per sweep, whereas exhaustive joint association requires JLk candidates. IV. A C OMPARISON WITH E XISTING AP A SSOCIATION M ETHODS The proposed AP association metric ψl,k reflects the postRHS scalar observation quality at AP l, including the desired

Algorithm 1 Two-stage ranking-based AP association and RHS configuration per association interval Require: {ql }, {Qk }, {Pk }, {Jk }, ϵ, and Imax . Ensure: Serving AP sets {Sk }K k=1 , associated-UAV sets L {Ul }L l=1 , and RHS weights {wl }l=1 . (0) H 1: Estimate (wl ) Hl,k and the local interference-plusnoise powers. 2: Pilot association phase: 3: for each AP l = 1, . . . , L do 4: Construct (or load from a codebook) the RHS basis patterns b̄l,k,m,n based on the UAV angular directions, (0) and form an initial probing weight wl (e.g., a widebeam setting) for pilot-based channel estimation. 5: end for 6: for each UAV k = 1, . . . , K do (0) 7: Compute the preliminary score ψl,k for all AP-UAV (0) pairs using the weight wl , before optimizing Al . 8: Select nthe Jk APs with o the largest scores: Sk = (0) (0) TopJk ψ1,k , . . . , ψL,k . 9: end for 10: for each AP l = 1, . . . , L do 11: Determine the associated UAV set Ul = {k | l ∈ Sk }. 12: if Ul ̸= ∅ then 13: Optimize Al over Ul and construct the data-phase RHS weight wl . 14: else 15: Keep AP l inactive in the data phase. 16: end if 17: end for 18: Data transmission phase: 19: for each active AP l with Ul ̸= ∅ do 20: Generate zl = wlH yl and forward zl to the CPU. 21: end for 22: for each UAV k = 1, . . . , K do 23: Stack the selected AP outputs as zSk = [zl ]l∈Sk . 24: end for L L 25: return {Sk }K k=1 , {Ul }l=1 , and {wl }l=1 .

signal power, residual inter-UAV leakage, and filtered noise power. This makes it a covariance-aware observation-quality score rather than a distance- or fading-only metric.

1) Distance-, LSF-, and received-power-based methods: Many user-centric cell-free schemes select APs according to distance, LSF, or received power, e.g., SkLSF = TopJk {β1k , . . . , βLk }, and Skdist = Topmin Jk {d1k , . . . , dLk }. Representative examples include strongest-channel selection [12], power-based association [13], and threshold-based activation [14]. These methods mainly rank APs by βlk or d−α lk , whereas ψl,k also depends on the RHS response wl , the residual leakage wlH Hl,i Pi HH l,i wl , i ̸= k, and the filtered noise power σl2 wlH wl . Thus, a nearby AP or an AP with strong LSF may still be unfavorable if its post-RHS observation suffers from strong interference. 2) Coverage-, load-, and pilot-based methods: CAPA [15] and CLSF [17] improve scalability by considering coverage, pilot, or load constraints, but their AP contribution metrics are still largely based on large-scale fading. In contrast, ψl,k penalizes APs whose RHS receive response causes strong residual leakage. Therefore, it can be used as a replacement P for βlk in ψl,k ψ k . coverage- or load-aware frameworks, e.g., αk = Pl∈S L ψ j=1 j,k 3) MINLP- and learning-based methods: MINLP- and learning-based methods jointly optimize AP association with beamforming, power control, or fronthaul constraints [18]– [20]. They can directly target weighted sum rate or QoS, but often require binary optimization, iterative solvers, offline training, or policy learning. By contrast, after the RHS receive-pattern configuration, the proposed method ranks APs using ψl,k . Under the diagonal or weak inter-AP disturbancecorrelation approximation, the Top-Jk rule provides a lowcomplexity solution for the adopted additive observationquality surrogate. 4) SIM/DMA-, mmWave-, and multi-criterion methods: SIM-enabled [21], DMA-based [20], and mmWave cell-free association methods often use distance, received power, effective channel gain, or weighted sum rate under their own hardware constraints. Multi-criterion fuzzy methods further combine indicators such as LSF, received power, and packetloss probability [40]. These metrics are useful in their respective settings, but they do not explicitly model the singlefeed amplitude-controlled RHS receive response. The proposed score instead follows the single-feed RHS receive model through wl and evaluates the post-RHS signal-todisturbance quality score. If reliability indicators are also required, they can be incorporated multiplicatively, e.g., ψ̃l,k = loss (1 − ploss l,k )ψl,k , where pl,k denotes the packet loss ratio. 5) Conventional SINR-based association methods in phased-array MIMO systems: For a conventional digitally H combined AP, a user-specific output zl,k = vl,k yl can be formed, with γl,k

H vl,k Hl,k Pk HH l,k vl,k P . H 2 vl,k H ( i̸=k l,i Pi HH l,i +σl INl )vl,k

In contrast, each single-feed RHS AP considered here produces one shared scalar output zl = wlH yl H with wlH = (vl∗ ) = vl⊤ . Its probing-stage score is (0)

(0)

(wl )H Hl,k Pk HH l,k wl P (0) . The two ratios 2 ( i̸=k Hl,i Pi HH l,i +σl INl )wl (0) are algebraically identical for vl,k = wl ; hence, the ratio (0)

ψl,k =

(0) (wl )H

itself is not claimed as new. Their structural difference is that vl,k is generally user-specific, whereas wl is shared by the associated UAVs and constrained by the RHS hardware.

TABLE I: Comparison of representative AP association methods. Method Distance/LSF/power [12]–[14] Coverage/load/pilot [15], [17] MINLP/learning [18]–[20] SIM/DMA/mmWave/ multi-criterion [20]–[22], [40] Conventional SINR Proposed

AP metric Distance, LSF, or power

Association strategy Ranking or thresholding

LSF with network constraints Constrained selection Rate, QoS, or system state

Optimization or learning

Effective gain, rate, or multiple indicators

Architecture-specific design

SINR with a user-specific combiner Post-RHS desired gain, leakage, and noise

SINR ranking Lower-bound Top-K ranking

Table I compares the AP metrics and association strategies of representative methods. Existing low-complexity schemes mainly use large-scale information or user-specific SINR, whereas optimization and learning methods incur higher complexity. The proposed method uses post-RHS observation quality under a shared probing pattern and yields a lowcomplexity Top-Jk solution for the lower-bound surrogate. V. A NALYTICAL F INDINGS AND P ROOFS A. A nearer AP is not necessarily better Consider UAV k and two candidate APs l and m. In conventional distance-based association, if dlk < dmk , AP l would usually be preferred. However, under the RHS-enabled uplink reception model, the AP association priority is not determined only by distance or large-scale fading. It also depends on the RHS-induced desired effective channel, the residual inter-UAV leakage after RHS reception, and the filtered noise power. For AP l and UAV k, define Dl,k = wlH Hl,k Pk HH l,k wl , and P H H 2 Il,k = wl i̸=k Hl,i Pi Hl,i + σl INl wl . Then the per-AP association score can be written as ψl,k = Dl,k /Il,k . Corollary 1 (Observation-quality order reversal condition). AP l should be preferred over AP m under the additive surrogate whenever ψl,k > ψm,k . Equivalently, even if AP l has a weaker desired effective signal power than AP m, namely Dl,k < Dm,k , AP l can still be preferred if its normalized association score is larger: Dl,k /Il,k > Dm,k /Im,k . This can happen when AP l has a sufficiently smaller residual disturbance power Il,k . Proof. Please refer to Appendix A.

■

B. Large scale height-angle tradeoff From the element-level channel model in (5), the large scale geometry-dependent gain of the AP-UAV link is βlk cos θlk . p 2 + z 2 , and cos θ r Using βlk = C̄d−α χ , d = lk = lk lk lk lk lk zlk /dlk , we have α+1 2 2 − 2 βlk cos θlk = C̄χlk zlk rlk + zlk . (43) To isolate the height-angle tradeoff, we consider a local comparison where the transmit covariance, RHS combining pattern, and shadowing term are fixed. Then the desired

RHS receive pattern cannot effectively combine. Because ψl,k evaluates the post-RHS signal quality, it naturally deprioritizes APs whose effective receive gain is degraded by clutter. In open, uncluttered settings with randomly distributed UAVs, Corollary 2 (Height-angle tradeoff). For any α > 0 and fixed these advantages largely disappear and simpler association rlk = r > 0, the function f (zlk ) in (44) attains a unique suffices. The system model closely reflects the geometry and operation of an indoor industrial hall. The AP-UAV maximum at r geometry (rlk , zlk , θlk ) is fundamental to the height-angle ⋆ (45) zlk = √ . tradeoff (Corollary 2); an optimal vertical separation exists α only because APs are ceiling-mounted and UAVs operate at a Moreover, fixed altitude. The configuration is characteristic of factories α+3 2 ∂f 2 2 − 2 2 = r + zlk r − αzlk . (46) and warehouses but absent in general deployments. The UAV ∂zlk motion is modeled as deterministic, straight-line, constant⋆ Therefore, f (zlk ) increases for 0 < zlk < zlk and decreases speed, constant-altitude flight, which matches inspection tasks ⋆ along aisles and shelves while enabling trajectory-predictable for zlk > zlk . AP association updates in Algorithm 1. Finally, the channel Proof. Please refer to Appendix B. ■ model employs a large path-loss exponent and a strong logNote that the straight-line, approximately constant-altitude normal shadowing variance that capture the severe, heterotrajectory is a mission-prescribed model for aisle and shelf geneous indoor environment; it is this large variance that inspection, rather than a requirement of the proposed asso- produces the distance-order reversal probability reported in ciation rule. If UAV positions were controllable, trajectory Corollary 1, confirming the unreliability of geometry-based association in heavily obstructed industrial spaces. optimization could improve the √ desired gain by reducing The above analysis leads to the following deployment rlk or moving zlk toward rlk / α, and could reduce interguidelines. UAV leakage through greater angular separation. For curved Rule 1: AP association should use the post-RHS signal-toor altitude-varying trajectories, the proposed method remains disturbance score ψl,k rather than large-scale fading βlk alone. applicable by updating Hl,k (t) and ψl,k (t) at each association Rule 2: An AP should preferably serve UAVs with suffiinterval. ciently distinct transverse wavevectors or angular directions to reduce post-RHS leakage. C. More APs do not always bring significant gains Rule 3: Increasing the serving-cluster size gives diminishing According to the association score, let the candidate APs for returns, so a small set of high-quality APs is often sufficient. UAV k be ordered as ψ(1)k ≥ ψ(2)k ≥ · · · ≥ ψ(L)k . Define Rule 4: The installation height of ceiling-mounted RHS APs γ(j)k = ψ(j)k . For the additive scalar surrogate used by the should jointly consider path loss and projection gain, rather low-complexity ranking rule, if the first APs are selected, than only minimizing distance. JP J the surrogate rate is Rk (J) = log2 1 + j=1 γ(j)k . The Rule 5: When UAVs are sparse and inter-UAV overlap is weak, conventional large scale fading-based or distance-based marginal gain of adding the J-th AP is ! clustering can still serve as a low-complexity scheme. γ(J)k ∆Rk (J) = Rk (J)−Rk (J−1) = log2 1 + . PJ−1 1 + j=1 γ(j)k VI. S IMULATION (47) A. Simulation setup Corollary 3 (Cluster saturation law for additive surrogate). theP We consider the uplink UAV-centric cell-free scenario, J−1 For any ε > 0, if γ(J)k ≤ ε 1 + j=1 γ(j)k , then where each single-feed RHS-enabled AP forms one scalar output zl = wlH yl in each resource block. The same scalar ∆Rk (J) ≤ log2 (1 + ε). output can be forwarded to the CPU and used for detecting Proof. Please refer to Appendix C. ■ different UAVs. For UAV k, the CPU stacks the selected AP outputs {zl : l ∈ Sk } and evaluates the achievable rate D. Design guidelines for indoor industrial AP deployment using (22). The proposed association rule ranks candidate APs Conventional distance- or fading-based association fails in according to the post-RHS score. For comparison, the following benchmark association rules indoor industrial UAV networks for two reasons. First, when UAVs are clustered along similar inspection paths, they present are considered: nearly identical βlk and ranges to a given AP; ranking by these 1) Proposed score-based association: AP association based scalars cannot distinguish good APs from those that suffer on the post-RHS score ψl,k , which jointly accounts for severe inter-UAV overlap. The proposed score ψl,k directly the link strength βlk , the RHS response wl , residual intersenses this interference in its denominator, penalizing APs UAV leakage, and the local filtered noise term. that cannot spatially separate the target UAV. Second, dense 2) Large-scale fading: AP association based only on βlk . blockages create strong but angularly mismatched links. An 3) Nearest AP: AP association based only on the distance AP with a large βlk may collect multipath energy that the dlk . received power is proportional to the geometry-dependent factor in (43). For a fixed horizontal distance rlk = r, define α+1 2 − 2 f (zlk ) = zlk r2 + zlk . (44)

TABLE II: Simulation parameters Parameter hall L, K, J Mk , N l λ, ks

Value Dxhall = 40 m, Dyhall = 30 m, Dzhall =12 m L = 16, K = 24, J = 4 Mk = 4, ∀k; Nl = 256, ∀l λ = 0.025 m, 2π/λ = 251.33 rad/m, ks = [251.33, 0, 0]⊤ ql Ceiling APs on a 4 × 4 grid: ql,x ∈ {5, 15, 25, 35} m, ql,y ∈ {3.75, 11.25, 18.75, 26.25} m, ql,z = 12 m ul,n Centered 16 × 16 uniform planar grid, element spacing 0.005 m; qk,1 Users 1-8: (5, 5, 1.5) + [ϵx , ϵy , 0] m; users 9-16: (18, 13, 1.5) + [ϵx , ϵy , 0] m; users 17-24: (32, 22, 1.5) + [ϵx , ϵy , 0] m, where ϵx , ϵy ∼ uniform[−1.5, 1.5] m q̄k qk,1 + [0.075, 0, 0]⊤ Qk [qk,1 , qk,1 + [0.05, 0, 0]⊤ , qk,1 + [0.10, 0, 0]⊤ , qk,1 + [0.15, 0, 0]⊤ ] dk , vk dk = [0, 1, 0]⊤ , vk = 1 m/s, ∀k α, χlk , ξlk α = 2.2, χlk = 10ξlk /10 , ξlk ∼ N (0, 42 ) ηl,n , αs ηl,n = 1; αs = 0 unless otherwise stated; Pk , pk Pk = 0.1IMk , pk = 0.1, ∀k σl2 4.0 × 10−13 , ∀l

4) Pathloss and projection: AP association based on d−α lk cos θlk , which accounts for path loss and the receiving angle factor but not residual interference. 5) CAPA: coverage-aware AP association [15]. 6) CLSF: load-constrained large-scale fading [17]. The considered performance metrics include: • the minimum UAV spectral efficiency, min1≤k≤K Rk ; PK 1 • the average spectral efficiency, K k=1 Rk ; PK 2 ( P k=1 Rk ) • Jain’s fairness index, J = 2 ; K K R k=1 k • the energy efficiency, PK transmit-power-normalized R PK k=1 k ; tr(P ) k

k=1

K k=1

L l=1

B. Simulation results and discussion Fig. 5 shows the minimum UAV data rate versus the number of UAVs. As the number of requesting UAVs increases, the minimum rate decreases for all association schemes because the uplink becomes more interference-limited and the weakest UAVs suffer from stronger inter-UAV overlap. The proposed method achieves the highest minimum data rate over the whole range of K, demonstrating its advantage in protecting weak UAVs. This is because the proposed score considers not only the desired effective RHS gain but also the residual overlap and local disturbance covariance. Among the benchmarks, the nearest-AP rule gives the lowest rate, which confirms that geometric proximity alone is insufficient for RHS-enabled indoor UAV cell-free reception. 3

Proposed Large-scale fading Nearest AP Pathloss and projection CAPA CLSF

2.5

1.5

(z)

the normalized single-AP score, maxzl,kψl,k (z) ; • the average marginal gain of adding APs to the serving cluster, as defined in (47); • the of distance-order reversal, P Pprobability P

•

vary the standard spatial spread of the UAVs around three localized inspection regions from 0.5 to 6 m. The other parameters follow the default setup with L = 16, K = 24, J = 4, Mk = 4, and Nl = 256. All association methods use the same channel realizations.

m=1 I(dlk <dmk , ψl,k <ψm,k ) m̸=l PL PL ; k=1 l=1 m=1 I(dlk <dmk ) m̸=l

0.5 12

Fig. 5: Minimum UAV data rate versus the number of UAVs.

the Top-J overlap ratio; The simulation scenario and default parameter values are summarized in Table II. The UAVs’ initial positions are clustered into three groups to emulate localized warehouse inspection task regions. All UAVs move along straight-line trajectories at a constant altitude with a constant speed of 1 m/s and a common heading direction d = [0, 1, 0]⊤ . The flight duration is 4 seconds. To evaluate the performance-loss trade-off related to exhaustive search or optimization/learning-based methods, we further consider a small-scale system with L = 5, K = 4, J = 2, Mk = 2, and Nl = 36; each marker represents one independent channel realization, and all methods use the same channels, RHS constraints, and CPU-side rate evaluator. The optimization/learning-based method uses one-swap refinement, which starts from the proposed Top-Jk association and repeatedly replaces one selected AP with one unselected AP whenever the exchange improves the exact CPU-side sum rate. To isolate the influence of industrial UAV clustering, we •

Fig. 6 plots the average spectral efficiency versus the number of UAVs. The average spectral efficiency decreases with K because more simultaneous UAV transmissions increase the aggregate interference and reduce the effective post-combining SINR. The proposed association consistently outperforms all benchmark methods. This indicates that post-RHS signal-todisturbance score ranking improves not only the worst-user performance but also the overall system throughput. The performance gap between the proposed method and the nearestAP rule is significant, showing that selecting APs according to distance may lead to poor AP choices when the nearest AP has unfavorable RHS angular response or strong multi-UAV overlap. Fig. 7 shows Jain’s fairness index versus the number of serving APs J. The fairness index increases as J becomes larger, because adding more serving APs provides additional macrodiversity and reduces the probability that a UAV is served only by weak or highly interfered APs. The proposed method achieves the best fairness performance among the compared schemes. This confirms that the proposed association score

5.5

Proposed Large-scale fading Nearest AP Pathloss and projection CAPA CLSF

13 12

4.5

3.5

9 8

7 2.5

Fig. 6: Average spectral efficiency versus the number of UAVs.

Fig. 8: Energy efficiency versus the number of UAVs.

is effective in balancing service quality across UAVs. The fairness gain becomes more visible when the serving-cluster size is moderate or large, where the proposed method can select APs that jointly provide strong desired gain and low disturbance.

weak UAVs is often more critical than peak throughput. The nearest-AP based scheme has the leftmost CDF, confirming that distance-based association leads to inferior rate reliability in the considered RHS-enabled cell-free network. 1 0.9 0.8

0.92

0.7 0.9

0.6

Proposed Large-scale fading Nearest AP Pathloss and projection CAPA CLSF

0.5

0.88

0.4 0.86

0.3 0.84

0.2

Proposed Large-scale fading Nearest AP Pathloss and projection CAPA CLSF

0.82

0.1 0 0

5.5

6.5

7.5

Fig. 9: CDF of the per-UAV data rate. Fig. 7: Jain fairness index versus the number of serving APs. Fig. 8 compares the energy efficiency of different AP association schemes. The energy efficiency decreases as the number of requesting UAVs increases, since the total transmit power grows with K while the achievable sum spectral efficiency is increasingly limited by inter-UAV overlap. The proposed method achieves the highest energy efficiency in all simulated cases. This means that, for the same transmit-power budget, the proposed ranking-based AP association can extract more useful information from the distributed RHS-enabled APs. The nearest-AP rule again gives the lowest energy efficiency because it may select APs with high disturbance even if they are close to the UAV. Fig. 9 presents the CDF of the per-UAV data rate. The CDF curve of the proposed method is shifted to the right compared with all benchmark schemes, which means that it improves the rate distribution of individual UAVs. In particular, for the same outage probability, the proposed method provides a higher perUAV data rate. This lower-tail improvement is important for indoor industrial UAV applications, where reliable service to

Fig. 10 verifies the first analytical finding that the nearest AP is not necessarily the best AP. The distance-order reversal probability is clearly nonzero for all considered shadowing standard deviations and UAV numbers. This means that a farther AP can provide a better association score than a nearer AP. The reason is that the proposed score depends on the effective RHS channel gain, angular separability, inter-UAV overlap, and disturbance covariance, rather than only on distance. Moreover, the reversal probability becomes higher when the shadowing standard deviation increases, which indicates that the distance order becomes less reliable in more heterogeneous indoor propagation environments. Fig. 11 verifies the second analytical finding, namely the AP-UAV height-angle tradeoff. For each horizontal distance r, the normalized single-AP score first increases and then decreases with the AP-UAV relative height difference z. This confirms the existence of an interior optimal height difference. When z is too small, the UAV observes the ceiling-mounted RHS with a large incidence angle, which reduces the projection gain. When z is too large, the increased propagation

0.11 K=8 K = 12 K = 16 K = 20 K = 24

0.1

0.35

0.09 Shadow std. 0 dB Shadow std. 2 dB Shadow std. 4 dB Shadow std. 6 dB Shadow std. 8 dB

0.3

0.08 0.07

0.25

0.06 0.2

0.05 0.04

0.15

0.03 0.1 12

0.02 5

5.5

6.5

7.5

Fig. 10: Distance-order reversal probability versus the number of UAVs.

Fig. 12: Average marginal gain versus the number of serving APs.

distance and path loss dominate. Therefore, AP deployment height should not be determined only by the shortest-distance rule, but should jointly consider path loss and RHS angular response.

select APs with strong average channels but severe multi-UAV overlap. Therefore, this result confirms the key motivation of the proposed method: AP association in RHS-enabled indoor UAV cell-free networks should be based on post-combining quality rather than distance or large-scale fading alone.

1 0.9

0.9 0.8

0.8 0.7

0.7

0.6 0.5

0.6

0.4

0.5 0.4

0.3

r=3m r=5m r=7m r=9m r = 11 m

0.2 0.1

Proposed Large-scale fading Nearest AP Pathloss and projection CAPA CLSF

0.2 0.1

0 2

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Fig. 11: Normalized single-AP score versus AP-UAV relative height difference.

Fig. 13: CDF of the selected AP overlap ratio.

Fig. 12 verifies the third analytical finding, i.e., the cluster saturation law. The average marginal gain ∆Rk (J) decreases as the number of serving APs increases. This shows that the first few selected APs provide most of the useful rate improvement, while adding more APs brings only a small additional gain. The result supports the proposed Top-J ranking rule and suggests that a practical system can use an adaptive stopping criterion: if the marginal gain of adding one more AP is below a prescribed threshold, the serving cluster can stop expanding. Fig. 13 shows the CDF of the selected AP overlap ratio. A smaller selected AP overlap ratio indicates that the chosen APs experience less residual inter-UAV leakage relative to the useful desired component. The proposed curve is shifted to the left, which means that the proposed method selects APs with lower effective overlap than the benchmark schemes. This behavior directly follows from the disturbance term in the proposed association score. In contrast, large-scale-fading, pathloss-and-projection, and nearest-AP based methods may

Fig. 14 shows a clear performance-complexity tradeoff. The proposed Top-Jk method requires only about 10−4 − 10−3 s, but achieves a lower average spectral efficiency. The one-swap optimization improves the spectral efficiency and approaches the exhaustive-search result while requiring only about 10−2 s. Exhaustive search provides the highest-performance reference, but its runtime is around 100 s. Thus, the proposed method offers the lowest online complexity while only about 14% performance loss. Fig. 15 evaluates the effect of localized industrial UAV operation. When the UAV cluster spread is small, candidate APs observe more similar UAV directions and hence stronger residual overlap. The proposed method consistently selects APs with lower overlap than LSF and CLSF because this interference is explicitly included in its score. As the UAVs become more dispersed, the overlap decreases for all methods. This result clarifies that the main scenario-specific advantage of the proposed rule arises in clustered industrial inspection

A PPENDIX A P ROOF OF C OROLLARY 1

m,k l,k , ψm,k = Im,k . Thus, Proof. ψl,k = Il,k

ψl,k > ψm,k

(48)

Dl,k Dm,k > . Il,k Im,k

(49)

is equivalent to 4

Since Il,k > 0, Im,k > 0, we have 2

Dl,k Im,k > Dm,k Il,k . -3.5

-3

-2.5

-2

-1.5

-1

-0.5

(50)

Fig. 14: Performance-runtime tradeoff (K = 4) deployments, rather than in open and sparsely populated environments.

Even if Dl,k < Dm,k , the inequality Dl,k Im,k > Dm,k Il,k Dl,k Il,k < Dm,k . Therefore, AP l can be can still hold when Im,k preferred over AP m even when its desired effective signal power is smaller, provided that its effective disturbance power is sufficiently smaller. This completes the proof. ■

0.935

A PPENDIX B P ROOF OF C OROLLARY 2

0.93 0.925 0.92 0.915 0.91 Proposed Large-scale fading CLSF

0.905 0.9 0.895 0.89 0.885 0.5

1.5

2.5

3.5

4.5

5.5

Fig. 15: Average selected AP overlap ratio versus the UAV cluster spread.

VII. C ONCLUSION This paper investigated AP association for uplink RHSenabled cell-free networks in indoor industrial UAV scenarios. A post-RHS signal-to-disturbance score was proposed as the association metric, which jointly captures large-scale fading, effective post-RHS channel gain, residual inter-UAV overlap after holographic combining, and local disturbance power. Under the assumption of weak inter-AP disturbance covariance, a low-complexity ranking rule based on per-AP scores was derived. The analysis established three findings: a nearer AP is not necessarily the optimal serving AP; the relative APUAV height difference creates a height-angle tradeoff with an interior optimum; and enlarging the serving cluster brings diminishing marginal gains. Simulations with clustered UAVs moving along straight-line constant-altitude inspection trajectories demonstrated that the proposed method improves the minimum UAV data rate, average spectral efficiency, fairness, and transmit-power-normalized energy efficiency compared with conventional distance-, fading-, and coverage-based association schemes.

Proof. From the definition of f (zlk ), f (zlk ) = α+1 2 − 2 zlk r2 + zlk . Then α+1 α+3 ∂f α+1 2 2 − 2 2 − 2 + zlk − 2zlk = r2 + zlk r + zlk ∂zlk 2 α+1 α+3 − 2 2 2 − 2 2 = r2 + zlk − (α + 1)zlk r2 + zlk α+3 2 2 2 2 − 2 r + zlk − (α + 1)zlk = r2 + zlk α+3 2 2 − 2 2 = r2 + zlk r − αzlk . (51) α+3 ∂f 2 − 2 2 Since r2 + zlk > 0, we have ∂z > 0 ⇐⇒ r − lk ∂f r r 2 √ √ αzlk > 0 ⇐⇒ 0 < zlk < α , ∂zlk = 0 ⇐⇒ zlk = α , ∂f ⋆ < 0 ⇐⇒ zlk > √rα . Therefore, zlk = √rα is the and ∂z lk unique maximizer of f (zlk ). ■ A PPENDIX C P ROOF OF C OROLLARY 3 γ(J)k Proof. From (47), ∆Rk (J) = log2 1 + 1+PJ−1 γ j=1

 γ(J)k ≤ ε 1 +

J−1 X

. If

(j)k

 γ(j)k  ,

(52)

γ(J)k PJ−1

≤ ε.

(53)

γ(J)k PJ−1

≤ 1 + ε.

(54)

j=1

then

Therefore, 1+

j=1 γ(j)k

Since log2 (·) is monotonically increasing, ∆Rk (J) log2 (1 + ε). This completes the proof.

≤ ■

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