On Performance of Fluid Antenna Relay (FAR)-Assisted AAV-NOMA Wireless Network

On Performance of Fluid Antenna Relay (F AR)-Assisted AA V -NOMA W ireless Network Ruopeng Xu ∗ , Songling Zhang ∗ , Zhaohui Y ang ∗ , Y ixuan Chen ∗ , Mingzhe Chen † , Zhaoyang Zhang ∗ , Kai-Kit W ong ‡ ∗ College of Information Science and Electronic Engineering, Zhejiang Univ ersity , Hangzhou, China † Department of Electrical and Computer Engineering, Uni versity of Miami ‡ Department of Electronic and Electrical Engineering, Uni versity College London, U.K. E-mails: (ruopengxu, sl-zhang, yang zhaohui, chen yixuan, ning ming)@zju.edu.cn, mingzhe.chen@miami.edu, kai-kit.wong@ucl.ac.uk Abstract —In this paper , we investigate the performance of a fluid antenna relay (F AR)-assisted downlink communication system utilizing non-orthogonal multiple access (NOMA). The F AR, which integrates a fluid antenna system (F AS), is equipped on an autonomous aerial vehicle (AA V), and introduces extra degrees of freedom to impro ve the perf ormance of the system. The transmission is divided into a first phase from the base station (BS) to the users and the F AR, and a second phase where the F AR forwards the signal using amplify-and-forward (AF) or decode- and-forward (DF) r elaying to reduce the outage probability (OP) for the user maintaining weaker channel conditions. T o analyze the OP perf ormance of the weak user , Copula theory and the Gaussian copula function are employed to model the statistical distribution of the F AS channels. Analytical expressions for weak user’ s OP are derived for both the AF and the DF schemes. Simulation results v alidate the effectiveness of the proposed scheme, sho wing that it consistently outperforms benchmark schemes without the F AR. In addition, numerical simulations also demonstrate the values of the relaying scheme selection parameter under different F AR positions and communication outage thresholds. Index T erms —Fluid antenna system (F AS), fluid antenna relay (F AR), autonomous aerial vehicle (AA V), non-orthogonal multiple access (NOMA), outage probability (OP) I . I N T RO D U C T I O N The de velopment of sixth-generation (6G) mobile commu- nication systems imposes new requirements on communication network performance [1]–[3]. Fluid antenna system (F AS), an emerging technology bringing additional spatial div ersity gains to the communication system [4]–[6], has recently been viewed as a promising candidate to help communication systems meet the 6G communication metrics. In particular, the use of div ersity techniques can mitigate signal fading in wireless networks [7], thus introducing F AS into existing relay communication systems deplo yed traditional antenna systems (T ASs) has great potential to deal with se vere signal attenuation in high-frequency 6G networks and expand the cov erage of the communication system. Meanwhile, another approach to enhance the quality of communications in relay This work was supported by the National Natural Science Foundation of China (NSFC) under Grants 62394292, 62394290, Zhejiang Ke y R&D Program under Grant 2023C01021, Y oung Elite Scientists Sponsorship Program by China Association for Science and T echnology under Grant 2023QNRC001, the Fundamental Research Funds for the Central Univ ersities under Grant 226-2024-00069. networks is the deployment of autonomous aerial vehicles (AA Vs) in lo w-altitude airspace [8]–[10] by establishing a high probability of line-of-sight (LoS) links. Research works that deploy F AS as a relay [11]–[13] or combine F AS with AA Vs [14]–[16] have previously been in vestigated. Ho wev er, existing works primarily consider the single relaying scheme, i.e., using either amplify-and-forw ard (AF) [11], [12] or decode-and-forward (DF) [13], [14] for relaying, ne glecting the need for different relaying schemes un- der different communication conditions. In particular , DF does not introduce extra noise during forwarding, but is susceptible to error propagation due to decoding process, while AF has no risk of decoding errors, b ut it amplifies noise, making the usage of a single fixed mode cannot always fit all communication conditions. In addition, some of the existing F AR-AA V relay work employs orthogonal multiple access (OMA) techniques [15]. OMA often allocates resources uniformly , leading to poor fairness where weak-channel users struggle to meet the required quality of service (QoS). Moreov er , coordination between relay links and direct links from the base station (BS) has not been fully utilized in [14]–[16]. Motiv ated by these research gaps, we propose to deploy F AS on a AA V to constitute an F AR relay node and utilize non-orthogonal multiple access (NOMA) coordinately serving users in high outage probability (OP) with only direct links, where the F AR adapti vely chooses relaying scheme between AF and DF to obtain a lo wer OP of the weak-channel user . The key contributions of this paper include: • W e inv estigate an F AR-assisted two-user do wnlink com- munication system, where the F AR integrates the F AS and AA V . The ov erall do wnlink transmission consists of the first phase, where a superposed signal is transmitted from BS to users and the F AR, and the second phase from the F AR to ground users. After receiving signals from BS in the first phase, the F AR forwards the signal with either AF or DF for relaying following the principle to obtain a lower OP of the user with a weaker channel (user 2 ). • T o compare the performance of the proposed system with different relaying schemes, we deriv e the transmission OP for the user 2 with the F AR using AF and DF , respectiv ely . Furthermore, we introduce Copular theory to represent statistical distrib ution of the F AS channels, AF DF         p o r ts   p o r t s U s e r 1 U s e r 2 F irs t pha s e Seco nd pha s e F lu id an t e n n a r e lay B ase st at ion A c t ivat e d p or t r e c e ivin g/ t r a n sm it t i n g sign al Fig. 1. System model of the proposed communication. and utilize the Gaussian copula function to approximate the jointly cumulative distribution function (CDF) of the random variables following abov e distributions of F AS. • W e ev aluate and compare the OP performance of user 2 under different conditions via numerical simulations. Simulation results validate its effecti veness and show the proposed scheme always outperforms the benchmark schemes. Moreov er , we also develop simulations about the results on relaying scheme selection under different positions of F AR and dif ferent outage thresholds. I I . S Y S T E M M O D E L As illustrated in Fig. 1, we consider an F AR-assisted down- link communication with NOMA, which consists of a BS, two ground users, and one AA V . BS and ground users are equipped with a single T AS, and the AA V is equipped with a 2-dimensional (2D) F AS. In particular , the AA V equipped with the F AS is considered as F AR working in half-duplex mode. W e assume that the channels between both users and the BS are poor so the communication directly from the BS to each user is in high probability of being outage. Hence, our objectiv e is to deploy the F AR to help establish relay links to impro ve communications between the BS and the ground users. Moreover , we assume that near user is closer to the BS (user 1 ) than the other (user 2 ), thus user 1 has a relati vely better channel condition. In the considered model, there are two phases in one downlink transmission. In the first phase, the BS transmits signals to the F AR and ground users, and in the second phase, the F AR transmits the received signals with either AF or DF relaying scheme. W ith acti vating different ports of F AS, the F AR can obtain different channel gains, and the port acquiring the largest channel gain is the optimal port [4]. Thus, by finding the optimal port, the F AR can greatly improve the communication qualities, while the process also introduces additional overhead for port selection. W ithout loss of generality , we assume that the F AR recei ves the signal from the BS with fixed port to sav e port selection overhead and transmits the signals to ground users by acti vating the optimal port of F AS to obtain better channel gains and improv e communication QoS. A. Fluid Antenna Relay Model It is assumed that the 2D F AS includes one RF chain and N = N 1 × N 2 preset ports, where the N i ports are uniformly distributed along a linear space of length L i λ for i ∈ { 1 , 2 } , taking up a grid surf ace size of L = L 1 × L 2 λ 2 with λ being the wa ve length. By introducing mapping function F ( · ) , we can denote the ( n 1 , n 2 ) -th port as the l -th port by l = F ( n 1 , n 2 ) = ( n 1 − 1) N 2 + n 2 . Based on this notation, we denote the channel gain from F AR to user j with activ ating the l -th port by h l FU j = q d − α FU j g l FU j , (1) where g l FU j ∼ C N (0 , 1) is the normalized channel gain using port l , following a complex Gaussian distribution with zero mean and unit v ariance. Then, the square of the amplitude of h l FU j follows the e xponential distribution with the parameter d α FU j , i.e., | h l FU j | 2 ∼ EXP( d α FU j ) . Moreover , the amplitude of the optimal port h FU j can be mathematically gi ven as | h FU j | 2 = max {| h 1 FU j | 2 , . . . , | h N FU j | 2 } . (2) B. Communication Model In downlink transmission, the BS transmits a superposed signal x with transmit power P B to the F AR and two ground users in the first transmission phase. The superposed signal consists of the desired symbols of the two users, where x i is intended to the user i , i = { 1 , 2 } . By performing NOMA, the transmit po wer P B is di vided by the ratio β B between the two symbols. Thus, the transmitted signal x can be expressed as x = p β B P B x 1 + p (1 − β B ) P B x 2 , (3) where x i ∼ C N (0 , 1) . Then, signal recei ved at the F AR, user 1 and user 2 in the first phase can be respectiv ely gi ven as y 1 i = q d − α B i g B i x + n 1 i = h B i x + n 1 i , i = { F , U 1 , U 2 } , (4) where the superscript 1 represents the first transmission phase, and n i is the additional white Gaussian noise (A WGN). W ithout loss of generality , we assume A WGN at all terminals maintains the v ariance σ 2 . According to the principles of NOMA, since user 1 holds a stronger channel, po wer allocation ratio β B should satisfies that 0 ≤ β B < 1 2 , and user 2 decodes its own message with treating the message of user 1 as the noise. As a result, with defining ρ B = P B /σ 2 , the signal-to-interference-plus-noise ratio (SINR) for user 2 to decode its o wn message is gi ven as γ 1 U 2 = d − α BU 2 | g BU 2 | 2 (1 − β B ) ρ B d − α BU 2 | g BU 2 | 2 β B ρ B + 1 . (5) C. AF Relaying If use AF for relaying, F AR receives the signal from the BS and transmits it with an amplify coefficient η to two ground users, respectiv ely . In particular , we set the transmit po wer at the F AR as P F and the amplify coefficient η can be set as η = q ρ F d − α BF | g BF | 2 ρ B +1 , where ρ F = P F σ 2 . Then, the received signal in the second transmission phase at user i can be given as y 11 U i = q d − α FU i g FU i η  x q d − α BF g BF + n 1 i  + n 11 i , (6) where the superscript 11 stands for the second transmission phase, and n 11 i is the corresponding A WGN at user i . In the second transmission phase, both users should first decode the message of user 2 . Hence, the SINR of user 2 decoding the message of user 2 can be given as γ 11 U 2 = | h BF | 2 | h FU 2 | 2 (1 − β B ) ρ B ρ F | h BF | 2 | h FU 2 | 2 β B ρ B ρ F + | h BF | 2 ρ B + | h FU 2 | 2 ρ F + 1 . (7) When γ 11 U 2 ≥ γ U 2 , user 2 successfully decodes its message. Based on (5) and (7), user 2 combines the recei ved signals y 1 U 2 and y 11 U 2 to decode its message with the SINR as Γ AF U 2 = γ 1 U 2 + γ 11 U 2 , where the superscript AF is used to show it is the combined SINR using AF relaying scheme. D. DF Relaying If use DF for relaying, the F AR first decodes the recei ved signal from the BS. The SINR and SNR for the F AR to decode x 2 and x 1 can be gi ven as γ 1 FU 2 = d − α BF | g BF | 2 (1 − β B ) ρ B d − α BF | g BF | 2 β B ρ B + 1 , (8) and γ 1 FU 1 = d − α BF | g BF | 2 β B ρ B , (9) respectiv ely . Based on the decoding results, if the F AR can decode x 1 successfully , the F AR is able to transmit the superimposed signal with a new power allocation scheme, where the transmitted signal can be expressed as x F = p β F P F x 1 + p (1 − β F ) P F x 2 , (10) where P F is the transmit po wer at the F AR and β F is the po wer allocation coefficient at the F AR with β F ∈ [0 , 1 2 ) following NOMA principles. Then, for user 2 , the received signal can be denoted by y 11 − F U 2 , where the superscript − F emphasizes that the received signal w as decoded by the F AR. Moreov er, user 2 decoding x 2 after receiving the signal from the F AR obtains the SINR γ 11 − F U 2 = d − α FU 2 | g FU 2 | 2 (1 − β F ) ρ F d − α FU 2 | g FU 2 | 2 β F ρ F + 1 . (11) In this case, user 2 combines y 1 U 2 and y 11 − F U 2 to decode x 2 with the SINR as Γ DF − F U 2 = γ 1 U 2 U 2 + γ 11 − F U 2 U 2 . On the other hand, when the F AR fails to decode x 1 , it transmits the decoded x 2 to the ground users, where the transmitted signal can be giv en as x F = √ P F x 2 . F or user i , the receiv ed signal can be denoted as y 11 − 2 U i , where the superscript − 2 emphasizes only x 2 was transmitted by the F AR. The SNR of user i to decode the recei ved signal can be expressed as γ 11 − 2 U 2 = d − α FU 2 | g FU 2 | 2 ρ F , (12) In this situation, user 2 combines y 1 U 2 and y 11 − 2 U 2 with SINR Γ DF − 2 U 2 = γ 1 U 2 U 2 + γ 11 − 2 U 2 U 2 to decode its o wn message. I I I . O U TAG E P R O BA B I L I T Y P E R F O R M A N C E A N A L Y S I S A. CDF of F AS with Copula Theory For a 2D F AS, the entry of spatial correlation matrix J of the F AS representing the spatial correlation between the ( n 1 , n 2 ) -th port and ( ˜ n 1 , ˜ n 2 ) -th port can be described as [17] J ( n 1 ,n 2 ) , ( ˜ n 1 , ˜ n 2 ) = j 0   2 π s  | n 1 − ˜ n 1 | N 1 − 1 L 1  2 +  | n 2 − ˜ n 2 | N 2 − 1 L 2  2   , (13) where j 0 ( · ) is the spherical Bessel function of the first kind. For the link between the F AR and user 2 , we introduce Cop- ula theory [18] to acquire the CDF of | h FU 2 | 2 , and specifically exploit the Gaussian copula function [19] to approximate its numerical value. By exploiting the analytical results in [19], F | h FU 2 | 2 ( x ) can be presented as F | h FU 2 | 2 ( x ) ≜ Φ J , 2 ( x ) = Φ J  ϕ − 1  F    h 1 FU 2    2 ( x )  , . . . , ϕ − 1  F    h N FU 2    2 ( x )  , (14) where F | h i FU 2 | 2 ( x ) = 1 − e − d α FU 2 x , Φ J ( · ) is the joint CDF of the multi variate normal distribution with zero mean v ector and correlation matrix J , ϕ − 1 ( · ) is the quantile function of the standard normal distribution, i.e., ϕ − 1 ( x ) = √ 2 erf − 1 (2 x − 1) , in which erf − 1 is the in verse function of error function erf ( x ) = 2 √ π R x 0 e − r 2 d r . B. OP with AF Relaying For the sake of notation simplicity , | h BU 1 | 2 , | h BU 2 | 2 , | h BF | 2 and | h FU 2 | 2 are denoted as independent R Vs W 1 , W 2 , X and Z , respecti vely . If use AF for relaying and define ξ B = 1 − β B − β B γ U 2 , the OP of the user 2 can be e xpressed as q AF = P (Γ AF U 2 < γ U 2 ) = P  W 2 (1 − β B ) ρ B W 2 β B ρ B + X Z (1 − β B ) ρ B ρ F X Z β B ρ B ρ F + X ρ B + Z ρ F + 1 < γ U 2  = P  Z ρ F n X ρ B  W 2 ρ B β B ( ξ B + 1 − β B ) + ξ B  + W 2 ρ B ξ B − γ U 2 o < ( γ U 2 − W 2 ρ B ξ B )(1 + X ρ B )  . (15) Define C w 2 = γ U 2 ξ B ρ B , C x = γ U 2 − ξ B w 2 ρ B ρ B [ ξ B + w 2 β B ρ B (1+ ξ B − β B )] , C z = ( γ U 2 − w 2 ρ B ξ B )(1+ xρ B ) ρ F { xρ B [ w 2 ρ B β B ( ξ B +1 − β B )+ ξ B ]+ w 2 ρ B ξ B − γ U 2 } , and C 0 = − ξ B ρ B β B ( ξ B +1 − β B ) . When ξ B > 0 , i.e., β B < 1 1+ γ U 2 , the transmission will always not outage with W 2 ≥ C w 2 , since the term on the right side is non-positi ve while the left-hand- side term is non-negati ve. W ith W 2 being less than C w 2 , the q DF = 1 − h P ( γ 1 FU 1 < γ U 1 | γ 1 FU 2 ≥ γ U 2 , Γ DF − 2 U 2 ≥ γ U 2 ) + P ( γ 1 FU 1 ≥ γ U 1 | γ 1 FU 2 ≥ γ U 2 , Γ DF − F U 2 ≥ γ U 2 ) i = 1 − [ P ( X < D w 1 | X ≥ C w 2 ) P ( Z ≥ γ U 2 − W 2 ξ B ρ B ρ F ( W 2 ρ B β B + 1) ) | {z } ≜ p DF 1 + P ( X ≥ D w 1 | X ≥ C w 2 ) P ( Z ρ F ( W 2 ρ B I 1 + ξ F ) ≥ ˆ γ U 2 | {z } ≜ p DF 2 ] , (20) term on the left of the equality is positiv e only when X ≥ C x and Z ≥ C z . Therefore, when β B > 1 1+ γ U 2 , the OP is q AF 1 = 1 − e − d α BU 2 C w 2 − C w 2 Z 0 ∞ Z C x  1 − Φ J , 2 ( C z )  × d α BF e − d α BF x dxd α BU 2 e − d α BU 2 w 2 dw 2 . (16) When ξ B ≤ 0 , we can find that if ξ B + 1 − β B ≤ 0 , i.e., β B ≥ 2 2+ γ U 2 , all terms on the left hand of the inequality are non-positiv e, while the term on the right hand side is positive. Hence, the transmission will always outage. On the other hand, when 1 1+ γ U 2 ≤ β B < 2 2+ γ U 2 , we need to promise W 2 ≥ C 0 and X ≥ C x to ensure the term on left hand side being positiv e. Then, the OP can be giv en as q AF 2 = 1 − P ( W 2 ≥ 0 , X ≥ C x , Z ≥ C z ) = 1 − ∞ Z C 0 ∞ Z C x  1 − Φ J , 2 ( C z )  d α BF e − d α BF x dx d α BU 2 e − d α BU 2 w 2 dw 2 , (17) Based on (16) and (17), OP of user 2 when using AF can be mathematically gi ven as q AF =            q AF 1 , if β B < 1 1 + γ U 2 q AF 2 , if 1 1 + γ U 2 ≤ β B < 2 2 + γ U 2 1 , otherwise . (18) C. OP with DF Relaying As we have assumed, if use DF for relaying, the F AR can always decode x 2 from the recei ved signal from BS, thus we hav e the follo wing conclusion as X ≥ γ U 2 ξ B ρ B = C w 2 , (19) from which we can also know ξ B is positiv e, i.e., β B < 1 1+ γ U 2 . OP of the user 2 can be expressed as in (20), where I 1 = ρ B [ β F  1 − β B  + ξ F β B ] > 0 and ˆ γ U 2 = γ U 2 − W 2 ξ B ρ B . Define D w 1 = γ U 1 ρ B β B and D z = γ U 2 − w 2 ξ B ρ B ρ F ( w 2 ρ B β B +1) , we can find that when D w 1 ≤ C w 2 , p DF 1 = 0 . When D w 1 > C w 2 , p DF 1 is p DF 1 =  1 − e d α BF ( C w 2 − D w 1 )  [ e − d α BU 2 C w 2 + C w 2 Z 0  1 − Φ J , 2 ( C z )  d α BU 2 e − d α BU 2 w 2 dw 2 ] . (21) T o deri ve the expression of p DF 2 , we define ξ F = 1 − β F − β F γ U 2 and D z ′ = γ U 2 − w 2 ξ B ρ B ρ F { w 2 ρ B [ β F (1 − β B )+ ξ F β B ]+ ξ F } . Then, when D w 1 > C w 2 , i.e., β B < γ U 1 γ U 1 + γ U 2 + γ U 1 γ U 2 , we can obtain that p DF 2 = e d α BF ( C w 2 − D w 1 ) [ e − d α BU 2 C w 2 + C w 2 Z max { 0 , − ξ F I 1 }  1 − Φ J , 2 ( D z ′ )  d α BU 2 e − d α BU 2 w 2 dw 2 ] . (22) When D w 1 ≤ C w 2 , i.e., β B ≥ γ U 1 γ U 1 + γ U 2 + γ U 1 γ U 2 , we ha ve p DF 2 = e − d α BU 2 C w 2 + C w 2 Z max { 0 , − ξ F I 1 }  1 − Φ J , 2 ( D z ′ )  d α BU 2 e − d α BU 2 w 2 dw 2 . (23) As a result, we can obtain q DF as given in (24). D. Relaying Scheme Selection Principle From (18) and (24), we can observe that the position of the F AR and power allocation coefficients all influence the OP of the transmission, and different relaying schemes also obtain different OP . T o guarantee and improv e the OP QoS of weak user 2 , the F AR always chooses the relaying scheme that maintains a lo wer transmission OP for user 2 . W e define µ as the relaying scheme selection parameter as µ = ε ( q AF − q DF ) , (25) where ε ( · ) is the Heaviside function, specified as ε ( a ) = 1 , when a ≥ 0 and ε ( a ) = 0 , when a < 0 . I V . S I M U L AT I O N R E S U L T S W ithout loss of generality , we assume equal transmit powers at the BS and the F AR and equal OP QoS of ground users [20]. In particular we set transmit powers as P B = P F , i.e., ρ B = ρ F = ρ , and γ U 1 = γ U 2 = γ . The noise power is set as the σ 2 = − 130 dBm . The F AS structure parameters are configured as N 1 = N 2 = 4 and L 1 = L 2 = 1 . In our simulations, we first present the results on the OP of user 2 under gi ven dif ferent power allocation ratio coef ficients by comparing our proposed scheme (labeled as ‘ Proposed ’) with the scheme only deploying the ground link between BS and users (labeled as ‘ Without F AR ’). Then, we ev aluate the value of µ under dif ferent F AR positions and outage thresholds. Fig. 2 shows the OP of user 2 when the F AR uses AF or DF to relay with different po wer allocation ratio coefficients, q DF =                                          1 − e − d α BU 2 C w 2 −  1 − e d α BF ( C w 2 − D w 1 )  C w 2 Z 0  1 − Φ J , 2 ( C z ) d α BU 2 e − d α BU 2 w 2 dw 2 − C w 2 Z max { 0 , − ξ F I 1 } e d α BF ( C w 2 − D w 1 )  1 − Φ J , 2 ( D z ′ )  d α BU 2 e − d α BU 2 w 2 dw 2 , if β B < γ U 1 γ U 1 + γ U 2 + γ U 1 γ U 2 1 − e − d α BU 2 C w 2 − C w 2 Z max { 0 , − ξ F I 1 }  1 − Φ J , 2 ( D z ′ )  d α BU 2 e − d α BU 2 w 2 dw 2 , if γ U 1 γ U 1 + γ U 2 + γ U 1 γ U 2 ≤ β B < 1 1 + γ U 2 1 , otherwise (24) 0 5 10 15 20 25 30 (dBm) -6 -5 -4 -3 -2 -1 0 lg(q AF ) B = 0.1 Proposed B = 0.1 Without FAR B = 0.2 Proposed B = 0.2 Without FAR B = 0.3 Proposed B = 0.3 Without FAR (a) 0 5 10 15 20 25 30 (dBm) -5 -4 -3 -2 -1 0 lg(q DF ) B = 0.1 Proposed B = 0.1 Without FAR B = 0.2 Proposed B = 0.2 Without FAR B = 0.3 (b) 0 5 10 15 20 25 30 (dBm) -6 -5 -4 -3 -2 -1 0 lg(OP) B = 0.1 AF B = 0.1 DF B = 0.2 AF B = 0.2 DF (c) Fig. 2. OP of user 2 when the F AR uses (a) AF for relaying, (b) DF for relaying, and (c) different relaying schemes with different power allocation ratios. where we set the outage threshold as γ U 2 = 3 . As illustrated in Fig. 2(a), we ev aluate the OP of user 2 when the F AR uses AF . As the transmit powers increase, the OP values of all schemes decrease. When β B = 0 . 1 or β B = 0 . 2 , the OP of the schemes transmitting without F AR first equals one and ranges within 10 − 1 ∼ 10 0 as SNR the system becomes sufficiently high. When the SNR is lo w , the OP of our proposed schemes falls in the order of magnitude similar to that of the comparison schemes mentioned earlier for high SNR. Meanwhile, the OP of the proposed schemes is less than 10 − 4 , demonstrating a much better performance than the schemes without F AR. When β B = 0 . 3 , which is close to the upper bound 2 2+ γ U 2 , the scheme without F AR is always in outage as the OP equals 1 and our proposed scheme can work with the OP falling in 10 − 2 ∼ 10 − 1 . Fig. 2(b) shows the OP of user 2 when the F AR uses DF for relaying, with changing trends of the OP similar to those of using AF . Dif ferent from using AF , OP of user 2 when using DF always equals 1 when β B = 0 . 3 , since the power allocation ratio is greater than the bound 1 1+ γ U 2 . T o better illustrate the relationship between the OP v alues of AF and DF under giv en conditions, we represent Fig. 2(c). W e can observe that when the SNR is low , the OP of the DF scheme with the same power allocation coefficient is smaller than that of the AF scheme, while at higher SNRs, the OP of the DF scheme becomes lar ger than that of the AF scheme. Furthermore, changes in the po wer allocation coef ficient also affect these conclusions. For example, when β B = 0 . 2 , the OP of the DF scheme is larger than the OP of the AF scheme with β B = 0 . 1 at lo w SNRs, rather than smaller . Fig. 3 depicts the v alues of µ as F AR is at different positions when three different outage thresholds are given, i.e., γ U 2 = 2 . 6 , γ U 2 = 2 . 8 and γ U 2 = 3 . In general, we set the power allocation ratio as β B = β F = 0 . 1 , and the value of µ varies depending on the outage threshold and the position of F AR, where µ is calculated based on (25). Furthermore, as the F AR height increases, the area where µ equals 1 gradually decreases when γ U 2 = 2 . 6 and increases when γ U 2 = 2 . 8 and when γ U 2 = 3 . Fig. 3(a) sho ws the scenario when γ U 2 = 2 . 6 . It can be observed that, under these circumstances, when the F AR is deployed in most areas, we should use AF for transmission to achiev e a lower OP for user 2 . When the F AR is located far from the BS and close to user 2 , we should use DF for transmission because the channel gain h FU 2 increases, resulting in a larger probability of p DF 2 than corresponding part of AF . This conclusion also holds true for the other two threshold values. The situation changes as the outage threshold (a) (b) (c) Fig. 3. V alue of µ with the F AR deployed at different feasible positions under the outage threshold given as (a) γ U 2 = 2 . 6 , (b) γ U 2 = 2 . 8 , and (c) γ U 2 = 3 . increases. As shown in Fig. 3(b), when the F AR is close to user 1, µ changes from value of 0 to 1 , indicating that the forwarding strategy at the same location may change as outage threshold increases or decreases. As γ U 2 further increases to 3 , we can observe in Fig. 3(c) that, at the same height, the area near the central where AF is used for forwarding further decreases. Howe ver , compared to when γ U 2 = 2 . 8 , a new area near user 2 appears where AF forwarding should be used. The change in µ reflects the highly nonlinear nature, making the analysis of OP particularly important. V . C O N C L U S I O N In this paper, we hav e analyzed the performance of an F AR- assisted downlink NOMA communication system and deriv ed the OP expressions for the user maintaining weaker channel conditions under both AF and DF relaying schemes. Simula- tion results demonstrate that deploying the F AR significantly reduces the OP compared to transmission without the F AR, especially when the channel conditions are poor . W ith given F AR position and outage threshold, the choice between AF and DF depends on parameters such as transmit po wer ratio and the SNR. In particular , at lower SNRs with gi ven simulation conditions, the DF scheme typically yields a lower OP than the AF scheme with the same po wer allocation, a trend that rev erses at higher SNRs. In addition, numerical simulations also show that the optimal relaying selection strategy is highly dependent on the position of F AR and the outage threshold, confirming that the relaying strategy can be dynamically adjusted accustomed to the communication conditions. R E F E R E N C E S [1] F . Dong, F . Liu, S. Lu, Y . Xiong, Q. Zhang, Z. Feng, and F . Gao, “Communication-assisted sensing in 6g networks, ” IEEE Journal on Selected Areas in Communications , 2025. [2] Z. Y ang, M. Chen, Z. Zhang, and C. Huang, “Energy ef ficient semantic communication over wireless networks with rate splitting, ” IEEE J. Sel. Ar eas Commun. , vol. 41, no. 5, pp. 1484–1495, 2023. [3] Z. Y ang, W . Xu, L. Liang, Y . Cui, Z. Qin, and M. Debbah, “On Priv acy , Security , and T rustworthiness in Distributed Wireless Large AI Models (WLAM), ” arXiv e-prints , p. arXiv:2412.02538, 2024. [4] K.-K. W ong, A. Shojaeifard, K.-F . T ong, and Y . Zhang, “Fluid antenna systems, ” IEEE T ransactions on W ir eless Communications , vol. 20, no. 3, pp. 1950–1962, 2020. [5] T . Zhang, Q. Li, S. W ang, W . Ni, J. Zhang, R. W ang, K.-K. W ong, and C.-B. Chae, “Indoor fluid antenna systems enabled by layout-specific modeling and group relative polic y optimization, ” IEEE T ransactions on W ireless Communications , vol. 25, pp. 9313–9329, 2026. [6] H. Xu, K.-K. W ong, W . K. Ne w , F . R. Ghadi, G. Zhou, R. Murch, C.-B. Chae, Y . Zhu, and S. Jin, “Capacity maximization for fas-assisted mul- tiple access channels, ” IEEE T ransactions on Communications , vol. 73, no. 7, pp. 4713–4731, 2024. [7] J. N. Laneman, D. N. Tse, and G. W . W ornell, “Cooperative div ersity in wireless networks: Ef ficient protocols and outage behavior , ” IEEE T ransactions on Information theory , vol. 50, no. 12, pp. 3062–3080, 2004. [8] Y . L yu, W . W ang, Y . Sun, H. Y ue, and J. Chai, “Low-altitude U A V air- to-ground multilink channel modeling and analysis at 2.4 and 5.9 ghz, ” IEEE Antennas and W ir eless Pr opagation Letters , vol. 22, no. 9, pp. 2135–2139, 2023. [9] Y . W ang, M. Y an, G. Feng, S. Qin, and F . W ei, “ Autonomous on-demand deployment for U A V assisted wireless networks, ” IEEE Tr ansactions on W ireless Communications , vol. 22, no. 12, pp. 9488–9501, 2023. [10] C. Jiang, X. Li, J. Xu, and J. Hou, “ A study of the impact of network ed low-altitude drone operations on the performance of big data services, ” in International Conference on Big Data . Springer , 2024, pp. 46–57. [11] B. E. Aka, W . K. New , C. Y . Leow , K.-K. W ong, and H. Shin, “Power minimization for half-duplex relay in fluid antenna system, ” IEEE W ireless Communications Letters , 2025. [12] R. Xu, Z. Y ang, Z. Zhang, M. Shikh-Bahaei, K. Huang, and D. Niyato, “Energy efficient fluid antenna relay (F AR)-assisted wireless communi- cations, ” IEEE Journal on Selected Areas in Communications , 2025. [13] L. Tlebaldiyev a, S. Arzykulov , T . A. Tsiftsis, and G. Nauryzbayev , “Full- duplex cooperative NOMA-based mmwa ve networks with fluid antenna system (F AS) receivers, ” in 2023 International Balkan Confer ence on Communications and Networking (BalkanCom) , 2023, pp. 1–6. [14] S. B. S. Abdou, W . K. New , C. Y . Leo w , S. W on, K.-K. W ong, and Z. Ding, “Sum-rate maximization for uav relay-aided fluid antenna system with noma, ” in 2024 IEEE 7th International Symposium on T elecommunication T echnologies (ISTT) . IEEE, 2024, pp. 53–58. [15] X. Y ang, Z. Guo, S. Liang, Z. Y ang, C. Zhu, and Z. Zhang, “Rate maximization for UA V-assisted ISA C system with fluid antennas, ” in 2025 IEEE/CIC International Conference on Communications in China (ICCC W orkshops) . IEEE, 2025, pp. 1–5. [16] X. Xu, H. Xu, D. W ei, W . Saad, M. Bennis, and M. Chen, “T ransformer based collaborativ e reinforcement learning for fluid antenna system (F AS)-enabled 3D U A V positioning, ” IEEE Journal on Selected Areas in Communications , 2025. [17] W . K. New , K.-K. W ong, H. Xu, K.-F . T ong, and C.-B. Chae, “ An information-theoretic characterization of MIMO-F AS: Optimization, div ersity-multiplexing tradeoff and q-outage capacity , ” IEEE T ransac- tions on W ireless Communications , vol. 23, no. 6, pp. 5541–5556, 2024. [18] R. B. Nelsen, An Introduction to Copulas . Springer Publishing Company , Incorporated, 2010. [19] F . Rostami Ghadi, K.-K. W ong, F . Javier L ´ opez-Mart ´ ınez, C.-B. Chae, K.-F . T ong, and Y . Zhang, “ A gaussian copula approach to the perfor- mance analysis of fluid antenna systems, ” IEEE Tr ansactions on W ireless Communications , vol. 23, no. 11, pp. 17 573–17 585, 2024. [20] X. Y ue, Y . Liu, S. Kang, A. Nallanathan, and Z. Ding, “Exploiting full/half-duplex user relaying in NOMA systems, ” IEEE T ransactions on Communications , vol. 66, no. 2, pp. 560–575, 2017.