Rotatable Antenna Assisted Mobile Edge Computing

1 Rotatable An tenna Assisted Mobile Edge Computing Ji W ang, Senior Mem b er, IEEE, Hao Chen, Yixuan Li, Jun Zhang, Xingw ang Li, Senior Mem b er, IEEE, Ming Zeng, and Octa via A. Dobre, F ello w, IEEE Abstract—This pap er inv estigates a rotatable antenna (RA) assisted mobile edge computing (MEC) netw ork, where multi- ple users ooad their computation tasks to an edge server equipp ed with an RA array under a time-division multiple access protocol. T o maximize the weigh ted sum computation rate, w e formulate a join t optimization problem ov er the RA rotation angles, time-slot allo cation, transmit pow er, and lo cal CPU frequencies. Due to the non-conv ex nature of the form ulated problem, a scenario-adaptive h ybrid optimization algorithm is prop osed. Sp ecically , for the dynamic rotating scenario, where RAs can exibly reorient within each time slot, we derive closed-form optimal antenna p ointing v ectors to enable a lo w-complexity sequen tial solution. In con trast, for the static rotating scenario where RAs maintain a unied orienta- tion, we develop an alternating optimization framew ork, where the non-con vex RA rotation constraints are handled using successiv e con v ex appro ximation iterativ ely with the resource allo cation. Sim ulation results demonstrate that the proposed RA assisted MEC netw ork signicantly outperforms conv en- tional xed-antenna MEC netw orks. Owing to the additional spatial degrees of freedom in tro duced b y mec hanical rotation, the exibility of RAs eectively mitigates the severe b eam misalignmen t inherent in xed-antenna systems, particularly under high an tenna directivit y . Index T erms—Rotatable antennas, mobile edge computing, task ooading, antenna p ointing, alternating optimization. I. Introduction T HE rapid proliferation of In ternet-of-Things (IoT) devices and articial intelligence–driv en applications is imp osing unpreceden ted computational and latency requiremen ts on sixth-generation wireless netw orks. The paradigm of mobile edge computing (MEC) has emerged as a piv otal arc hitecture to mitigate these bottlenecks, primarily via the migration of computationally demanding w orkloads from capacity-limited terminals to proximal edge infrastructure [1]. Nev ertheless, the p erformance Ji W ang, Hao Chen, and Yixuan Li are with the De- partment of Electronics and Information Engineering, College of Ph ysical Science and T echnology , Cen tral China Normal Universit y , W uhan 430079, China (e-mail: jiwang@ccn u.edu.cn; 1280904251ch@mails.ccn u.edu.cn; yixuanli@mails.ccnu.edu.cn). Jun Zhang is with the School of Physics and Electronic Engi- neering, Hub ei Universit y of Arts and Science, Xiangyang 441053, China, and also with the Hub ei Provincial Engineering Research Center of Emergency Comm unication T echnology and System, Xi- angyang 441053, China (e-mail: hbuas_zhangjun@hbuas.edu.cn). (Corresponding author: Jun Zhang.) Xingwang Li is with the School of Physics and Electronic Infor- mation Engineering, Henan Polytec hnic Universit y , Jiaozuo 454003, China (e-mail: lixingwang@hpu.edu.cn). Ming Zeng is with the Departmen t of Electrical and Computer Engineering, Lav al Universit y , Queb ec City , QC G1V 0A6, Canada (e-mail: ming.zeng@gel.ulav al.ca). Octavia A. Dobre is with the F aculty of Engineering and Applied Science, Memorial Universit y , St. John’s, NL A1C 5S7, Canada (e- mail: o dobre@mun.ca). Fig. 1. The prop osed RA assisted MEC system mo del. gains achiev able b y MEC are fundamentally limited by the quality of the wireless computation ooading links, making communication eciency a critical b ottlenec k [2]. Most existing MEC systems rely on xed antennas (F As) at the base station. While directional antennas are desirable for their high gain, extended transmission range, and strong interference resistance, their inherent narro w b eamwidths make them highly sensitiv e to direc- tionalit y . Once a user’s p osition deviates from the xed p oin ting direction, the adv antage of high gain instantly b ecomes a disadv antage, leading to a sharp decline in link qualit y . This physical rigidity often results in sev ere b eam misalignment and degraded ooading eciency , particularly in scenarios with uneven user distributions or dynamically changing channel conditions [3]. Although con v entional multiple-input multiple-output architectures partially exploit spatial diversit y , the xed placement and orien tation of antenna elemen ts inherently constrain their abilit y to fully capitalize on spatial c hannel v ariations in data-in tensiv e MEC applications. T o address these limitations, recongurable intelligen t surfaces (RISs) [4]–[7] and pinching an tennas (P As) [8], [9] explore spatial degrees of freedom, but they face c hallenges suc h as double-fading eects and hardware implementa- tion complexity , resp ectively . In contrast to RIS- and P A-based approac hes that manipulate the propagation medium or radiation lo cation, rotatable antennas (RAs) exploit spatial adaptability by mec hanically steering the an tenna b oresight in three-dimensional (3D) space to align with dominant c hannel directions [10]. By leveraging mec hanical degrees of freedom to trade for spatial degrees of freedom, RAs provide more precise and stronger b eam alignmen t. This mec hanism eectiv ely mitigates the severe b eam misalignment inheren t in xed-antenna systems, ensuring that the high gain of directional antennas is fully utilized ev en for disp ersed users. Moreo ver, compared with mo v able antennas, which require contin uous p osi- 2 tional adjustments and inc ur signicant mechanical and con trol complexity [11], RAs oer a substantially low er- complexit y solution by leveraging rotational motion only , making them particularly attractive for practical MEC deplo ymen ts. Recen t studies hav e established a growing b o dy of work on RA-assisted wireless systems, encompassing channel mo deling [10], ecient channel estimation strategies [12], and adv anced applications suc h as integrated sensing and communications [13], physical-la y er security [14], and h ybrid mov able–rotatable antenna architectures [15]. No- tably , these works ha v e theoretically and exp erimentally v eried that RA-assisted systems outp erform con ven tional xed-an tenna systems in v arious scenarios [10], [12]–[14]. It has b een demonstrated that the p erformance gain of RAs increases with the antenna directivity factor, conrming that rotational exibilit y is essen tial to un- lo c k the p oten tial of narro w-b eam directional an tennas. F urthermore, the feasibility of RA implemen tation has b een v alidated through hardware prototypes and dynamic demonstrations [10]. How ever, the integration of RAs into MEC frameworks has received scant attention in the existing literature. In particular, existing MEC-orien ted resource allo cation framew orks do not account for the rotational degrees of freedom oered by RAs, nor do they in v estigate the synergistic orchestration of antenna orien- tation alongside transmission and pro cessing resources to impro v e ooading eciency . T o fully unlo ck the p otential of RAs in MEC, we form ulate a joint resource optimization problem that maximizes the weigh ted sum computation rate by jointly optimizing the RA rotation angles, time-slot durations, transmit p ow er allo cation, and lo cal CPU frequencies. T o address the non-conv ex problem, we develop a scenario- adaptiv e hybrid optimization algorithm (SAHO). This strategy eciently adapts the solution structure to the RA op erating mo de to balance p erformance and complex- it y . Specically , for the dynamic rotating scenario, w e exploit the derived closed-form optimal pointing solution to decouple the problem, allowing for a fast sequential optimization of antenna orientation and ooading re- sources. Conv ersely , for the practical static rotating sce- nario, where v ariables are intricately coupled, we prop ose an alternating optimization (AO) metho d. This metho d iterativ ely up dates the RA rotation angles via successiv e con v ex approximation (SCA) and the ooading resources via conv ex optimization until conv ergence. I I. System Mo del Fig. 1 depicts the considered uplink MEC framework, wherein a base station (BS) in tegrated with an edge serv er supp orts M users, each ha ving a single antenna. The BS utilizes a uniform planar array (UP A) comp osed of K = K x × K y RAs, with K x and K y represen ting the arra y dimensions along the x- and y-axes. T ransmission is go v erned b y a time-division multiple access (TDMA) proto col with a frame length of T . A. Netw ork Geometry and Channel Model The UP A is deploy ed in the x-y plane, with ad- jacen t elemen ts separated b y a distance ∆ . The co ordinate of the k -th RA is given b y w k = [ k x ∆ , k y ∆ , 0] T , where k x and k y are indices relativ e to the arra y cen ter. The m -th user is lo cated at u m = [ r m sin ψ m cos φ m , r m sin ψ m sin φ m , r m cos ψ m ] T , where r m denotes the distance of user m from the origin, and ψ m ∈ [0 , π ] and φ m ∈  − π 2 , π 2  represen t the zenith and azimuth angles of the m -th user relative to the co ordinate origin, resp ectively . Unlik e xed antenna systems, each RA k can mec hani- cally rotate its b oresight direction, c haracterized by a unit p oin ting vector f k ∈ R 3 . Let θ z ,k and ϕ a,k represen t the zenith and azim uth denitions for the rotation of the k - th RA. Accordingly , its p ointing v ector is formulated as f k = [sin θ z ,k cos ϕ a,k , sin θ z ,k sin ϕ a,k , cos θ z ,k ] T . T o av oid hardw are coupling, the rotation is constrained by a max- im um zenith angle θ max , i.e., 0 ≤ θ z ,k ≤ θ max . Here, ( ϵ, ϕ ) denotes the incident angle tuple c haracterizing an arbitrary spatial direction relativ e to the RA’s boresight axis. Due to the symmetry of the antenna pattern, the gain dep ends only on ϵ . A ccordingly , the eective antenna gain from user m to RA k follows G k,m = G 0 cos 2 p ( ϵ k,m ) , where G 0 is the maximum gain, p is the directivity factor, and cos( ϵ k,m ) ≜ f T k q k,m represen ts the cosine of the misalignmen t angle, with q k,m ≜ u m − w k ∥ u m − w k ∥ . Assuming quasi-static at fading, the ov erall m ultipath c hannel betw een user m and the k -th RA at the BS is mo deled as h k,m ( f k ) =  L ( d k,m ) G k,m g k,m . Here, L ( d k,m ) characterizes the large-scale attenuation, whic h is formulated as L ( d k,m ) = A 0 ( d 0 /d k,m ) α m . In this ex- pression, d k,m represen ts the spatial separation b et w een user m and the k -th RA, while A 0 and α m denote the c hannel gain at the reference distance d 0 = 1 m and the path-loss exp onent, resp ectively . The small-scale fading coecient g k,m is mo deled as a sup erp osition of a deterministic line-of-sight (LoS) path and a scattered comp onent, go verned b y the Rician factor κ m . This is formulated as g k,m =  κ m / ( κ m + 1) ¯ g k,m +  1 / ( κ m + 1) ˜ g k,m , wherein g k,m = e − j 2 πd k,m λ signies the LoS phase rotation, and ˜ g k,m ∼ C N (0 , 1) captures the non- LoS Ra yleigh fading eects. W e dene the p oin ting matrix collecting all RA boresight vectors as F ≜ [ f 1 , f 2 , . . . , f K ] . Then, the channel vector from user m to the BS is written as h m ( F ) ≜ [ h 1 ,m ( f 1 ) , h 2 ,m ( f 2 ) , . . . , h K,m ( f K )] T .F or ana- lytical con venience, we assume that the BS has acquired the global channel state information of all links. B. Computation and Ooading Mo dels W e adopt a partial ooading mo del where tasks are executed lo cally or ooaded to the RA assisted edge server via TDMA. 1) Lo cal Computing: F or user m , let f m b e the CPU frequency . W e dene the lo cal CPU frequency v ector for all users as f ≜ [ f 1 , f 2 , . . . , f M ] T . The lo cally processed data size is R loc ,m = T f m /C , and the energy consumption is E loc ,m = T r c f 3 m , with T and r c represen ting the duration 3 of the en tire time frame and the eective capacitance parameter, resp ectively . 2) Computation Ooading: Under the TDMA sc heme, users transmit in orthogonal slots τ m , eliminating inter- user interference. Considering a comm unication o verhead factor v m > 1 , which accoun ts for channel co ding redun- dancy and protocol headers, the ooaded data size R of f ,m is given by R o ,m = τ m B v m log 2 ( 1 + p m ∥ h m ( F ) ∥ 2 σ 2 ) , (1) where B is the bandwidth, p m is the transmit pow er, and σ 2 is the noise pow er. The corresp onding energy consumption E o ,m is denoted as E o ,m = τ m ( p m + p c,m ) , where p c,m is the circuit p ow er consumption. C. Problem F orm ulation W e establish the computation rate maximization mo del (P1) b y join tly optimizing the RA p ointing matrix F , lo cal CPU frequency vector f , time-slot allocation v ector τ , and transmit p o w er v ector p . Specically , F determines the antenna p ointing directions of the RAs sub ject to the ph ysical rotation constraints, while f , τ , and p co ordinate the computation and communication resources under en- ergy and latency budgets. The problem is formulated as (P1) : max p , τ , f , F M  m =1  R loc ,m + R o ,m  (2a) s.t. E o ,m + E loc ,m ≤ E max , ∀ m, (2b) M  m =1 τ m ≤ T , 0 ≤ τ m ≤ T , ∀ m, (2c) p m ≥ 0 , f m ≥ 0 , ∀ m, (2d) R loc ,m + R o ,m ≥ R min , ∀ m, (2e) 0 ≤ θ z ,m ≤ θ max , ∀ m. (2f ) I I I. Joint Optimization Solution and Algorithm The non-conv exity inherent in (P1) arises principally from the complex in terplay in volving the RA p ointing matrix F , the resource allocation v ariables ( { f , p , τ } ), and the non-conv ex unit-mo dulus constrain ts on the p ointing v ectors. Considering the diculty of directly solving the problem P1, w e decouple the problem in to RA rotation optimization and ooading optimization subproblems. F or RA rotation optimization, w e separately address the dynamic and static rotatable antenna scenarios, account- ing for the rotation speed of RAs relativ e to the TDMA frame length. In the ooading optimization stage, the p oin ting matrix is held xed, and the remaining resource allo cation problem b ecomes conv ex, allowing it to b e solv ed eciently . A. RA Rotation Optimization In the RA rotation optimization pro cedure, we focus on optimizing the RA p ointing matrix F to maximize the directional gain, while k eeping the ooading parameters { f , p , τ } xed. W e consider tw o scenarios based on the RA’s rotation timescale: 1) dynamic rotation, and 2) static rotation. 1) Dynamic rotation: Under the uplink rate within the time slot, the optimization of antenna orientation aims to maximize pro jection b et w een f k and q k,m , whic h can b e form ulated as (P2) : max f k f T k q k,m (3a) s.t. ∥ f k ∥ = 1 , (3b) 0 ≤ arccos( f T k e 3 ) ≤ θ max , (3c) where, e 3 = [0 , 0 , 1] T corresp onds to the standard basis v ector aligned with the z-axis. The ob jectiv e f T k q k,m = cos( ϵ k,m ) represen ts the directional projection b etw een the RA b oresight and the user direction. Maximizing this v alue is equiv alent to minimizing the p ointing deviation ϵ k,m . The (P2) is a constrained linear optimization ov er a unit sphere and admits a closed-form global optim um whic h is given by f ⋆ n =            q k,m , if arccos( u T m,n e 3 ) ≤ θ max ,    sin θ max cos ϕ a,k sin θ max sin ϕ a,k cos θ max    , otherwise , (4) where the rotation angles are calculated as θ z ,k ≜ min  arccos  q T k,m e 3  , θ max  , (5) ϕ a,k ≜ arctan2  q T k,m e 2 , q T k,m e 1  , (6) and the standard basis vectors are dened as e 1 = [1 , 0 , 0] T , e 2 = [0 , 1 , 0] T , and e 3 = [0 , 0 , 1] T . When the user direction lies within the rotation range (i.e., arccos( q T k,m e 3 ) ≤ θ max ), the RA b oresigh t is steered to coincide exactly with the user’s angular direction, thereb y attaining the peak directional gain. Otherwise, the RA is rotated to its maximum zenith angle θ max while maintaining the azimuth alignmen t, ac hieving “edge alignmen t” within the feasible region. Consequen tly , the optimal pointing matrix for all RAs in time slot m is F ⋆ = [ f ⋆ 1 , f ⋆ 2 , . . . , f ⋆ K ] . This result aligns with theoretical predictions, as the BS realizes the p eak directional gain K G 0 pro vided that the b oresigh t axis of ev ery RA is strictly steered to ward the user’s angle of arriv al, i.e., f k = q k,m . 2) Static rotation: How ever, the assumption of exible re-orien tation within eac h time slot is ideal but practi- cally challenging. Due to the inheren t mechanical inertia, the rotation sp eed of RAs is signican tly slo w er than the time-slot switc hing frequency in TDMA proto cols. Consequen tly , it is ph ysically impossible for RAs to instan taneously realign their b oresight for dieren t users in consecutive slots. Instead, a unied antenna orientation m ust b e determined to serve all users eectively through- out the entire timeframe. F or a given ooading parameter { f , p , τ } , problem (P1) can b e reform ulated as (P3) max F M  m =1 ( R loc ,m + R o ,m ) (7a) s.t. 0 ≤ θ z ,k ≤ θ max , ∀ k . (7b) 4 Crucially , the deection angles primarily mo dulate the c hannel p o w er gain via the pro jection term cos( ϵ k,m ) . T o facilitate the SCA-based algorithm, we rewrite the channel co ecien t b y grouping the constan t terms and explicitly expressing the dep endence on the p ointing vector f k . The c hannel is reformulated as h m ( f k ) = ˜ β m,k  f T k q k,m  p , (8) where ˜ β m,k ≜  L ( d m,k ) G 0 g k,m . By substituting the reform ulated scalar c hannel ele- men ts from (8) in to the system c hannel v ector h m ( F ) , it b ecomes evident that the eective channel gain is directly determined b y the RA p ointing matrix F . Consequently , the optimization in (P3) is equiv alent to maximizing the ooading sum rate with resp ect to F . (P4) max F M  m =1 τ m B v m log 2  1 + p m ∥ h m ( F ) ∥ 2 τ m σ 2  (9a) s.t. cos( θ max ) ≤ f T k e 3 ≤ 1 , ∀ k, (9b) ∥ f k ∥ = 1 , ∀ k . (9c) Here, (9b) mirrors the constraint in (7b), while (9c) strictly enforces the unit-norm requirement on f k . Since Problem (9) retains its non-conv ex character, rendering a direct solution in tractable, we resort to the SCA frame- w ork to construct a con vex surrogate, thereb y iterativ ely approac hing a lo cal optimum. Sp ecically , during the ( i + 1) -th up date, given the prior estimates F ( i ) and R ( i ) of f , w e linearize the logarithmic term in (9) via a rst-order T aylor expansion around f ( i ) k , yielding the approximation Λ ( i +1) r ( F ) formulated b elow ˜ h m,k = ∂ h m,k ( f ( i ) k ) ∂ f ( i ) k = ˜ β m,k p  ( f ( i ) k ) T q k,m  p − 1 q k,m . (10) Consequen tly , for the ( i + 1) -th iteration, problem (P4) is reform ulated via approximation as (P5) max F Λ ( i +1) r ( F ) (11a) s.t. (9b) , (9c) . (11b) Nev ertheless, (P5) retains its non-conv ex character arising from the unit-mo dulus restriction in (9c). Con- sequen tly , w e apply a relaxation to ∥ f k ∥ ≤ 1 , thereby establishing the conv ex formulation presented b elow (P6) max F Λ ( i +1) r ( F ) (13a) s.t. cos( θ max ) ≤ f T k e 3 ≤ 1 , ∀ k, (13b) ∥ f k ∥ ≤ 1 , ∀ k . (13c) Since (P6) constitutes a standard conv ex optimization form ulation, it admits ecient n umerical solutions using the CVX to olkit. F urthermore, o wing to the relaxation applied to the equalit y restriction (13c), the resulting optimal v alue of (P6) serves as a theoretical upp er b ound for the original problem (P5). After obtaining the optimal solutions of the CPU frequencies, w e normalize each p oint- ing vector f k in F to satisfy constraint (9c), i.e., f ∗ k = f k ∥ f k ∥ . This normalization only scales f k to a unit vector without c hanging its direction; hence, f ∗ k also satises (9b). B. Ooading Optimization Giv en the RA p ointing matrix F , the eective c han- nel gains b ecome xed parameters. Consequently , the remaining optimization for ooading resources { f , p , τ } shares the same mathematical form ulation. A ccordingly , the signal captured b y the base station during the m - th transmission interv al is y m = √ p m h m ( F ) x m + n m , where x m denotes the information sym b ol satisfying E [ | x m | 2 ] = 1 , and n m ∼ C N ( 0 , σ 2 I ) characterizes the v ector of additive white Gaussian noise. Consequen tly , problem (2) can b e reduced to (P7) : max y , τ , f M  m =1  T f m C + τ m B v m L m ( F ( i ) )  (14a) s.t. y m + τ m p c,m + T r c f 3 m ≤ E max , ∀ m, (14b) (2c) , (2e) , y m ≥ 0 , f m ≥ 0 , ∀ m. (14c) Let L m ( F ( i ) ) = log 2  1 + y m ∥ h m ( F ( i ) ) ∥ 2 τ m σ 2  . (15) Up on insp ection, the conv exity of the constraints (14c) within (P7) is readily v eried. This is b ecause (2e) exhibits the structure of a function low er-b ounded by a constan t, while the remaining conditions are comp osed en tirely of linear inequalities. In (14b), the left-hand side y m + τ m p c,m + T r c f 3 m is con v ex with resp ected to ( y m , τ m , f m ) due to the cubic term with p ositive coe- cien t), hence (14b) is conv ex. F or the ob jective (P7), the term τ m B v m log 2  1 + y m ∥ h m ( F ( i ) ) ∥ 2 τ m σ 2  is the p ersp ective of the conca v e function B v m log 2  1 + y m ∥ h m ( F ( i ) ) ∥ 2 σ 2  , and is therefore jointly concav e in ( τ m , y m ) (p ersp ective preserves conca vit y [16]). The remaining term T f m C is linear in f m . Consequently , (P7) constitutes a conv ex optimization form ulation, which is amenable to ecient resolution via established standard solvers. C. Overall Solution Strategy and Its Complexit y Algorithm 1 outlines the proposed joint optimization framew ork. The complexity is O ( M K + M 3 ) for the dynamic case and ˜ O ( I iter ( I SCA K 3 . 5 + M 3 )) for the static case, where I iter is the num b er of outer iterations. IV. Simulation Results This section is dedicated to assessing the ecacy of the dev elop ed RA-assisted MEC framework. W e assume a carrier frequency of 2.4 GHz ( λ = 0 . 125 m). The BS is equipp ed with a UP A of K = K x × K y RAs with spacing ∆ = λ/ 2 . Unless otherwise stated, the default settings are: K = 9 ( 3 × 3 ), p = 4 , θ max = π / 3 , M = 4 users, T = 1 s, B = 10 MHz, C = 1000 cycles/bit, E max = 10 J, σ 2 = − 100 dBm, and Rician factor κ m = 1 . User terminals are spatially dispersed with uniform density within a 3D cylindrical volume enclosing the central BS. Sp ecically , the horizontal distance of eac h user from the BS follows a uniform distribution in [20 , 50] m, and the user height is uniformly distributed in [10 , 30] m. W e b enchmark the prop osed Static Rotatable Antenna (SRA) sc heme against t w o baselines: a Fixed Antenna 5 Λ ( i +1) r ( F ) ≜ log 2  1 + p m ∥ h m ( F ( i ) ) ∥ 2 τ m σ 2  + 2 p m τ m σ 2 ln 2  1 + p m ∥ h m ( F ( i ) ) ∥ 2 τ m σ 2  K  k =1 ℜ  h m,k ( f ( i ) k ) ∗ ( ˜ h ′ m,k ) T ( f k − f ( i ) k )  (12) 1 3 5 7 9 11 13 15 Iteration 100 120 140 160 180 200 220 240 Total Computation Rate (Mbps) DRA (p=4) SRA (p=4) FA (p=4) DRA (p=8) SRA (p=8) FA (p=8) (a) T otal computation rate versus iteration num b er for dieren t direc- tivity factors p . 15 30 45 60 75 90 Maximum Rotation Angle max (degrees) 120 130 140 150 160 170 180 Total Computation Rate (Mbps) DRA SRA FA (b) T otal computation rate versus maximum rotation angle θ max . 4 9 16 25 36 49 Number of Antennas (K) 100 110 120 130 140 150 160 170 180 190 200 Total Computation Rate (Mbps) DRA SRA FA (c) T otal computation rate v ersus num b er of antennas K . Fig. 2. Performance comparison. (a) Conv ergence b ehavior; (b) Impact of rotation angle limit; (c) Impact of antenna n um b er. Algorithm 1 Prop osed SAHO Algorithm for (P3) 1: Initialization: Set iteration index i = 0 . Initialize fea- sible F (0) and ooading parameters { f (0) , p (0) , τ (0) } . 2: if Dynamic rotating scenario then 3: Compute optimal p ointing matrix F ∗ directly uti- lizing the closed-form solution in (4). 4: Up date ooading resources { f ∗ , p ∗ , τ ∗ } b y solving problem (P3) with xed F ∗ . 5: else if Static rotating scenario then 6: rep eat 7: Up date F ( i +1) b y solving the SCA approximation problem (P6) with xed ooading parameters { f ( i ) , p ( i ) , τ ( i ) } . 8: Up date eective channel gains h m ( F ( i +1) ) . 9: Up date ooading resources { f ( i +1) , p ( i +1) , τ ( i +1) } by solving problem (P3) with xed F ( i +1) . 10: Up date iteration index i ← i + 1 . 11: un til The weigh ted sum computation rate conv erges. 12: Set { F ∗ , f ∗ , τ ∗ , p ∗ } ← { F ( i ) , f ( i ) , τ ( i ) , p ( i ) } . 13: end if 14: Output: Optimal solution { F ∗ , f ∗ , τ ∗ , p ∗ } . (F A) system ( f = [0 , 0 , 1] T ) serving as a low er b ound, and a theoretical Dynamic Rotatable Antenna (DRA) scheme where antennas reorien t p er time slot, serving as an upp er b ound. Fig. 2(a) conrms the eciency of our algorithm, which con v erges within 10 iterations. More critically , it reveals a fundamental limitation of xed antennas: as directivity p increases, the F A p erformance collapses due to sev ere b eam misalignment. In contrast, the RA scheme exploits mec hanical steering to maintain alignmen t, doubling the computation rate at p = 8 . Fig. 2(b) reveals that the computation rate improv es with θ max but saturates b eyond 60 ◦ . This suggests that a restricted rotation range of ± 60 ◦ co v ers the ma jority of user distributions. Crucially , this implies that low- complexit y , limited-range rotators are sucient to achiev e near-optimal p erformance, av oiding the hardware costs of full-steering mechanisms while still outp erforming xed an tennas. Finally , Fig. 2(c) examines the impact of the antenna n um b er, K . While expanding the array size generally impro v es the computation rate, the marginal gain dimin- ishes as the system becomes energy-limited. Throughout this range, the RA scheme consistently outp erforms the xed baseline, conrming its abilit y to correct b eam misalignmen t and fully unlo ck the p otential array gain. V. Conclusion This pap er inv estigated an RA-assisted MEC system to mitigate b eam misalignment through mechanical antenna rotation. W e formulated a w eighted sum computation rate maximization problem and proposed a SAHO algorithm to join tly optimize RA orien tation and ooading resources. Sp ecically , w e prop osed a sequential solution based on closed-form an tenna pointing for dynamic scenarios to sho w the maximum p otential of RA, and emplo yed an SCA-based AO scheme for static scenarios to eectively handle coupled constraints. Simulation results conrm that the prop osed design signicantly outp erforms xed- an tenna b enchmarks, particularly under high antenna directivit y , v alidating its practical eectiv eness. References [1] Q. M. Cui, X. H. Y ou, W. Ni et al., “Overview of AI and communication for 6G netw ork: F undamentals, challenges, and future research opportunities,” Science China Information Sci- ences, vol. 68, no. 7, p. 171301, Jul. 2025. [2] F. W ang, J. Xu, X. W ang, and S. Cui, “Joint ooading and com- puting optimization in wireless p ow ered mobile-edge computing systems,” IEEE T ransactions on Wireless Communications, vol. 17, no. 3, pp. 1784–1797, Mar. 2018. [3] C. Y ou, K. Huang, H. Chae, and B.-H. Kim, “Energy-ecient resource allo cation for mobile-edge computation ooading,” IEEE T ransactions on Wireless Communications, vol. 16, no. 3, pp. 1397–1411, Mar. 2017. [4] C. Huang, A. Zappone, G. C. Alexandrop oulos, M. Debbah, and C. Y uen, “Recongurable intelligen t surfaces for energy eciency in wireless communication,” IEEE T ransactions on Wireless Communications, vol. 18, no. 8, pp. 4157–4170, Aug. 2019. [5] Y. Li, J. W ang, Y. Zou, W. Xie, and Y. Liu, “W eighted sum power maximization for star-ris assisted swipt systems,” IEEE T ransactions on Wireless Communications, v ol. 23, no. 12, pp. 18 394–18 408, Dec. 2024. 6 [6] J. Li, L. Y ang, W. Hao, I. Ahmad, H. Liu, F. Sh u, and D. Niyato, “Multi-lay er transmitting RIS-aided receiver for collaborative jamming and anti-jamming net works,” IEEE T rans. Wireless Commun., v ol. 24, no. 8, pp. 6518–6534, Aug. 2025. [7] Y. Liang, L. Y ang, I. Ahmad, and M. V alkama, “Cov ert transmission and physical-la yer security of ST AR-RIS-assisted uplink SGF-NOMA systems,” IEEE T rans. Commun., vol. 73, no. 10, pp. 8811–8823, Oct. 2025. [8] Y. Li, J. W ang, Y. Liu, and Z. Ding, “Pinching-an tenna assisted simultaneous wireless information and p ow er transfer,” IEEE Communications Letters, vol. 29, no. 10, pp. 2341–2345, Oct. 2025. [9] M. Zeng, J. W ang, O. A. Dobre, Z. Ding, G. K. Karagiannidis, R. Schober, and H. V. Poor, “Resource allocation for pinching-an tenna systems: State-of-the-art, k ey techniques and open issues,” 2025. [Online]. A v ailable: [10] B. Zheng, Q. W u, T. Ma, and R. Zhang, “Rotatable antenna enabled wireless communication: Mo deling and optimization,” arXiv preprint, v ol. arXiv:2501.02595, 2025. [11] L. Zhu, W. Ma, and R. Zhang, “Mo deling and p erformance analysis for mov able an tenna enabled wireless communications,” IEEE T ransactions on Wireless Communications, vol. 23, no. 6, pp. 6234–6250, Jun. 2024. [12] X. Xiong, B. Zheng, W. W u, X. Shao, L. Dai, M.-M. Zhao, and J. T ang, “Ecient c hannel estimation for rotatable antenna- enabled wireless communication,” IEEE Wireless Communica- tions Letters, vol. 14, no. 11, pp. 3719–3723, Nov. 2025. [13] C. Zhou, C. Y ou, B. Zheng, X. Shao, and R. Zhang, “Rotatable antennas for integrated sensing and communications,” IEEE Wireless Comm unications Letters, vol. 14, no. 9, pp. 2838–2842, Sep. 2025. [14] L. Dai, B. Zheng, Q. W u, C. Y ou, R. Schober, and R. Zhang, “Rotatable an tenna-enabled secure wireless comm unication,” IEEE Wireless Communications Letters, vol. 14, no. 11, pp. 3440–3444, Nov. 2025. [15] R. Zhao, Y. Xu, S. Y ang, H. Chen, and C. Assi, “Beamforming for mo v able and rotatable antenna enabled multi-user com- munications,” in 2025 IEEE International Conference on High Performance Computing and Communications (HPCC), A ug. 2025, pp. 688–693. [16] B. Zheng, C. Y ou, and R. Zhang, “Ecien t channel estimation for double-irs aided multi-user mimo system,” IEEE T ransac- tions on Communications, vol. 69, no. 6, pp. 3818–3832, Aug. 2021.