A Bipartite Matching Based User Pairing Scheme for Hybrid VLC-RF NOMA Systems

Yu Han, Xiaotian Zhou, Liuqing Yang, Shanshan Li

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

In this paper, we present a hybrid Visible Light Communication (VLC) and Radio Frequency (RF) based Non-Orthogonal Multiple Access (NOMA) system to extend the coverage of VLC and support multi-user communications at the same time. In the proposed system, all users are divided into multiple user pairs, where the near user who can receive the visible light signal directly would help forward the information to its paired far user through RF transmission. To achieve that, NOMA is adopted during the VLC phase so the near user is able to receive not only its own but also the information for its paired user. Aiming at minimizing the outage probability of system, we formulate the optimal user pairing problem and convert it into the one of finding the maximum weighted matching in a bipartite graph. Kuhn-Munkres (KM) algorithm is utilized to solve the problem. Simulation results demonstrate that the system performance is markedly improved with our proposed scheme.

Original languageEnglish (US)
Title of host publication2018 International Conference on Computing, Networking and Communications, ICNC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages480-485
Number of pages6
ISBN (Electronic)9781538636527
DOIs
StatePublished - Jun 19 2018
Externally publishedYes
Event2018 International Conference on Computing, Networking and Communications, ICNC 2018 - Maui, United States
Duration: Mar 5 2018Mar 8 2018

Publication series

Name2018 International Conference on Computing, Networking and Communications, ICNC 2018

Conference

Conference2018 International Conference on Computing, Networking and Communications, ICNC 2018
CountryUnited States
CityMaui
Period3/5/183/8/18

Bibliographical note

Funding Information:
ACKNOWLEDGEMENT This work is in part supported by National Natural Science Foundation of China (NSFC) under No. 61401254 and 61671278, and the fundamental Research Funds of Shandong University under No. 2017JC002.

Funding Information:
Fig. 2. Bipartite graph presentation of user pairing problem. B. Bipartite Matching Based User Pairing Method In this subsection, we propose the bipartite matching based user pairing (BMUP) method. Our objective is to minimize the outage probability of the system. We further assume that Kn = Kf = K/2 to guarantee that each FU can be paired with one NU. Such assumption is reasonable wh√en considering all users are uniformly distributed and Rf = 2Rn. Define Kg(i, j) to be the two-dimensional set of the g-th user pair, containing the i-th NU and j-th FU. The user pairing problem can be formulated as following: min s.t. P (Ω) = 1 − ∏G P (Ωg¯) g=1 Kg∩Kg′=∅,g∕ g′, g=1∑G ‖ Kg(i) ‖= Kn , ∑G g=1 ‖ Kg(j) ‖= Kf . (22) (23) (24) (25) where ‖ · ‖ denotes the cardinality of the set. The first constraint indicates that each NU and FU can be allocated to only one user pair. While the second and third constraints ensure that all NUs and FUs to be paired. We find that the user pairing problem in (22) is quite similar to the matching problem in a bipartite graph [7]. As depicted in Fig. 2, the relationship between the paired NUs and FUs can be represented by a bipartite graph B(V1, V2, E), where V1 and V2 are two vertex sets containing NUs and FUs, respectively. E is the set of edges connecting every vertex in V1 to every vertex in V2 and the number of edges in E is KnKf. It reveals that each NU has the potential to be paired with any FU. In addition, each edge in E has its own weight. Thus, the user pairing problem can be re-formulated as finding an one- ξjr ξ RnRn to-one matching in the graph, where every vertex in V1 is connected by one and only one edge and so that to the vertices in V2. Moreover, such one-to-one matching should be the one can minimize the outage probability of the system among all possibilities. In fact, there exists one low complexity method called Kuhn-Munkres (KM) algorithm to find the one-to-one matching with maximum sum weights of the edges [10]. However, according to (22), the minimal outage probability is obtained by maximizing the product rather than summation of P (Ωg¯). To make the KM method implementable to the proposed problem, we introduce the logarithmic function and define the weight of edge connecting the i-th NU and j-th FU in the g-th pair as: wijg = log P (Ωg¯) , i,j∈Kg. (26) Owing to the monotonically increasing property of logarithmic function, the original problem in (22) is equivalent to the following maximization problem: {∏G}{∏G P (Ωg¯) log P (Ωg¯) g={1}g=1 ∑G(g) logP(Ω¯g)=wij g=1 By such conversion, KM method is now applicable to the proposed problem and the user pairing solution that minimize the system outage probability can be obtained. The details of KM algorithm can be found in [10]. } max ⇔ max (27) ⇔ max . IV. SIMULATION RESULTS In this section, simulation results are provided to evaluate the performance of the proposed BMUP scheme. The parameters are summarized in Table I. For comparison, the performance of the Nearest Near user and Nearest Far user (NNNF) scheme in [6] is also provided. Fig. 3 illustrates the outage probability of system versus the SNR with the proposed BMUP scheme and NNNF one. Note that the transmit power of LED and each FU are set to be Pij = 0.3P . And the target SINR thresholds are Γi = Γj = 1dB for both FU and NU. Moreover, we also considered the cases with different number of users when K = 8 , 16 , 32. It can be observed that for both schemes the outage probability of system decreases along with the increase of SNR. In addition, the performance of system is better when the number of users is small. It is reasonable since the fewer users are involved, the more power is assigned to the NUs from LED. Hence the VLC phase is less likely to be in outage, leading to a better performance achieved. Nevertheless, it can be found that the Outage Probability TABLE I SIMULATION PARAMETERS Parameter Distance between the LED and horizontal plane, L Annular outer radius, Rf Circular radius, Rn PD area, A Optical filter gain, T(ψ) Reflective index, n LED semi-angle, Φ1/2 PD FOV, ΨFOV Power allocation coefficients, ai, aj Path loss exponent, β 1 Value 2.15 m 5m 3m 1 cm2 1 1.5 60◦ 30◦ 0.2, 0.8 2 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 BMUP K=8 NNNF K=8 BMUP K=16 NNNF K=16 BMUP K=32 NNNF K=32 0100 105 110 SNR (dB) 115 120 Fig. 3. Outage probability of system versus SNR for different user paring schemes. proposed BMUP scheme always outperforms the NNNF one invariant of the user numbers. Moreover, the performance of BMUP scheme with K = 32 is even better than that of NNNF with K = 16, which indicates the efficiency of the proposed scheme especially in the dense scenario with large number of users. In Fig. 4 we evaluate the outage probability of system with different target SINRs at NUs and FUs, where Γj = 3dB and Γi = {1, 3, 5} dB. The number of users K = 16. Again it can be seen that the performance of BMUP scheme is better than that of NNNF one under any situations. In addition, we observe that the performance of {Γj = 3, Γi = 1} case is the same as that of {Γj = 3, Γi = 3} case. That makes sense since both cases satisfy Γi ≤ aj−aiΓjaiΓj in (16). With Γj fixed and according to (20), the outage probability of these two cases is identical. In such scenario, the performance of the system is mainly dominated by the target SINR of FU Γj. While on the hand for the case of {Γj = 3, Γi = 5}, it satisfies Γi > aj−aiΓjaiΓj. Then the system performance is mainly determined 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 i j=3 i i i j=3 j=3 j=3 i i j=3 j=3 0 100 102 104 106 108 110 112 SNR (dB) 114 116 118 120 Fig. 4. Outage probability of system versus SNR for different target SINR thresholds in K = 16 case. by the requirement of NU Γi, where the performance will degrade as Γi increase. V. CONCLUSIONS In this paper, we proposed a novel hybrid VLC-RF NOMA system to simultaneously extend the coverage of VLC and support multi-user communications. With respect to the proposed system, we investigated the outage probability of the system and formulated the user pairing problem to maximize the system outage performance. By utilizing graph theory and the logarithmic function, the original problem was converted into the one of finding the maximum weighted matching in a bipartite graph. The KM algorithm was then employed to get the solution. Simulations confirmed that the system performance is greatly improved with the proposed user pairing scheme. ACKNOWLEDGEMENT This work is in part supported by National Natural Science Foundation of China (NSFC) under No. 61401254 and 61671278, and the fundamental Research Funds of Shandong University under No. 2017JC002. REFERENCES [1] A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Communications Magazine, vol. 51, no. 12, pp. 26–32, 2013. [2] L. Grobe, A. Paraskevopoulos, J. Hilt, D. Schulz, F. Lassak, F. Hartlieb, C. Kottke, V. Jungnickel, and K. D. Langer, “High-speed visible light communication systems,” IEEE Communications Magazine, vol. 51, no. 12, pp. 60–66, 2013. [3] T. Rakia, H. C. Yang, F. Gebali, and M. S. Alouini, “Optimal design of dual-hop vlc/rf communication system with energy harvesting,” IEEE Communications Letters, vol. 20, no. 10, pp. 60–66, 2016. [4] Y. Wang, B. Ren, S. Sun, S. Kang, and X. Yue, “Analysis of non-orthogonal multiple access for 5g,” China Communications, vol. 13, no. 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