TELK OMNIKA T elecommunication, Computing, Electr onics and Contr ol V ol. 24, No. 1, February 2026, pp. 14 ∼ 21 ISSN: 1693-6930, DOI: 10.12928/TELK OMNIKA.v24i1.26892 ❒ 14 Secur e h ybrid po wer -fr equency multiple access in satellite terr estrial communication systems: a perf ormance study Huu Q . T ran and V iet-Thanh Pham 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 Article Inf o Article history: Recei v ed Jan 3, 2025 Re vised Oct 29, 2025 Accepted Dec 8, 2025 K eyw ords: Hybrid po wer -frequenc y multiple access Intercept probability Outage probability Satellite-terrestrial systems Shado wed-Rician f ading ABSTRA CT This paper in v estig ates a secure h ybrid po wer –frequenc y multiple access (PFMA) frame w ork for satellite–terrestrial communications. By inte grating po wer - and frequenc y-domain multiple xing, PFMA achie v es approximately 4 dB lo wer transmit signal-to-noise ratio (SNR) than non-orthogonal multiple access (NOMA) for the same connection outage probabi lity (COP) at SNR > 0 dB, and it reduces the COP by up to 30% at lo w-to-medium SNRs. It further decreases the intercept probability (IP) by 20–25% at P S = 10 dBm. Closed-form COP and IP e xpressions are deri v ed under shado wed-Rician f ad- ing with both internal and e xterna l ea v esdroppers and v alidated via Monte Carlo simulations. P arameter analysis indicates that PFMA ’ s SNR g ain can either e x- tend co v erage by 60% or sa v e 37% ener gy , pro viding design guidel ines for 6G, satellite IoT , and emer genc y communication syst ems. The single-cell assump- tion points to future w ork on multi-cell and mobility scenarios. 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 Satellite–terrestrial communication systems are a foundation for ne xt-generation netw orks, enabling reliable and ubiquitous connecti vity . Among multiple access techniques, h ybrid po wer–frequenc y multiple ac- cess (HPFMA) combines po wer - and frequenc y-domain multiple xing to enhance spectral ef cienc y . Ho we v er , its security and performance can be hindered by shared channels and the comple xities of h ybrid architectures [1], [2]. Existing studies ha v e e xplored impro v ements via relay protocols, ener gy harv esting, intelligent re- ecting surf aces (IRS), and spectrum sharing [3]-[10]. Secure HPFMA performance under realistic f ading and dual ea v esdropping scenarios is still undere xplored. This w ork lls that g ap via a comprehensi v e performance analysis of secure HPFMA i n satellite–terrestrial systems, focusing on reliability–security trade-of fs and design insights for 6G and satellite IoT . T able 1 contrasts our w ork with prior studies. Unlik e [11]-[13], which focus on non-orthogonal mul- tiple access (NOMA) or simplied f ading, we deri v e closed-form connection outage probability (COP) and intercept probability (IP) for po wer -f actor multiple access (PFMA) under shado wed-Rician f ading with both internal and e xternal ea v esdroppers. Contrib utions: (i) closed-form COP , IP , their asymptotics, and di v ersity order for PFMA under shado wed–Rician f ading with both internal and e xternal ea v esdroppers; PFMA requires J ournal homepage: https://telk omnika.uad.ac.id/inde x.php/TELK OMNIKA Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 15 ≈ 4 dB lo wer SNR than NOMA for the same COP at SNR > 0 dB; (ii) Monte Carlo v alidation across di v erse parameters, sho wing superior COP o v er NOMA at lo w-to-medium signal-to-noise ratio (SNR); and (iii) pa- rameter study (po wer , antennas, shado wed–Rician parameters, bandwidth) re v ealing up to 60% co v erage g ain or 37% ener gy sa ving. T able 1. Comparison with related w orks Ref. Model Metrics Channel Ea v esdropping Limi tations Our contrib ution [3] NOMA Secrec y rate Rayleigh External No closed-form COP/IP Closed-form COP and IP for PFMA [4] NOMA Outage, er godic capacity (EC) Nakag ami- m None Simplied f ading Shado wed–Rician, dual ea v esdroppers [13] NOMA COP Rician Internal No e xternal cas e Dual ea v esdroppers with PFMA [14] P artial- NOMA Secrec y rate Rayleigh Internal No frequenc y-domain analysis Hybrid po wer–frequenc y , closed-form metrics [15] NOMA IP Rayleigh Internal Simpli ed channel Shado wed–Rician with asymptotics Ours PFMA COP , IP , di v er - sity order (DO) Shado wed–Rician Internal and e x- ternal – First closed-form COP/IP for PFMA; ∼ 4 dB SNR g ain o v er NOMA 2. SYSTEM MODEL Consider Figure 1, where a satellite (S) emplo ys three subcarriers ( s B , s R , s RB ) to transmit the con- dential signal x R to Ro y (R) and the secure signal x B to Bob (B). Subcarriers s B and s R occup y bandwidth portions (BPs) α B and α R , respecti v ely , and carry x B and x R using orthogonal multiple access (OMA). Mean- while, a superposition signal x RB = √ β R x R + √ β B x B with po wer -allocation (P A) f actors β R , β B corresponds to NOMA on s RB with BP α RB . Bob and Ro y combine their recei v ed signals after baseband reco v ery without successi v e interference cancellation (SIC). The BP/P A rules are α R + α B + α RB = 1 , β B + β R = 1 , and α RB ≤ α B , α R . Here, α Q ( Q ∈ { B , R } ) denotes the OMA BPs, while α RB is the PFMA superposition BP; β B and β R are NOMA P A f actors . Unless stated otherwise, recei v ers are assumed to ha v e perfect SIC when required by a scheme denition. S a t e l l i t e   ( S ) K   a n t e n n a s R o y   ( R ) B o b   ( B ) R h B h B x R x B x R x   B a n d w i d t h   P o w e r RB s B s R s R B RB B R   F r e q u e n c y M a i n   c h a n n e l S e c u r e   c h a n n e l Figure 1. System model of h ybrid PFMA in satellite–terrestrial communication 2.1. Pr opagation and beamf orming Ro y acts as an internal ea v esdropper and may use SIC to reco v er Bob’ s message. All channels h Q are quasi-static shado wed–Rician with Q ∈ { R , B } . channel estimation errors (CEEs) render perfect channel state information (CSI) dif cult; CSI is estimated via minimum mean square error (MMSE). The ef fecti v e channel is: h Q = g † Q w Q q L SQ ϑ S ϑ ( θ Q ) (1) Secur e hybrid power -fr equency multiple access in satellite terr estrial communication ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
16 ❒ ISSN: 1693-6930 Here, g Q ∈ C K × 1 is the shado wed–Rician v ector (S → Q), w Q ∈ C K × 1 is maximum ratio transmis- sion (MR T): w Q = g Q ∥ g Q ∥ F (2) The free-space loss is: L SQ = 1 K B T W c 4 π f c d SQ 2 (3) with K B = 1 . 38 × 10 − 23 J/K, T the noise temperature, W the bandwidth, c the speed of light, f c the carrier , and d SQ the S–Q distance [16]. The satellite beam g ain is: ϑ ( θ Q ) = ϑ Q   I 1 ( ¯ ρ Q ) 2 ¯ ρ Q + 36 I 3 ( ¯ ρ Q ) ¯ ρ 3 Q ! (4) where I i ( · ) is the i th-order Bessel function (rst kind), ¯ ρ Q = 2 . 07123 sin θ Q sin θ Q , 3dB , and θ Q , 3dB is the 3 dB beamwidth. 2.2. Signal pr ocessing at Q The recei v ed baseband signal at Q ∈ { R , B } is: ¯ y Q = ( p α Q P S L SQ ϑ S ϑ ( θ Q ) x Q g † Q w Q + n Q , s Q p α RB P S L SQ ϑ S ϑ ( θ Q ) x RB g † Q w Q + n Q , s RB (5) where P S is the satellite transmit po wer and n Q ∼ C N (0 , σ 2 Q ) . Dene ν Q = α Q + α RB β Q and µ Q = α Q + α RB . The aggre g ate SINR for decoding x Q at Q is [17]. ¯ γ Q = ν Q δ Q ∥ g Q ∥ 2 F ν Q δ Q ∥ g Q ∥ 2 F + µ Q = ν Q A Q ν Q A Q + µ Q (6) where ϱ S = P S /σ 2 Q is the SNR, A Q = δ Q ∥ g Q ∥ 2 F , and δ Q = ϱ S L SQ ϑ S ϑ ( θ Q ) . After canceling its o wn data via SIC, Ro y tries to intercept x B with: ˆ γ R = α RB β B δ R ∥ g R ∥ 2 F µ R = ν R A R µ R (7) 2.3. T err estrial channel model Assuming i.i.d. coef cients, the probability density function (PDF) of | g ( k ) Q | 2 (S → Q, k th antenna) under shado wed–Rician f ading is: f | g ( k ) Q | 2 ( x ) = α Q e − β Q x 1 F 1 ( m Q ; 1; ϖ Q x ) , x ≥ 0 (8) with, α Q = 2 b Q m Q 2 b Q m Q + Ω Q m Q . (2 b Q ) , β Q = 1 2 b Q , ϖ Q = Ω Q (2 b Q m Q + Ω Q ) 2 b Q Here, Ω Q (LOS po wer), 2 b Q (dif fuse po wer), and m Q (f ading se v erity) follo w [18]. F or inte ger m Q , f | g ( k ) Q | 2 ( x ) = α Q e − ( β Q − ϖ Q ) x m Q − 1 X t =0 ζ Q ( t ) x t , ζ Q ( t ) = ( − 1) t (1 − m Q ) t ϖ t Q ( t !) 2 (9) Using Bank e y et al . [19], the PDF of A Q is: TELK OMNIKA T elecommun Comput El Control, V ol. 24, No. 1, February 2026: 14–21 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 17 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 exp − ψ Q δ Q x (10) where, Λ Q ( K ) = α K Q K Y l =1 ζ Q ( j l ) K − 1 Y u =1 B   u X p =1 j p + u, j u +1 + 1 ! , ∆ Q = K X l =1 j l + K , ψ Q = β Q − δ Q (11) The cumulati v e distrib ution function (CDF) follo ws from ([18] (8.352.6)): 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 exp − ψ Q x δ Q x p (12) 3. CONNECTION OUT A GE PERFORMANCE Let R B and R R be the tar get rates. The capacity is C ( ¯ γ Q ) = log 2 (1 + ¯ γ Q ) . The COP is: COP = 1 − Pr( C ( ¯ γ R ) > R R , C ( ¯ γ B ) > R B ) = 1 − [1 − F ¯ γ R ( u R )] [1 − F ¯ γ B ( u B )] (13) where u Q = 2 R Q − 1 . W e need F ¯ γ Q ( x ) : Theor em 1 Under uncorr elated shadowed–Rician fading , the CDF of ¯ γ Q is: F ¯ γ 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 exp − ψ Q ς Q x δ Q ( ε Q − x ) ς Q x ε Q − x p (14) v alid for 0 ≤ x < ε Q , where ε Q = ν Q / ( α RB β T ) for T ∈ { R , B } , T ̸ = Q , and ς Q = µ Q / ( α RB β T ) Pr oof 1 Use F ¯ γ Q ( x ) = Pr ( ¯ γ Q < x ) and (12) Substituting (14) into (13) gi v es the e xact COP: COP = 1 − Y Q ∈{ R , B } 1 − F ¯ γ Q ( u Q ) (15) Di v ersity order (high SNR). F ollo wing the high-SNR asymptotic e xpansion approach in [20], from (12), for ϱ S → ∞ , a Maclaurin e xpansion yields ([21], (51)). F ∞ A Q ( x ) ≃ α K Q x K K ! δ K Q (16) Combining with (15), the asymptotic COP is: COP ∞ = α K Q K ! δ K Q " ς R u R ε R − u R K + ς B u B ε B − u B K # (17) IP = m B − 1 X j 1 =0 · · · m B − 1 X j K =0 ∆ B − 1 X p =0 Λ B ( K )Γ(∆ B ) p ! ψ ∆ B − p B δ p B exp − ψ B ς B u B δ B ( ε B − u B ) ς B u B ε B − u B p (18) Remark 1 The closed-form COP and IP depend on long-term c hannel statistics (not instantaneous coef - cients), enabling low-cost e valuation and design for inte gr ated satellite–terr estrial networks with perfect-CSI baselines. Remark 2 The fr ame work aligns with pr actical deployments wher e sat ellites of fer bac khaul and gap-ller aided access for indoor handhelds, supporting str eaming and br oadband connectivity . Secur e hybrid power -fr equency multiple access in satellite terr estrial communication ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
18 ❒ ISSN: 1693-6930 4. RESUL TS AND DISCUSSIONS This section pro vides numerical simulations to v erify the analytical e xpressions. Shado wed–Rician parameters for the S–Q link follo w [22]: hea vy shado wing (HS) ( m Q , b Q , Ω Q ) = (1 , 0 . 063 , 0 . 0007) and a v erage shado wing (AS) (5 , 0 . 251 , 0 . 279) . Unless otherwise st ated [16], parameters are K ∈ { 1 , 2 , 3 } , R R = 1 bits per channel use (BPCU), R B = 0 . 5 BPCU, β B = 0 . 7 , β R = 0 . 3 , α B = α R = (1 − α RB ) / 2 , f c = 2 GHz, W = 15 MHz, T = 300 K, c = 3 × 10 8 m/s, d S Q = 35786 km, ϑ S = 5 3 . 45 dB, ϑ Q = 4 . 8 dB, θ Q = 0 . 8 ◦ , θ Q , 3dB = 0 . 3 ◦ , bandwidth (BW) = 10 M H z , noisef ig ur e ( N F ) = 10 dB, N 0 = − 174 dBm/Hz. The noise po wer is σ 2 Q [dBm] = N 0 + 10 log 10 (BW ) + NF [23]. T able 2 summarizes k e y settings. T able 2. Simulation parameters P arameter V alue Description K 1, 2, 3 Number of satellite antennas P S [ − 10 , 30] dBm Satellite transmit po wer α R B 0.1, 0.2, 0.3 BP for superposition signal m Q 1 (HS), 5 (AS) F ading se v erity β B 0.7 Po wer a llocation for Bob Figure 2 sho ws COP vs. P S (dBm). Increasing K reduces COP via spatial di v ersity . PFMA with α RB ∈ { 0 . 1 , 0 . 2 , 0 . 3 } consistently outperforms NOMA. At higher P S ( > 10 dBm), COP saturates. Agreement between e xact and asymptotic curv es v alidates the analysis. Smaller α RB further impro v es COP by reducing inter -user interference in the combined SINRs. The observ ed ≈ 4 dB SNR g ain (see Figure 3) translates to ∼ 60% co v erage e xtension or up to 37% po wer sa ving via the free-space loss with traceability in [15]. L S Q = 4 π f d S Q c 2 (19) Figure 3 presents COP vs. P S for HS and AS, comparing PFMA and NOMA. Exact (solid) and asymptotic (dashed) curv es match closely . PFMA consistently outperform s NOMA, with lar ger g ains under HS. Under HS ( m Q =1 , b Q =0 . 063 , Ω Q =0 . 0007 ), COP increases by up to 20% at lo w P S relati v e to AS ( m Q =5 , b Q =0 . 251 , Ω Q =0 . 279 ). Imperfect CSI (MMSE with estimation errors) further de grades COP: a 10% error -v ariance rise adds ≈ 5–10% COP , highlighting PFMA ’ s reliance on accurate CSI and its vulnerability to se v ere shado wing. Figure 4 sho ws COP vs. β B for K ∈ { 1 , 2 , 3 } and α RB = 0 . 4 . Lar ger K reduces COP for both schemes, with PFMA dominating across all β B . The curv es demonstrate the reliability trade-of f as β B v aries. In Figure 5 , IP is plotted vs. P S for PFMA and NOMA. V arying α RB ∈ { 0 . 1 , 0 . 2 , 0 . 3 } sho ws PFMA achie v es lo wer IP for the same P S . As P S increases, IP approaches 1 for all schemes, while smaller α RB benets lo w- P S security . Exact curv es v alidate the analysis. Future re search may consider additional practical aspects, e.g., hardw are RF impairments such as I/Q imbalance [24], security–reliability trade-of f with no n- ideal untrusted relaying [25], and simultaneous secure-and-co v ert transmission under practical assumptions [26]. -25 -20 -15 -10 -5 0 5 10 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Figure 2. COP comparison: PFMA vs. NOMA -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. COP vs. P S under dif ferent shado wing; K = 3 , α RB = 0 . 2 TELK OMNIKA T elecommun Comput El Control, V ol. 24, No. 1, February 2026: 14–21 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 19 0 0.2 0.4 0.6 0.8 1 10 -4 10 -3 10 -2 10 -1 10 0 Figure 4. COP vs. β B , α RB = 0 . 4 5 10 15 20 25 30 35 40 45 50 10 -4 10 -3 10 -2 10 -1 10 0 Figure 5. IP vs. P S (dBm); K =2 , R R = R B =1 5. CONCLUSION W e proposed and analyzed a PFMA-based h ybrid multiple access frame w ork for secure sat el- lite–terrestrial netw orks. Closed-form COP and IP e xpressions (with asymptotics and di v ersity) under shad- o wed–Rician f ading and dual ea v esdroppers re v eal ∼ 4 dB SNR g ain o v er NOMA, up to 30% COP reduction, and 20–25% IP reduction at P S =10 dBm. Simulations conrm potential ∼ 60% co v erage increase or up to 37% ener gy sa ving. Future w ork will consider m ulti-cell and mobility scenarios, imperfect self-interference mitig ation, optimized BP/P A, multi-antenna transcei v ers, colluding ea v esdroppers, and broader f ading models. A CKNO WLEDGMENT Authors w ould lik e to thank Industrial Uni v ersity of Ho Chi Minh City (IUH) 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 Contri b ut or 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 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ V iet-Thanh Pham ✓ ✓ ✓ ✓ 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 Authors state no conict of interest. Secur e hybrid power -fr equency multiple access in satellite terr estrial communication ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.
20 ❒ ISSN: 1693-6930 D A T A A V AILABILITY No ne w data were generated or analyzed. REFERENCES [1] Y . Gu et al ., “ISA C to w ards 6G Satellite–T errestrial Communications: Principles, Status, and Prospects, ” Electr onics , v ol. 13, no. 7, p. 1369, 2024, doi: 10.3390/electronics13071369. [2] S. B. R. T irmizi, Y . Chen, S. Lakshminarayana, W . Feng, and A. A. Khuw aja, “Hybrid Satellite–T errestrial Netw orks to w ard 6G: K e y T echnologies and Open Issues, ” Sensor s , v ol. 22, no. 21, p. 8544, 2022, doi: 10.3390/s22218544. [3] R . Xu, X. Da, H. Hu, L. Ni, and Y . P an, “ A Secure Hybrid S atellite-T errestrial Communication Netw ork W ith AF/DF and Relay Selection, ” IEEE Access , v ol. 7, pp. 171980–171994, 2019, doi: 10.1109/A CCESS.2019.2955541. [4] D. T . Do, A. T . Le, R. Kharel, A. Silv a, and M. A. Shattal, “Hybrid Satellite-T errestrial Relay Netw ork: Proposed Model and Application of Po wer Splitting Multiple Access, ” Sensor s , v ol. 20, no. 15, p. 4296, 2020, doi: 10.3390/s20154296. [5] Q. Ngo, T . K. Phan, A. Mahmood, W . Xiang, “Hybrid IRS-Assisted Secure Satellite-T errestr ial Communications: A F ast Deep Reinforcement Learning Approach, ” Institute of Electrical and Electr onics Engineer s (IEEE) , Aug. 2022, doi: 10.36227/techrxi v .20478438.v1. [6] H . Li, et al. , “Capacity Upper Bound Analysis of the Hybrid Satellite T errestrial Communication Systems, ” IEEE Commun. Lett. , v ol. 20, no. 12, pp. 2402–2405, 2016, doi: 10.1109/LCOMM.2016.2604387. [7] H . Li et al. , “Performance analysis of the return link for the h ybrid satelli te terrestrial communication systems, ” 2016 IEEE 13th International Confer ence on Signal Pr ocessing (ICSP) , 2016, pp. 1283-1287, doi: 10.1109/ICSP .2016.7878033. [8] K. An et al. , “Performance Analysis of Multi-Antenna Hybrid Satellite-T errestrial Relay Netw orks in the Pres ence of Interference, ” in IEEE T r ansactions on Communications , v ol. 63, no. 11, pp. 4390-4404, No v . 2015, doi: 10.1109/TCOMM.2015.2474865. [9] X. Zhang, D. Guo, K. An, G. Zhe ng, S. Chatzinotas and B. Zhang, “ Auction-Based Multichannel Cooperati v e Spectrum Shar - ing in Hybrid Satell ite-T errestrial IoT Netw orks, ” in IEEE Internet of Things J ournal , v ol. 8, no. 8, pp. 7009-7023, 2021, doi: 10.1109/JIO T .2020.3037408. [10] P . Iv ani ˇ s, J. Milojk o vi ´ c, V . Blagoje vi ´ c, and S. Brki ´ c, “Capacity Analysis of Hybrid Satellite–T errestrial Systems with Selection Relaying, ” Entr opy , v ol. 26, no. 5, p. 419, 2024, doi: 10.3390/e26050419. [11] K. Cao et al. , “Secure T ransmission Designs for NOMA Systems Ag ainst Internal and External Ea v esdropping, ” IEEE T r ansactions on Information F or ensics and Security , v ol. 15, pp. 2930–2943, 2020, doi: 10.1109/TIFS.2020.2980202. [12] K . S. Ali, A. Al-Dweik, E. Hossain and M. Chai, “Ph ysical Layer Security of P artial-NOMA and NOMA in Poisson Netw orks, ” in IEEE T r ansactions on W ir eless Communications , v ol. 23, no. 6, pp. 6562-6579, June 2024, doi: 10.1109/TWC.2023.3334020. [13] C .-B. Le, D.-T . Do, and M. V oznak, “Secure transmission in backhaul NOMA systems: A ph ysical layer security design with untrusted user and ea v esdropper , ” Digital Communications and Networks , v ol. 10, no. 4, pp. 1001–1013, 2024, doi: 10.1016/j.dcan.2022.12.005. [14] B. Zhuo et al. , “P artial-NOMA Based Ph ysical Layer Security: F orw arding Design and Secrec y Analysis, ” in IEEE T r ansactions on Intellig ent T r ansportation Systems , v ol. 24, no. 7, pp. 7471-7484, 2023, doi: 10.1109/TITS.2022.3166837. [15] Q. Li, D. Xu, K. Na v aie and Z. Ding, “Co v ert and Secure Communications in NOMA Netw orks W ith Internal Ea v esdropping, ” in IEEE W ir eless Communications Letter s , v ol. 12, no. 12, pp. 2178-2182, 2023, doi: 10.1109/L WC.2023.3312689. [16] P . K. Sharma, D. Deepthi, and D. I. Kim, “Outage probability of 3-D mobile U A V relaying for h ybrid satellite-terrestrial netw orks, ” IEEE Communications Letter s , v ol. 24, no. 2, pp. 418–422, 2020, doi: 10.1109/LCOMM.2019.2956526. [17] M. W . Akhtar , A. Mahmood, and M. Gidlund, “P artial NOMA for semi-inte grated sensing and communication, ” in 2023 IEEE Globecom W orkshops (GC Wkshps) , 2023, pp. 1129-1134, doi: 10.1109/GCWkshps58843.2023.10464754. [18] I. S. Gradshte yn, I. M. Ryzhik, A. Jef fre y , Y . V . Geronimus, M. Y . Tse ytlin, and Y . C. Fung, “T able of Inte grals, Series, and Products, ” J ournal of Biomec hanical Engineering , v ol. 103, no. 1, pp. 58–58, 1981, doi: 10.1115/1.3138251. [19] V . Bank e y , P . K. Upadh yay , D. B. Da Costa, P . S. Bithas, A. G. Kanatas, and U. S. Dias, “Performance Analysis of Multi-Antenna Multiuser Hybrid Satellite-T errest rial Relay Systems for Mobile Services Deli v ery , ” IEEE Access , v ol. 6, pp. 24729–24745, 2018, doi: 10.1109/A CCESS.2018.2830801. [20] C.-B. Le, et al. , “Joint design of impro v ed spectrum and ener gy ef cienc y with backscatter NOMA for IoT , ” IEEE Access , v ol. 10, pp. 7504–7519, 2022, doi: 10.1109/A CCESS.2021.3139118. [21] K. Guo et al. , “Po wer Allocation and Performance Ev aluation for NOMA-Aided Inte grated Satellite-HAP-T errestrial Net- w orks Under Practical Limitations, ” in IEEE Internet of Things J ournal , v ol. 11, no. 7, pp. 13002-13017, 2024, doi: 10.1109/JIO T .2023.3337124. [22] N. I. Miridakis, D. D. V er g ados, and A. Michalas , “Dual-hop communication o v er a satellite relay and shado wed Rician channels, ” in IEEE T r ansactions on V ehicular T ec hnolo gy , v ol. 64, no. 9, pp. 4031-4040, Sept. 2015, doi: 10.1109/TVT .2014.2361832. [23] H. Q. T ran and B. M. Lee, “RIS-NOMA-assisted short-pack et communication with direct links, ” J ournal of King Saud Univer sity - Computer and Information Sciences , v ol. 36, no. 3, p. 101979, 2024, doi: 10.1016/j.jksuci.2024.101979. [24] X. Li, M. Zhao, Y . Liu, L. Li, Z. Ding, and A. Nallanathan, “Secrec y analysis of ambient backscatter NOMA systems under I/Q imbalance, ” IEEE T r ansactions on V ehicular T ec hnolo gy , v ol. 69, no. 10, pp. 12286–12290, 2020, doi: 10.1109/TVT .2020.3006478. [25] A. K uhestani, A. Mohammadi, and P . L. Y eoh, “Security-reliability trade-of f in c yber -ph ysical cooperati v e systems with non- ideal untrusted relaying, ” in 2018 IEEE 4th W orld F orum on Internet of Things (WF-IoT) , 2018, pp. 552–557, doi: 10.1109/WF- IoT .2018.8355190. [26] M. F orouzesh, F . S. Khodadad, P . Azmi, A. K uhestani, and H. Ahmadi, “Simultaneous Secure and Co v ert T ransmissions Ag ainst T w o Attacks Under Practical Assumptions, ” IEEE Internet Things J ournal , v ol. 10, no. 12, pp. 10160–10171, 2023, doi: 10.1109/JIO T .2023.3237640. TELK OMNIKA T elecommun Comput El Control, V ol. 24, No. 1, February 2026: 14–21 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control ❒ 21 BIOGRAPHIES OF A UTHORS Huu Q . T ran (Member , IEEE) recei v ed the M.S. de gree in El ectronics Engineering 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. V iet-Thanh Pham recei v ed the Ph.D. de gree in Electronics, Automation, and Control of Comple x Systems from the Uni v ersity of Catania. He is with the Industrial Uni v ersity of Ho Chi Minh City . His research interests include chaos, nonlinear control, fractional-order systems, mathe- matical modelling, and applications of nonlinear systems. He can be contacted at email: phamviet- thanh@iuh.edu.vn. Secur e hybrid power -fr equency multiple access in satellite terr estrial communication ... (Huu Q. T r an) Evaluation Warning : The document was created with Spire.PDF for Python.