Performance Evaluation Of Reconfigurable Intelligent Surface Aided Multi-Hop Relaying Schemes With Short Packet Communication

INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH Performance Evaluation Of Reconfigurable Intelligent Surface Aided Multi-Hop Relaying Schemes With Short Packet Communication Pham Minh QUANG1, Nguyen Trong KIEN1, Tran Trung DUY1, Ngo Hoang AN2,3, Nguyen Tien TUNG2, Anh-Vu LE4 1Posts and Telecommunications Institute of Technology Ho Chi Minh City, Vietnam 2Faculty of Electronics Technology, Industrial University of Ho Chi Minh City (IUH), Ho Chi Minh City 700000, Viet Nam 3Ho Chi Minh City University of Industry and Trade, Ho Chi Minh City, Vietnam 4Communication and Signal Processing Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam [email protected], n[email protected], [email protected], [email protected], nguyentien[email protected], leanh[email protected] DOI: 10.15598/aeee.v22i1.5583 Article history: Received Dec 06, 2023; Revised Feb 19, 2024; Accepted Mar 23, 2024; Published Mar 31, 2024. This is an open access article under the BY-CC license. Abstract. This paper proposes and studies performance of reconfigurable intelligent surface (RIS)- assisted multi-hop schemes employing short packet communication (SPC). In the proposed schemes, a source sends its data to a destination, and one RIS is deployed to assist the data transmission at each hop. For complexity reduction purposes, we propose two RIS-assisted data transmission methods at each hop. In the first one, the RIS is only used when the quality of the direct link is not good. In the second one, the direct link or the relay link via the RIS is selected for the data transmission. We evaluate performance of the two proposed schemes by deriving formulas of end-to-end block error rate (BLER-e2e) over Rayleigh fading channel. Finally, the derived BLER-e2e expressions are validated by computer simulations. Keywords Intelligent reflecting surface, short packet communication, multi-hop relaying, cooperative communication. 1. Introduction Relaying techniques [1–13] are often applied to wireless communication networks to improve network performance under the impact of fading channels. In [1,2], intermediate nodes within radio range of both source and destination nodes (called relay nodes) are employed to assist in source-to-destination data transmission. In [3], multi-hop schemes using multiple relays are studied because the destination is far from the source. In [4], route selection algorithms are applied for multihop multi-path wireless sensor networks, where sensor nodes, whose transceiver hardware is imperfect, have to harvest energy from radio signals for data transmission. Moreover, the published work [4] considers the presence of active eavesdroppers, and therefore, sensor nodes have to reduce their transmit power to protect the source data. In [5], a multi-hop network using fullduplex relaying techniques and operating in a near-field path-loss environment is proposed and evaluated. Additionally, the authors in [5] consider non-orthogonal multiple access techniques and the issue of imperfect interference cancellation. Published works [6–13] introduce various practical applications of the relaying techniques in wireless communication networks. Recently, relaying networks that use reconfigurable intelligent surfaces (RIS) have been studied. Unlike the conventional relaying methods, in [14–18], the RIS, c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 97 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH which consists of a lot of small reflectors, is deployed to optimally reflect the source signals to the desired destination. In particular, the RIS uses controllers to appropriately adjust the phases of the radio waves so that they can be reflected to the destination optimally. In [19], the authors study secrecy performance for a down-link relaying scenario using the RIS. As in [19], the RIS-aided scenario obtains better performance than the corresponding one using the conventional relays. In [20], the authors analyze average secrecy capacity of secure transmission relaying models using the RIS with discrete phase shift. The authors in [21] investigate secrecy performance of RIS-assisted vehicleto-vehicle and vehicle-to-infrastructure networks. Short packet communication (SPC) has garnered a lot of attention of researchers for its applications in ultra-reliable low-latency communication networks. In [22], the authors propose and optimize block error rate (BLER) performance of dual-hop relaying schemes employing SPC. Published works [23, 24] study clusterbased multi-hop relaying models utilizing SPC, and incorporating relay selection at each hop. Notably, the transmitting nodes in these models are required to harvest wireless energy from power stations. In [25], the authors assessed BLER performance of dual-hop underlay cognitive radio networks with the assistance of the RIS. In this paper, we propose the RIS-aided multi-hop scheme using SPC. In particular, the RIS is employed to assist the data transmission at each hop on the source-to-destination route. Although published works [26, 27] also study multi-hop networks using hop-byhop cooperative transmission, [26, 27] do not consider the SPC and RIS techniques. In contrast to [28–33], this paper considers the multi-hop relaying networks, while these published works consider RIS-aided dualhop networks. In [34], the authors evaluate outage performance of the RIS-aided multi-hop networks, but they] do not study the SPC technique. Next, this paper briefly introduces motivation, new points and main contributions: •We propose two new RIS-aided hop-by-hop transmission methods for the proposed scheme. In the first one (named RIS-IC), Incremental Cooperation strategy is applied at each hop, where the RIS is only used if the direct link is not good. In the second one (named RIS-AE), the RIS is always employed at each hop. However, only the direct link or the relay link via the RIS is selected for the data transmission. •Our proposed RIS-IC and RIS-AE methods reduce implementation complexity, as compared to the corresponding RIS-aided hop-by-hop transmission one proposed in [8] (named RIS-Opt). •We derive expressions of the end-to-end block error rate (BLER-e2e) for the RIS-IC and RIS-AE over Rayleigh fading channels. •All the derived BLER-e2e formulas will be validated by computer simulations. •Impact of the important parameters such as the number of hops, the number of reflectors at the RIS, the threshold value in the RIS-IC scheme on the performance of the proposed schemes is investigated. The remaining contents of this paper is outlined as follows: Section 2. presents system model of the RISIC and RIS-AE schemes. Derivation of the BLER-e2e performance over Rayleigh fading channel is performed in Section 3. . Simulation and theoretical results are presented in Section 4. , and Section 5. concludes the paper. 2. System Model In Fig. 1, the source node (T0)attempts to send the data to the destination node (TN)via a pre-established Nhop route, i.e., T0→T1→...TN−1→TN. The RIS (R) with Kreflectors is deployed to assist the T0→TNtransmisison. We denote Kelements of the RIS by Rk,k= 1,2, . . . , K. Assume that each node Tn(n= 0,1, ..., N)is equipped with single antenna, and therefore, the T0→TNtransmission is realized via Ntime slots. Using SPC, T0sends a δ-bit packet to TNwith a blocklength m(m > 100), and the coding rate at each hop is given as r=δ/m [35]. Next, we denote hTn−1Tn,hTn−1Rkand hRkTnas channel coefficients of the Tn−1→Tn, Tn−1→Rk and Rk→Tnlinks, respectively, where n= 1, ..., N. Then, we denote the corresponding channel gains as gTn−1Tn=|hTn−1Tn|2,gTn−1Rk=|hTn−1Rk|2and gRkTn=|hRkTn|2. Once the X →Y channel is Rayleigh fading, gXY has the following distribution functions: fgXY (x) = λXY exp (−λXYx), FgXY (x)=1−exp (−λXYx),(1) where X ∈ {Tn−1,Rk}, Y ∈ {Tn,Rk}.fgXY (.)and FgXY (.)denote probability density function (PDF) and cumulative distribution function (CDF) of gXY, respectively, and λXY =dβ XY [36,37] (βis a path-loss factor and dXY is distance between X and Y). For ease of presentation, we can denote the link distances as: dTn−1Rk=dTn−1Rand dRkTn=dRTn for all Rk. Hence, we have λTn−1Rk=λTn−1Rand λRkTn=λRTn, for all Rk. Let Pn−1and σ2 0denote transmit power of Tn−1and variance of Gaussian c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 98 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH Fig. 1: System model of the proposed RISA-MHR-SPC model. noises at all the receivers Tn, respectively. We also denote ∆n−1=PTn−1/σ2 0as transmit signal-to-noise ratio (SNR). Next, considering the hop in the RIS-IC scheme. If Tn−1directly the source packet to Tn, SNR of the Tn−1→Tnlink is written as ψDT Tn−1Tn=PTn−1gTn−1Tn σ2 0 = ∆n−1gTn−1Tn.(2) Using (1), the CDF of the SNR ψDT Tn−1Tncan be obtained as FψDT Tn−1Tn(x) = Pr ψDT Tn−1Tn< x =FgTn−1Tnx ∆n−1 = 1 −exp −λTn−1Tn ∆n−1 x.(3) If ψDT Tn−1Tnis higher than a pre-designed threshold (ψth), the direct link (Tn−1→Tn) is used for the data transmission. Otherwise, if ψDT Tn−1Tn⩽ψth, the RIS is employed, and the obtained maximal SNR of the Tn−1→R→Tnlink can be given as in [25, Eq. (3)]: ψRIS Tn−1Tn= PTn−1K P k=1 |hTn−1Rk||hRkTn|2 σ2 0 = ∆n−1(Zsum n)2,(4) where Zsum n= K P k=1 |hTn−1Rk||hRkTn|.Using [25, Eq. (13)], the CDF FZsum n(x)can be expressed as FZsum n(x)≈γ(αn+ 1, x/ωn) Γ (αn+ 1) ,(5) where Γ (.)and γ(.)are Gamma function and lower incomplete Gamma function [38], respectively, and αn=(E{Zsum n})2 Var {Zsum n}−1, ωn=Var {Zsum n} E{Zsum n},(6) where, E {Zsum n}and Var {Zsum n}are expected value and variance of Zsum n, respectively. As [15, Eq. (13)], we have E{Zsum n}=Kπ 4pλTn−1RλRTn , Var {Zsum n}=16 −π2K 16λTn−1RλRTn .(7) From (5), the CDF of the SNR ψRIS Tn−1Tnin (4) is written as FψRIS Tn−1Tn(x) = FZsum nrx ∆n−1 ≈1 Γ (αn+ 1)γαn+ 1,1 ωnrx ∆n−1.(8) Remark 1: When the Tn−1→Tnlink is strong, Tn−1can sends the source bits directly to Tnwithout utilizing the RIS. Therefore, implementing the RIS-IC is simpler than that of the RIS-AE and the RIS-Opt. However, in the RIS-IC, the threshold ψth needs to be designed carefully. Indeed, if ψth is set to low values, the direct link is used more frequently than the relay link, and in this case, the RIS is not exploited effectively. Otherwise, if ψth is set to high values, the RIS is more frequently but the implementation complexity is higher. Now, we consider the RISA-AE scheme; at the nth hop, the obtained SNR can be formulated as ψAE Tn−1Tn= max ψDT Tn−1Tn, ψRIS Tn−1Tn.(9) where ψDT Tn−1Tnand ψRIS Tn−1Tnare given as in (2) and (4), respectively. Using (3) and (8), we can obtain the CDF of ψAE Tn−1Tnas FψAE Tn−1Tn(x) = Pr ψAE Tn−1Tn< x =FψDT Tn−1Tn(x)FψRIS Tn−1Tn(x) =1−exp −λTn−1Tn ∆n−1 x ×1 Γ (αn+ 1)γαn+ 1,1 ωnrx ∆n−1.(10) Remark 2: Equation (9) implies that the direct link (Tn−1→Tn) is chosen if ψDT Tn−1Tn⩾ψRIS Tn−1Tn. Otherwise, the relay link is selected. This also means that when the direct link is better than the relay link (e.g., the RIS is far Tn−1and Tnor Tn−1and Tnare close each other), the direct link is used. Hence, the RIS-AE achieves better performance, but the implementation of the RIS-AE is more complex than that of the RISIC. c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 99 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH For performance comparison, this paper also introduces the RIS-Opt scheme. In this scheme, the SNR at the nth hop determined by an optimal phase shift strategy, and it is provided similarly to [18, Eq. (3)], as ψOpt Tn−1Tn= ∆Tn−1 |hTn−1Tn|+ K X k=1 |hTn−1Rk||hRkTn|!2 . (11) Note that ψOpt Tn−1Tn⩾ψAE Tn−1Tn(∀n), which means the RIS-Opt outperforms the RIS-AE. However, implementing the RIS-Opt is most complex due to the optimal phase shift strategy [18]. Next, we analyze BLER-e2e of the Z scheme, where Z∈ {RIS - IC,RIS - AE}. When the selective decodeand-forward technique is applied, BLER-e2e of the Z scheme can be expressed as in [35] as BLERZ e2e =BLERZ 1 + N X n=2 "BLERZ n× n−1 Y u=1 1−BLERZ u#,(12) where BLERZ nis BLER at the nth hop in the Z scheme, 1−BLERZ udenotes the successful decoding at the u-th hop, and BLERZ n× n−1 Q u=1 1−BLERZ uimplies that the source packet is dropped at the nth hop. 3. Performance Analysis In this section, we derive expressions of BLERZ n, and then substituting the derived BLERZ ninto (12) to obtain BLERZ e2e of the Z scheme. At first, we considering the RIS-IC scheme; BLER at nth hop in this scheme can be formulated as BLERRIS - IC n=BLERRIS - IC n,DT + Pr ψDT Tn−1Tn⩽ψthBLERRIS - IC n,RIS .(13) In (13), BLERRIS - IC n,DT and BLERRIS - IC n,RIS are BLERs in the cases where the direct and relay links are used, respectively. Also in (13), Pr ψDT Tn−1Tn⩽ψthis probability that the RIS is used, and it is calculated as Pr ψDT Tn−1Tn⩽ψth=FψDT Tn−1Tn(ψth) = 1 −exp −λTn−1Tn ∆n−1 x.(14) For BLERRIS - IC n,DT in (13), we can formulate it as (see [35]): BLERRIS - IC n,DT ≈Z+∞ 0 Q C(x)−r pV(x)/m! ×fψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x)dx, (15) where Q(.)is Gaussian Q-function [38], V(x)and C(x)are given, respectively as (see [35]): V(x) = 1−1 (1 + x)2!(log2(e))2, C(x) = log2(1 + x).(16) In (15), fψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x)is the PDF of ψDT Tn−1Tnconditioned on ψDT Tn−1Tn> ψth. To find fψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x), we first find the conditioned CDF FψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x): FψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x) = Pr ψDT Tn−1Tn< x, ψDT Tn−1Tn> ψth =             0, x ⩽ψth exp −λTn−1Tnψth ∆n−1 −exp −λTn−1Tnx ∆n−1, x > ψth (17) From (17), we obtain the conditioned PDF fψDT Tn−1Tn|ψDT Tn−1Tn>ψth (x)as fψTn−1Tn|ψTn−1Tn>ψth (x) =     0, x ⩽ψth λTn−1Tnx ∆n−1 exp −λTn−1Tnx ∆n−1, x > ψth (18) Substituting (18) into (15), we have BLERRIS - IC n,DT ≈Z+∞ ψth Q C(x)−r pV(x)/m! ×λTn−1Tnx ∆n−1 exp −λTn−1Tnx ∆n−1dx. (19) Similarly, BLERRIS - IC n,RIS in (13) can be expressed as BLERRIS - IC n,RIS ≈Z+∞ 0 Q C(x)−r pV(x)/m!fψRIS Tn−1Tn(x)dx. (20) Moreover, BLERRIS - IC n,RIS in (20) can be rewritten under the following form (see [35, Eq. (11)]): BLERRIS - IC n,RIS ≈ϑ√mZρH ρL FψRIS Tn−1Tn(x)dx, (21) c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 100 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH Fig. 2: BLER-e2e as a function of ∆(dB) when N= 2 and K= 3. where ϑ=1 2π√22r−1, θ = 2r−1, ρH=θ+1 2ϑ√m, ρL=θ−1 2ϑ√m.(22) Substituting (8) into (21), after some careful manipulation, we obtain BLERRIS - IC n,RIS ≈ϑ√m Γ (αn+ 1) ×ZρH ρL γαn+ 1,1 ωnrx ∆n−1dx ≈ϑ√m Γ (αn+ 1) (In,H−In,L),(23) where In,H=ρHγ 1 + αn,√ρH ωnp∆n−1! −1 (ωn)2∆n−1 γ 3 + αn,√ρH ωnp∆n−1!, In,L=ρLγ 1 + αn,√ρL ωnp∆n−1! −1 (ωn)2∆n−1 γ 3 + αn,√ρL ωnp∆n−1!,(24) Fig. 3: BLER-e2e as a function of ψth when N= 4. Substituting (14), (19) and (23) into (13), we can obtain BLERRIS - IC nas follows: BLERRIS - IC n≈Z+∞ ψth Q C(x)−r pV(x)/m! ×λTn−1Tnx ∆n−1 exp −λTn−1Tnx ∆n−1dx +1−exp −λTn−1Tn ∆n−1 x ×ϑ√m Γ (αn+ 1) (In,H−In,L).(25) Similar to (21), we can calculate BLERRIS - AE nas BLERRIS - AE n≈ϑ√mZρH ρL FψRIS Tn−1Tn(x)dx. (26) Substituting (10) into (26), we have BLERRIS - AE n≈ϑ√m Γ (αn+ 1) ×ZρH ρL1−exp −λTn−1Tn ∆n−1 x ×γαn+ 1,1 ωnrx ∆n−1dx. (27) Finally, substituting (25) and (27) into (12), we obtain expressions of BLERRIS - IC e2e and BLERRIS - AE e2e , respectively. 4. Results This section provides both simulation results (Monte Carlo simulation) and theoretical results of the BLERc 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 101 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH Fig. 4: BLER-e2e as a function of ψth when K= 4 and ∆ = 5dB. e2e performance of the RIS-IC and RIS-AE schemes. For a fair comparison, the total transmit power is fixed by Ptot, i.e., N−1 P n=0 PTn=Ptot. We also assume that all the transmitters have the same transmit power, and we hence have PTn=Ptot/N. In all simulations, we place Tnat position (n/N, 0) and the RIS at (0.5,0.75). We also fix the values of the parameters as follows: β= 3, σ2 0= 1,δ= 256 and m= 128. Fig. 2 depicts the BLER-e2e performance of the RIS-IC and RIS-AE schemes as a function of transmit SNR ∆ = Ptot/σ2 0in dB with different values of the threshold ψth, i.e., ψth ∈ {1,5,20}. The remaining parameters are set to N= 2 and K= 3. As observed, BLER-e2e of the RIS-AE is consistently lower than that of the RIS-IC for all values of ψth. It is evident that the threshold ψth significantly impacts the performance of the RIS-IC. Specifically, when ψth = 1, BLER-e2e of the RIS-IC is highest, whereas with ψth = 5, it reaches to the lowest value. As highlighted in Remark 1, a very low value of ψth implies that the RIS-IC predominantly utilizes the direct link for data transmission at each hop. Conversely, with a very high value of ψth, the relay link is predominantly used, resulting in the omission of the role of the direct link. This explains why BLER-e2e of the RIS-IC with ψth = 20 is higher than that with ψth = 5. Finally, Fig. 2 illustrates that the simulation (Sim) and theoretical (Theory) results are in a good agreement, confirming the correctness of our derivations in the previous sections. Fig. 3 illustrates the BLER-e2e performance of the RIS-IC as a function of ψth with N= 4 and varying values of ∆and K. As expected, BLER-e2e of the RIS-IC Fig. 5: BLER-e2e as a function of ∆(dB) when K= 2,N= 6 and ψth = 4. is lower with higher values of ∆and K. Furthermore, Fig. 3 reveals presence of an optimal value for ψth that minimizes BLER-e2e of the RIS-IC. For instance, in Fig. 3, with ∆=0dB, K= 2 and ∆=2.5dB, K= 3, the optimal value of ψth is 3. Similarly, with ∆=5dB, K= 5, the optimal value of ψth is 4. This highlights the need for careful design considerations when selecting ψth to optimize the performance of the RIS-IC. Fig. 4 illustrates BLER-e2e of the RIS-IC and RISAE schemes as a function of ψth with K= 4 and ∆=5dB. In this figure, the number of hops (N) is set to 2 and 5. Similar to Fig. 3, it is evident that an optimal value of ψth exists so that the performance of the RIS-IC is best. For instance, the optimal value of ψth is 4 in both cases of N= 2 and N= 5. However, it is worth noting that the RIS-AE consistently outperforms the RIS-IC for all values of ψth. To find the optimal values of ψth, the derived expressions of BLER can be used efficiently. Additionally, we observe that the number of hops significantly influences the BLER-e2e performance. In the RIS-AE scheme, the BLER-e2e value is lower with M= 2, and in the RIS-IC scheme, the performance is superior with N= 2 and ψth ⩾4. Fig. 5 compares the performacne of the RIS-IC, RISAE and RIS-Opt schemes with K= 2,N= 6 and ψth = 4. As observed, the RIS-Opt achieves the best performance, while the RIS-AE again outperforms the RIS-IC. As mentioned earlier, implementing the RISOpt is the most complex because it requires all channel state information of the links for realizing the optimal phase shift strategy. Additionally, it is worth noting that the performance gap between the RIS-AE and the c 2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 102 INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 22 |NUMBER: 1 |2024 |MARCH Fig. 6: BLER-e2e as a function of Nwhen ψth = 3.5and ∆ = 5(dB). RIS-IC is small because ψth is designed with an appropriate value, i.e., ψth = 4. Fig. 6 presents the performance of the RIS-IC and RIS-AE schemes as a function of the number of hops (N) when ψth = 3.5and ∆=5(dB). Fig. 6 demonstrates that BLER-e2e of the RIS-IC and RIS-AE schemes increases with the increasing of N. It is due to the fact that when the number of hops increases, the transmit power of each node decreases due to the fixed total transmit power, i.e., PTn=Ptot/N for all n= 0,1, ..., N −1. Again, we can see that the performance of the proposed schemes is better with higher number of reflectors at the RIS. 5. Conclusion In this paper, we proposed two RIS-aided multi-hop relaying schemes using SPC. Implementing the proposed RIS-IC and RIS-AE schemes are much simpler than the RIS-Opt one. We evaluated the BLER-e2e performance of the proposed schemes through both simulations and analysis. The results indicated that the RIS-AE outperforms the RIS-IC although the implementation of the RIS-IC is simpler. In the RIS-IC, the threshold needs to be optimized to achieve the best performance. Furthermore, the BLER-e2e performance of the proposed schemes can be enhanced by increasing the transmit power and the number of reflectors at the RIS. Acknowledgment This research is funded by Posts and Telecommunications Institute of Technology under grant number 112023-HV-VT2. Author Contributions The main contributions of Pham Minh Quang and Ngo Hoang An were to create the main ideas and execute performance evaluation by extensive simulations, while Tran Trung Duy, Nguyen Tien Tung and Anh-Vu Le worked as the advisers of Pham Minh Quang and Ngo Hoang An to discuss, create, and advise the main ideas and performance evaluations together. References [1] TIN, P. T., HUNG, D. T., DUY, T. T. and VOZNAK, M. Security-Reliability Analysis of NOMA – Based Multi-Hop Relay Networks In Presence Of an Active Eavesdropper With Imperfect Eavesdropping CSI. 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