TELK OMNIKA T elecommunication, Computing, Electr onics and Contr ol V ol. 23, No. 5, October 2025, pp. 1137 ∼ 1146 ISSN: 1693-6930, DOI: 10.12928/TELK OMNIKA.v23i5.26854 ❒ 1137 Rate-splitting multiple access in satellite-terr estrial communication systems: perf ormance analysis Huu Q . T ran 1 , Khuong Ho-V an 2 1 Department of Electronics and T elecommunication, F aculty of Electronics T echnology , Industrial Uni v ersity of Ho Chi Minh City , Ho Chi Minh City , V ietnam 2 Department of T elecommunication Engineering, F aculty of Electrical and Electronics Engineering, Ho Chi Minh City Uni v ersity of T echnology (HCMUT), VNU-HCM, Ho Chi Minh City , V ietnam Article Inf o Article history: Recei v ed Dec 16, 2024 Re vised Jun 25, 2025 Accepted Aug 1, 2025 K eyw ords: Non-orthogonal multiple access Outage probability Rate-splitting multiple access Satellite-terrestrial systems Shado wed-Rician f ading ABSTRA CT This paper in v estig ates the throughput and outage probability (OP) of rate- splitting multiple access (RSMA) in satellite–terrestrial communication net- w orks. By di viding user messages into common and pri v ate parts, RSMA enhances spectral ef cienc y and user f airness while addressing hardw are im- pairments and co-channel interference. The proposed h ybrid system model is analyzed and compared with non-orthogonal multiple access (NOMA) un- der v arious po wer allocation coef cients and channel conditions. Results sho w that RSMA achie v es lo wer OP and higher throughput than NOMA, particularly in dense multi-cel l deplo yments. Numerical e v aluations further demonstrate RSMA ’ s rob ustness ag ai nst interference and hardw are limitations, underscoring its potenti al as a reliable solution for ne xt-generation sat ellite–terrestrial relay netw orks. This is an open access article under the CC BY -SA license . Corresponding A uthor: Huu Q. T ran Department of Electronics and T elecommunication, F aculty of Electronics T echnology Industrial Uni v ersity of Ho Chi Minh City Go V ap District, Ho Chi Minh City , V ietnam Email: tranquyhuu@iuh.edu.vn 1. INTR ODUCTION In rapidly e v olving landscape of wireless communication, achie ving higher spectral ef cienc y , ener gy ef cienc y , and reliability is crucial to addressing the rising dema nd for seamless and ubiquitous connecti vity . The e xponential gro wth of de vices connected to the Internet, combined with the e v er -increasing demands for data-intensi v e applications, underscores the need for inno v ati v e multiple access techniques capable of o v er - coming the limitations of con v entional schemes. Among these adv anced techniques, rate-splitting multiple access (RSMA) becomes a feasible candidate for 6G netw orks and be yond, poised to redene the paradigms of wireless communication [1]-[5]. RSMA le v erages an intelligent and adapti v e approach to interference man- agement by di viding user signals into common and pri v ate components, enabling a more granular and ef fecti v e handling of inter -user interference [6], [7]. Unlik e traditional schemes, RSMA empo wers recei v ers to imple- ment e xible signal decoding strate gies through successi v e interference cancellation (SIC). This allo ws partial decoding of interference whilst considering the residual interference as noise, leading to more rob ust communi- cation performance in di v erse netw ork conditions [3], [8], [9]. Such e xibility mak es RSMA uniquely suitable for scenarios characterized by heterogeneous user channel conditions and non-ideal propag ation en vironments, J ournal homepage: http://journal.uad.ac.id/inde x.php/TELK OMNIKA Evaluation Warning : The document was created with Spire.PDF for Python.
1138 ❒ ISSN: 1693-6930 where con v entional t echniques lik e non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) struggle to maintain reliability consistenc y [10], [11]. Furthermore, the adoption of RSMA isn’ t con- strained to terrestrial communication netw orks yet widens to satellite-terrestrial communication syst ems, where unique challenges such as long propag ation delays, limite d spectrum, and coe xistence of multiple service layers create a comple x operational en vironment [12]-[14]. The inte gration of RSMA in satellite-terrestrial netw orks enhances resource utilization and interference management, addressing traditional performance bottlenecks. These netw orks are crucial for ne xt-generation wireless infrastructure, supporting wide-area co v erage, high data rates, and lo w l atenc y , especially in remote or under serv ed re gions. The y also pro vide rob ust support during peak demand and for disaster reco v ery . Ho we v er , the y f ace challenges lik e se v ere co-channel interfer - ence, dynamic user distri b ut ions, and stringent quality-of-service (QoS) requirements [15], [16]. The escalating demand for satellite-terrestrial connecti vity , dri v en by emer ging technologies lik e 6G, the Internet of Things (IoT), and disaster reco v ery systems, has intensied the u r genc y to address these challenges. By 2030, the quantity of IoT de vices is estimated to be o v er 30 billion, while 6G netw orks will require ultra-reliable lo w- latenc y (URLL) communications to support mission-critical applications [17]. Additionally , satellite-terrestrial systems are vital for ensuring connecti vity during natural disasters, where terrestrial infrastructure may be com- promised [15]. Ho we v er , con v entional multiple access schemes lik e NOMA and orthogonal multiple access (OMA) struggle to meet these demands due to their l imited ability to manage se v ere co-channel interference and dynamic user distrib utions ef fecti v ely . NOMA, while impro ving spectral ef cienc y , often f ails to ensure f air - ness among users with heterogeneous channel conditions [2], and OMA ’ s orthogonal resource allocation leads to suboptimal spectrum utilization [10]. These limitations result in de graded QoS, particularly in scenarios requiring high reliability and lo w latenc y , underscoring the need for adv anced techniques lik e RSMA to bridge the performance g ap. RSMA ’ s ability to split signals into common and pri v ate streams of fers a transformati v e approach, impro ving spectral ef cienc y , ener gy utilization, and f airness among users, e v en with heterogeneous channel conditions and unpredictable interference. This mak es RSMA particularly benecial for optimizing the throughput of satellite-terrestrial communication netw orks. Ne v ertheless, the deplo yment of RSMA in satellite-terrestrial communications netw orks has not been thoroughly e xplored, resulting in a lack of crucial insights needed to achie v e QoS standards. The rapid e xpansion of connected de vices and data intensi v e appli- cations, e xpected to gro w signicantly by 2030 [17], underscores the critical need for rob ust satellite-terrestrial communication systems to ensure seamless connecti vity in remote and underserv ed re gions. Con v entional multiple access schemes, such as NOMA and OMA, f ace signicant challenges due to co-channel interference and dynamic user distrib utions, limiting their ability to meet stringent QoS requirements. Moreo v er , satellite communications also f ace en vironmental impairments such as rain attenuation, which can signicantly de grade link reliability in multibeam satellite systems [18]. In parallel, cooperati v e relaying with ener gy harv esting has been in v estig ated as a promising solution to enhance both security and reliability in future wireless netw orks, despite the presence of hardw are impairments [19]. These studies highlight the importance of considering both en vironmental and hardw are constraints when designing rob ust satellite–terrestrial multiple access systems. T o bridge this g ap, our paper continues to contri b ut e to this eld with the k e y contrib utions itemized as follo ws: (i) we deri v e mathematical e xpressions for outage probability (OP) and conduct asymptotic analysis to e v aluate system performance comprehensi v ely and (ii) this study e v aluates the inuence of po wer distrib ution f actors and the quantity of satellite antennas on the o v erall reliability and dependability of the system. The subsequent section describes RSMA in satellite-terrestrial communication systems. Subsequently , section 3 performs the OP analyses. Section 4 dis cusses the simulated and analytical results under v arious practical settings. Ev entually , section 5 presents conclusions. 2. RSMA IN SA TELLITE-TERRESTRIAL COMMUNICA TION SYSTEMS 2.1. System model This subsecti on pro vides an o v ervie w of RSMA in wireless communications, co v ering both sat ellite and terrestrial systems, as in Figure 1. A satellite with K antennas communicates with Q terrestrial users using RSMA to serv e all users simultaneously . Modern satellite communications often uses multi-beam technology to enhance spectral ef cienc y , especi ally in geosynchronous earth orbit (GEO) satellites, where array-fed re- ectors generate multiple beams more ef ciently than direct radiation arrays. This setup x es each beam’ s radiation pattern, reducing the need for comple x on-board processing. Ho we v er , achie ving accurate channel state information (CSI) is challenging because of erroneous channel estimation. T echniques lik e the linear TELK OMNIKA T elecommun Comput El Control, V ol. 23, No. 5, October 2025: 1137–1146 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 1139 minimal mean square error method are used to predict CSI, yielding the combined channel coef cient between S and the q th user as: h U q = g † U q w U q + e U q q L S U q ϑ S ϑ θ U q (1) where w U q is K × 1 transmit weight v ector , e U q means channel estimation error with e U q ∼ C N 0 , µ 2 U q , ϑ S is satellite antenna g ain, g U q is the estimated K × 1 shado wed-Rician channel coef cient v ector between K antennas at S and the q th user , and ( . ) † denotes conjug ate transpose. The transmit beamforming v ector w U q ∈ C K × 1 is selected in accordance wit h the maximum ratio transmission (MR T) principle, gi v en that w U q = ∥ g U q ∥ ∥ g U q ∥ F in which ∥ . ∥ F denotes the Frobenius norm. Moreo v er , L S U q = 1 K B T W c 4 π f c d S U q 2 means instantaneous free space loss [20] wherein d S U q is distance between S and U q , f c is carrier frequenc y , W is transmission bandwidth, T is noise temperature at the recei v er , K B = 1 . 38 × 10 − 23 J / K is Boltzmann constant, c is speed of light. Furthermore, the satellite’ s beam g ain ϑ θ U q is e xpressed to be: ϑ θ U q = ϑ U q   I 1 ¯ ρ U q 2 ¯ ρ U q + 36 I 3 ¯ ρ U q ¯ ρ 3 U q ! (2) where θ U q is the angular separation, ϑ U q is the antenna g ain at U q , I i is the rst-kind Bessel function with order i , ¯ ρ U q = 2 . 07123 sin θ U q sin θ U q 3dB in which sin θ U q 3dB represents 3 dB beamwidth. S Given Area K   antennas U 1 U 2 U q h U 1 h U 2 h Uq S Given Area K   antennas U 1 U 2 U q h U 1 h U 2 h Uq Figure 1. The considered system model 2.2. Signal pr ocessing at transcei v ers This research emplo ys RSMA signaling at the transmitter to f acilitate concurrent communication wi th all recipients. RSMA operates by di viding the trans mitted information into a shared signal ( x c ) distrib uted across all recipients and personali zed messages tailored for each recipient. The transmitter designates a po wer distrib ution f actor ( a c ) for the shared signal, with the residual po wer assigned to the personalized messages. Subsequently , it transmits a composite of the shared and personalized messages to the recipients. x = p P S √ a c x c + X Q q =1 √ a q x q (3) wherein P S represents the po wer allocated at S for do wnlink communication, and x q signies the pri v ate mes- sage designated for the q th user , accompanied by a po wer allocation coef cient denoted as a q . It is important to note that a c + P Q q =1 a q = 1 . The i th user obtains the signal articulated to be: y U q = h U q x + n U q = g † U q w U q + e U q q L S U q ϑ S ϑ θ U q a c P S x c | {z } Common Message + g † U q w U q + e U q q L S U q ϑ S ϑ θ U q a q P S x q | {z } Desired Priv ate Message + g † U q w U q + e U q X Q j =1 ,q ̸ = j q L S U q ϑ S ϑ θ U q a j P S x j | {z } In terfernce + n U q |{z} A W GN (4) Rate-splitting multiple access in satellite-terr estrial communication systems: performance ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
1140 ❒ ISSN: 1693-6930 wherein n U q represents zero-mean σ 2 q -v ariance additi v e white Gaussian noise (A WGN). The (4) clearly un v eils that each user recei v es not only pri v ate and common information dedicated to itse lf b ut also pri v ate informa- tion intended for other users, yielding interference when reco v ering information. T o mitig ate this, each user conducts a tw o-stage restoring process to retrie v e e xpected m essages from its recei v ed signal. By considering all other data as noise, shared information is retrie v ed in the initial phase. The signal-to-noise-plus-interference ratio (SINR) for e xtracting the shared signal at the q th recipient measures ho w ef fecti v ely the recipient can isolate the communal data amidst disruptions from personalized messages designated for other recipients. This SINR reects the po wer assigned to the shared signal, channel characteristics (including antenna g ains and free space loss), and the ef fects of channel estimation inaccuracies and ambient noise. A higher SINR signi- es impro v ed decoding reliability for the shared signal, which is essential for RSMA ’ s interference mitig ation approach. Consequently , the qth recipient retrie v es shared information with SINR as: ¯ γ c,q = a c L S U q ϑ S ϑ θ U q P S g U q 2 F L S U q ϑ S ϑ θ U q P S (1 − a c ) g U q 2 F + L S U q ϑ S ϑ θ U q P S µ 2 U q + σ 2 q = a c A q (1 − a c ) A q + δ q µ 2 U q + 1 (5) wherein ϱ S = P S σ 2 q is transmit signal-to-noise radio (SNR), A q = δ q g U q 2 F and δ q = ϱ S L S U q ϑ S ϑ θ U q . Upon the successful decryption of the shared message, the subsequent stage entails each user e xtracting its intended pri v ate information by deducting the reco v ered shared information from the recei v ed signal whereas presuming the pri v ate information from all other users to be sources of interference. After decoding the com- mon message, the q th user focus es on e xtracting its pri v ate message. The SINR for this pri v ate message reects the po wer allotted to specic data of the user relati v e to the interference caused by pri v ate messages intended for other users, along with residual channel estimation errors and noise. This equation is crucial as it determines the reliability of personalized data deli v ery , highlighting the trade-of f in po wer allocation between pri v ate and common messages in RSMA. Thereby , the SINR for the q th user to successfully decode their pri v ate message can be articulated as: ¯ γ p,q = a q A q A q P Q j =1 ,q ̸ = j a j + δ q µ 2 U q + 1 (6) Owing to identical po wer transmission associated with L training symbols utilized for channel estimation, µ 2 U q = 1/ δ q L is modeled as the v ariance of channel estimation error [21]. 2.3. T err estrial channel model Assuming independent and identically distrib uted (IID) f ading channels yields the probability density function (PDF) of g ( k ) q e xpressed to be: f g ( k ) q 2 ( x ) = α q e − β q x 1 F 1 ( m q ; 1; ϖ q x ) , x ≥ 0 (7) wherein 1 F 1 ( · ; · ; · ) means the conuent h yper geometric function of the rst kind [22]. Moreo v er , g ( k ) q , ∀ q ∈ Q , is channel coef cient from satellite’ s k th antenna to q th user , β q = 1/2 b q , α q = (2 b q m q /(2 b q m q + Ω q )) m q /2 b q , ϖ q = Ω q /(2 b q ) (2 b q m q + Ω q ) in which 2 b q , Ω q , and m q represents a v erage po wer of multi-path elements, a v- erage po wer of line-of-sight element, and f ading se v erity parameter , correspondingly . F or the purposes of this paper , the shado wed-Rician f ading se v erity parameter m q is assumed to be inte ger v alues. This assumption f acilitates a streamlined e v aluation of channel characteristics and their inuence on performance indicators. W e no w reformulate (7) as: f g ( k ) q 2 ( x ) = α q e − ( β q − ϖ q ) x m q − 1 P t =0 ζ q ( t ) x t , x ≥ 0 (8) Here, ζ q ( t ) = ( − 1) t (1 − m q ) t ϖ t q . ( t !) 2 , where ( . ) t represents the Pochhammer symbol. Dra wing on the nd- ings from [23], the probability density function (PDF) of A q under i.i.d. shado wed-Rician f ading is e xpressed as: f A q ( x ) = m q − 1 X j 1 =0 · · · m q − 1 X j K =0 Λ q ( K ) δ ∆ q q x ∆ q − 1 e − ψ q δ q x (9) TELK OMNIKA T elecommun Comput El Control, V ol. 23, No. 5, October 2025: 1137–1146 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 1141 where ∆ q = P K l =1 j l + K , ψ q = β q − δ q , B ( ., . ) means the Beta function [22], and Λ q ( K ) = α K q Q K l =1 ζ q ( j l ) Q K − 1 u =1 B P u p =1 j p + u, j u +1 + 1 (10) T o obtain the CDF of A , we utilize the ndings from [22], resulting in F A q ( x ) e xpressed as: F A q ( x ) = 1 − m q − 1 X j 1 =0 · · · m q − 1 X j K =0 ∆ q − 1 X p =0 Λ q ( K ) Γ (∆ q ) p ! ψ ∆ q − p q δ p q e − ψ q x δ q x p (11) 3. OUT A GE PR OB ABILITY It is recalled from RSMA that e v ery user gets the mix of the shared information, its o wn pri v a te information, the pri v ate information of all other users. Thereby , it decodes both types of information through a tw o-stage reco v ering process, as sho wn in (5) and (6). If these SINRs drop belo w the required thresholds γ c,q th and γ p,q th , respecti v ely , the connection between S and the q th user will e xperience an outage. Here, γ c,q th = 2 2 R c,q − 1 and γ p,q th = 2 2 R p,q − 1 , where R p,q and R c,q denote preset spectral ef ciencies to restore pri v ate and common information, correspondingly . The outage probability (OP) for the q th user quanties the lik elihood that the SINR for either the pri- v ate or common message f alls belo w the required threshold, leading to a communication f ailure. This equation combines the ef fects of channel conditions, po wer allocation, and f ading characteristics under shado wed-Rician f ading. It distinguishes between cases where the common or pri v ate message decoding is the limiting f actor , pro viding a comprehensi v e metric to e v aluate system reliabil ity and guide optimization of po wer allocation and antenna congurations. Pr oposition 1 The OP for the q th user is: O U q = 1 − m q − 1 P j 1 =0 · · · m q − 1 P j K =0 ∆ q − 1 P p =0 Λ q ( K )Γ(∆ q ) p ! ψ ∆ q − p q δ p q e − ψ q γ p,q th δ q µ 2 U q +1 δ q [ a q − ( 1 − a c − a q ) γ p,q th ] γ p,q th δ q µ 2 U q +1 a q − (1 − a c − a q ) γ p,q th p , if ¯ γ c,q th < ¯ γ p,q th 1 − m q − 1 P j 1 =0 · · · m q − 1 P j K =0 ∆ q − 1 P p =0 Λ q ( K )Γ(∆ q ) p ! ψ ∆ q − p q δ p q e − ψ q γ c,q th δ q µ 2 U q +1 δ q [ a c − (1 − a c ) γ c,q th ] γ c,q th δ q µ 2 U q +1 a c − (1 − a c ) γ c,q th p , if ¯ γ c,q th ≥ ¯ γ p,q th (12) where ¯ γ c,q th = γ c,q th δ q µ 2 U q + 1 /( a c − (1 − a c ) γ c,q th ) and ¯ γ p,q th = γ p,q th δ q µ 2 U q + 1 /( a q − (1 − a c − a q ) γ p,q th ) . Note (12) is deri v ed on the condition of a c > γ c,q th /(1 + γ c,q th ) and a i > (1 − a c ) γ p,q th /(1 + γ p,q th ) . Pr oof 1 The OP for the q th user is e xpressed as: O U q =1 − Pr ( ¯ γ c,q > γ c,q th , ¯ γ p,q > γ p,q th ) =1 − Pr   a c A q (1 − a c ) A q + δ q µ 2 U q + 1 > γ c,q th , a q A q A q P Q j =1 ,q ̸ = j a j + δ q µ 2 U q + 1 > γ p,q th ! (13) After certain algebraic simplications, the (13) is represented as: O U q = 1 − Pr ( A q > ¯ γ c,q th , A q > ¯ γ p,q th ) = 1 − Pr ( A q > ¯ γ q max ) , (14) where ¯ γ q max = max ( ¯ γ c,q th , ¯ γ p,q th ) . Further , we re write O U q as: O U q = 1 − 1 − F A q ( ¯ γ q max ) = F A q ( ¯ γ q max ) (15) Substituting (11) into (15), (12) can be obtained and the proof is completed. When ϱ S → ∞ , one applies the approximation e − z ≈ 1 − z as [24] into (13) to achie v e the approxi- mated CDF of A q , yielding asymptotic beha vior as: F ∞ A q ( x ) ≃ α K q x K K ! δ K q (16) Rate-splitting multiple access in satellite-terr estrial communication systems: performance ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
1142 ❒ ISSN: 1693-6930 Substituting (16) into (15) results in the asymptotic OP at U q as: O ∞ U q = 1 K ! α q γ p,q th δ q µ 2 U q +1 δ q [ a q − (1 − a c − a q ) γ p,q th ] K , if ¯ γ c,q th < ¯ γ p,q th 1 K ! α q γ c,q th δ q µ 2 U q +1 δ q [ a c − (1 − a c ) γ c,q th ] K , if ¯ γ c,q th ≥ ¯ γ p,q th (17) 4. PERFORMANCE EV ALU A TION This section presents demonstrati v e ndings to v alidate the proposed formulas. The shado wed-Rician f ading conguration for the satellite to q th user ( S - U q ) connection is considered as Ω q , m q , b q = 0 . 279 , 5 , 0 . 251 in a v erage shado wing (AS) scenario and (Ω q , m q , b q = 0 . 0007 , 1 , 0 . 063) under hea vy shado wing (HS) in [25]. The equi v alent noise po wer at U q is calculated as σ 2 q = N 0 + 10 log 10 ( W ) + NF [dBm], as referenced in [26], where NF is noise gure. Unless otherwise stated in [20], the parameters are set to K = 2 , Q = 2 , R c,q = 0 . 1 bits per channel usage (BPCU), R p, 1 = 0 . 25 BPCU, R p, 2 = 0 . 1 BPCU, a c = 0 . 4 , f c = 2 GHz, W = 15 Mhz, T = 300 ◦ K , c = 3 × 10 8 m/s, d S U q = 35786 Km, ϑ S = 53 . 45 dB, ϑ U q = 4 . 8 dB, θ U q = 0 . 8 ◦ , θ U q 3dB = 0 . 3 ◦ , NF = 10 dBm, N 0 = − 174 dBm/Hz, a 2 = 0 . 4 (1 − a c ) , a 1 = 0 . 6 (1 − a c ) , with BPCU representing bits per channel use. Figure 2 illustrates OP v ersus satellite transmits po wer P S in dBm. It compares analytical results (for both HS and AS conditions) with simulation results and asymptotic e xpressions. The curv es for U 1 and U 2 under HS and AS conditions sho w a close match between the analytical and simulation ndings, v alidating the accurac y of the analysis. Furthermore, the asymptotic e xpressions pro vide a good approximati on at higher v alues of P S , highli g ht ing the adv antage of the proposed model. This also indicates the signicant inuence of shado wing se v erity on the OP of satellite communications systems. Figure 3 presents OP ag ainst satellite transmit po wer P S in dBm for numerous numbers of satellite antennas K , specically K = 1 , 2 , 3 . The analytical curv es for U 1 and U 2 closely match the simulation outcomes, conrming the preciseness of the analysis. As K increases, the OP decreases for a gi v en P S , highlighting the adv antage of using multiple antennas in sa tellite systems to enhance reliability . F or instance, at higher P S , the p e rformance impro v ement is more prominent due to the additional spatial di v ersity of fered by the rising quantity of antennas. The asymptotic curv es also align well at higher po wer le v els, further v alidating the rob ustness of the deri v ed e xpressions under high transmit po wer scenarios. Figure 4 illustrates OP v ersus po wer coef cient a c for tw o satellite transmit po wer le v els: P S = 0 dBm (dashed lines) and P S = 5 dBm (sol id lines). The analytical results for U 1 and U 2 closely align with the simulation outcomes, v alidating the analysis. The OP e xhibits a U-shaped beha vior , decreasing as a c increases from 0, reaching a minimum near a c = 0 . 5 , and then increasing as a c approaches 1. This beha vior highlights the trade-of f in po wer allocation between the users, where balanced po wer allocation ( a c ≈ 0 . 5 ) minimizes the OP . Furthermore, higher satellite po wer ( P S = 5 dBm) consistently results in lo wer outage probabilities compared to P S = 0 dBm, demonstrating the adv antage of increased transmit po wer . The gure also emphasizes the importance of optimizing a c to enhance system performance under v arying po wer le v els. Figure 5 presents OP v ersus t he lengths of training symbols L with P S = 0 dBm for K = 1 (dashed lines) and K = 3 (solid lines). This gure demonstrates that the OP of U 1 is consistently belo w that of U 2 , indicating that U 1 e xperiences better information quality compared to U 2 . Additionally , the case with K = 1 e xhibits higher OP compared to K = 3 . This observ ation implies that rising the quantity of antennas enhances the communication quality and ef cienc y . Figure 6 clearly illustrates that RSMA consistently outperforms NOMA in reducing OP for both users across all transmit po wer le v els. Under HS, RSMA ’ s curv es decrease more rapidly , demonstrating rob ust reliability e v en at lo w PS, whereas NOMA sustains higher o ut age probabilities. The AS further amplies RSMA ’ s adv antage, reducing its OP to e xtremely lo w v alues more quickly than NOMA. User 1 consistently e xperiences a lo wer OP than User 2, reecting superior channel conditions and RSMA ’ s ability to e xploit this disparity . As PS increases from –25 dBm to +5 dBm, all curv es decline; ho we v er , RSMA maintains a distinct adv antage o v er NOMA, underscoring its resilience to shado wing. Ov erall, Figure 6 clearly demonstrates that RSMA pro vides a more reliable link under both HS and AS, establishing it as t he superior approach for ne xt- generation satellite communications. TELK OMNIKA T elecommun Comput El Control, V ol. 23, No. 5, October 2025: 1137–1146 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 1143 -25 -20 -15 -10 -5 0 5 10 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Figure 2. Outage probability v ersus P S under v arious shado w f ading, with L = 5 -25 -20 -15 -10 -5 0 5 10 15 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 K = 1 K = 3 K = 5 Figure 3. Outage probability v ersus P S and the numbers of antennas of the satellite, with L = 10 0 0.2 0.4 0.6 0.8 1 10 -4 10 -3 10 -2 10 -1 10 0 Figure 4. OP ag ainst a c with K = 2 and L = 20 5 10 15 20 25 30 35 40 45 50 10 -4 10 -3 10 -2 10 -1 10 0 Figure 5. OP v ersus L with P S = 0 dBm -25 -20 -15 -10 -5 0 5 10 -4 10 -3 10 -2 10 -1 10 0 Figure 6. Comparison between RSMA and NOMA for the outage probability v ersus P S with K = 2 and L = 5 5. CONCLUSION This st udy le v erages the inte gration of RSMA into satellite-terrestrial communication systems to s ig- nicantly enhance quality of service. By deri ving mathematical e xpressions for outage probability and con- Rate-splitting multiple access in satellite-terr estrial communication systems: performance ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
1144 ❒ ISSN: 1693-6930 ducting asymptotic analysis, the research underscores the critical roles of satellite antenna conguration and optimized po wer distrib ution in enhancing communication reliability . Numerical simulation v alidates the accu- rac y of the theoretical ndings, demonstrating that RSMA reduces out age probability by up to 20% compared to NOMA under hea vy shado wing conditions, o wing to its superior interference management and e xible signal decoding capabilities. The results highlight the ef cac y of emplo ying multiple antennas and balanced po wer allocation (e.g., a c ≈ 0.5) to minimize outage probability and enhance reliability , particularly in challenging propag ation en vironments. The study pro vides practical guidelines for optimizing satellite-terrestrial netw orks, such as increasing the number of satellite antennas to e xploit spatial di v ersity and carefully tuning po wer al- location coef cients to balance common and pri v ate message transmission. Future research directions include e xploring RSMA ’ s applicability i n dynamic en vironments, such as lo w earth orbit (LEO) satellite systems, which of fer lo wer latenc y b ut introduce challenges lik e rapid hando v ers and Doppler ef fects. Additionally , inte grating RSMA with 6G edge netw orks could further enhance performance by le v eraging edge comput- ing for real-time interference management and resource allocation. Further in v estig ations should also focus on impro ving ener gy ef cienc y , reducing latenc y , and ensuring scalability to support the gro wing demands of ne xt-generation wireless netw orks. A CKNO WLEDGMENT Khuong Ho-V an w ould lik e to thank Ho Chi Minh City Uni v ersity of T echnology (HCMUT), VNU- HCM for the support of time and f acilities for this study . FUNDING INFORMA TION This study w as self-funded by the authors. A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the C ontrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib u- tions, reduce authorship disputes, and f acilitate collaboration. Name of A uthor C M So V a F o I R D O E V i Su P Fu Huu Q. T ran ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Khuong Ho-V an ✓ ✓ ✓ ✓ C : C onceptualization I : I n v estig ation V i : V i sualization M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administration V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisition F o : F o rmal Analysis E : Writing - Re vie w & E diting CONFLICTS OF INTEREST The authors declare no conict of interest in this manuscript. INFORMED CONSENT W e ha v e obtained informed consent from all indi viduals included in this study . ETHICAL APPR O V AL Not applicable. D A T A A V AILABILITY Data a v ailability is not applicable to this paper as no ne w data were created or analyzed in this study . TELK OMNIKA T elecommun Comput El Control, V ol. 23, No. 5, October 2025: 1137–1146 Evaluation Warning : The document was created with Spire.PDF for Python.
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1146 ❒ ISSN: 1693-6930 BIOGRAPHIES OF A UTHORS Huu Q . T ran (Member , IEEE) recei v ed the M.S. de gree in Electronics Engine ering from Ho Chi Minh City Uni v ersity of T echnology and Education (HCMUTE), V ietnam in 2010. Currently , he has been w orking as a lecturer at F aculty of Electronics T echnology , Industrial Uni v ersity of Ho Chi Minh City (IUH), V ietnam. He obtained his doctorate from the F aculty of Electrical and Elec- tronics Engineering at HCMUTE, V ietnam. His research interests include wireless communications, non-orthogonal multiple access (NOMA), ener gy harv esting (EH), wireless cooperati v e relaying net- w orks, heterogeneous netw orks (HetNet), cloud radio access netw orks (C-RAN), unmanned aerial v ehicles (U A V), recongurable intelligent surf aces (RIS), short-pack et communication (SPC) and internet of things (IoT). He can be contacted at email: tranquyhuu@iuh.edu.vn. Khuong Ho-V an (Member , IEEE) recei v ed the B.E. (rst-rank ed honor) and M.S. de grees in Electronics and T elecommunications Engineering from Ho Chi Minh City Uni v ersity of T echnol- ogy , V ietnam, in 2001 and 2003, respecti v ely , and the Ph.D. de gree in Electrical Engineering from the Uni v ersity of Ulsan, South K orea, in 2007. From 2007 to 2011, he joined McGill Uni v ersity , Canada, as a Postdoctoral Fello w . Currently , he is an Associate Professor with Ho Chi Minh City Uni v ersity of T echnology , V ietnam. His major research interests include modulation and coding techniques, di- v ersity techniques, digital signal processing, ener gy harv esting, ph ysical layer security , and cogniti v e radio. He can be contacted at email: hvkhuong@hcmut.edu.vn. TELK OMNIKA T elecommun Comput El Control, V ol. 23, No. 5, October 2025: 1137–1146 Evaluation Warning : The document was created with Spire.PDF for Python.