Poster Abstract: Hierarchical Subchannel Allocation for Mode-3 Vehicle-to-Vehicle Sidelink Communications

P oster Abstract: Hiera rchical Sub channel Allo cation fo r Mo de-3 V ehicle-to-V ehicle Sidelink Communications Luis F. Aban to-Leon Eindho v en Univ ersit y of T ec hnology Eindho v en, Netherlands l.f.aban to@tue.nl Arie K opp elaar NXP Semiconductors Eindho v en, Netherlands arie.k opp elaar@nxp.com Sonia Heemstra de Gro ot Eindho v en Univ ersit y of T ec hnology Eindho v en, Netherlands sheemstradegro ot@tue.nl ABSTRA CT In this p oster w e presen t a graph-based hierarchical subchan- nel allo cation scheme for V2V sidelink communications in Mo de-3. Under this sc heme, the eNodeB allocates subchan- nels for in-cov erage vehicles. Then, v ehicles will broadcast directly without the eNo deB in terv ening in the pro cess. There- fore, in eac h comm unications cluster, it will become crucial to preven t allocation conflicts in time domain since vehicles will not be able to transmit and receiv e sim ultaneously . W e presen t a solution where the time-domain requiremen t can b e enforced through vertex aggregation. A dditionally , allo cation of subchannels is p erformed sequentially from the most to the least allo cation-constrained cluster. W e show through simu- lations that the prop osed approach attains near-optimality . CCS CONCEPTS • Netw orks → Network r esour c es al lo c ation ; KEYW ORDS resource allo cation; mode-3 V2V; sidelink 1 MOTIV A TION AND CONTRIBUTIONS In V2V Mode-3, eNo deBs assign sub channels to v ehicles in order for them to perio dically broadcast CAM messages [ 1 ]. A crucial asp ect is to ensure that vehicles in the same cluster will broadcast in orthogonal time subchannels 1 to av oid conflicts. In general, resource/subchannel allo cation problems can b e represen ted as w eighted bipartite graphs. How ever, in this scenario there is an additional time orthogonalit y constrain t whic h cannot be straigh tforwardly handled by conv entional graph matc hing metho ds [ 2 ]. Th us, in our approac h the men tioned constraint has been tak en in to accoun t. W e also 1 A subchannel is a time-frequency resource ch unk capable of sufficiently conv eying a CAM message. Permission to make digital or hard copies of all or part of this work for personal or classroom use is gran ted without fee pro vided that copies are not made or distributed for profit or commercial adv antage and that copies b ear this notice and the full citation on the first page. Copyrigh ts for comp onents of this work owned by others than the au- thor(s) must b e honored. Abstracting with credit is p ermitted. T o copy otherwise, or republish, to p ost on servers or to redistribute to lists, requires prior sp ecific p ermission and /or a fee. Request permissions from permissions@acm.org. SenSys ’17, Novemb er 6–8, 2017, Delft, Netherlands © 2017 Copyright held by the owner/author(s). Publication rights licensed to Asso ciation for Computing Machinery . ACM ISBN 978-1-4503-5459-2/17/11. . . $15.00 https://doi.org/10.1145/3131672.3136987 𝐾 𝐿 Figure 1: V2V broadcast comm unications scenario p erform the allocation task in a sequential manner based on the constrainedness of each cluster. T o illustrate the gist of the problem, in Fig. 1 we show tw o partially ov erlapping clusters where a conflict b etw een vehicles 𝑉 8 and 𝑉 10 is generated as the allotted subchannels are in the same subframe. 2 PR OPOSED APPRO ACH The ob jective is to find an assignment of sub channels to v ehicles such that the system capacit y is maximized while re- sp ecting the constraints that preven t conflicts. This allo cation problem is form ulated as max c 𝑇 x (1a) sub ject to  I 𝑁 × 𝑁 ⊗ 1 1 × 𝐿 U 𝐽 × 𝑁 ⊗ I 𝐿 × 𝐿  ⊗ 1 1 × 𝐾 x = 1 (1b) where c ∈ R 𝑀 , x ∈ B 𝑀 with 𝑀 = 𝑁 𝐿𝐾 . The amount of clusters is 𝐽 (eac h consisting of 𝑁 𝑗 v ehicles, 𝑗 = 1 , . . . , 𝐽 ); the total n umber of vehicles is 𝑁 ; 𝐿 is the n umber of time subframes and 𝐾 represen ts the n umber of sub channels p er subframe. U is the membership matrix which depicts the asso ciation of vehicles to the different clusters. Instead of approac hing (1) optimally through exhaustive search, we can solv e the allo cation in a hierarchical and sequential man- ner for each cluster 𝒱 ( 𝑗 ) while retaining the solutions from previous allo cations. Thus, we solve several subproblems in order of constrainedness, which will lead to a sub optimal solution. Each subproblem can b e mo deled as a weigh ted bipartite graph 𝐺 ( 𝑗 ) =  𝒱 ( 𝑗 ) , ℛ , ℰ ( 𝑗 )  as shown in Fig. 2, where vehicles and subchannels are modeled as vertices. The sub c hannels 𝑟 𝑘 in ℛ ha ve been assembled into 𝐿 disjoin t 𝑣 ( 𝑗 ) 1 𝑣 ( 𝑗 ) 2 . . . 𝑣 ( 𝑗 ) 𝑁 𝑗 𝑟 1 𝑟 2 ... 𝑟 𝐾 𝑟 𝐾 + 1 𝑟 𝐾 + 2 ... 𝑟 2 𝐾 . . . 𝑟 𝐾 𝐿 − 1 + 1 𝑟 𝐾 𝐿 − 1 + 2 ... 𝑟 𝐾 𝐿 macro- macro- macro- v ertex ℛ 1 v ertex ℛ 2 v ertex ℛ 𝐿 𝒱 ( 𝑗 ) V ehicles ℛ Sub channels Figure 2: Constrained weigh ted bipartite graph groups {ℛ 𝑙 } 𝐿 𝑙 = 1 called macro-vertices in order to manage the time-domain constrain ts (vertex aggregation). The edge w eight 𝑐 ( 𝑗 ) 𝑖𝑘 = 𝐵 log 2  1 + SINR ( 𝑗 ) 𝑖𝑘  represen ts the ac hiev able capacit y of vehicle 𝑣 ( 𝑗 ) 𝑖 ∈ 𝒱 ( 𝑗 ) in sub channel 𝑟 𝑘 ∈ ℛ . Thus, the following formulation maximizes the capacity p er cluster max c 𝑇 𝑗 x 𝑗 (2a) sub ject to  I 𝑁 𝑗 × 𝑁 𝑗 ⊗ 1 1 × 𝐿 1 1 × 𝑁 𝑗 ⊗ I 𝐿 × 𝐿  ⊗ 1 1 × 𝐾 x 𝑗 = 1 . (2b) F or completeness, w e assume that 𝑁 1 = · · · = 𝑁 𝑗 = 𝐿 , th us x 𝑗 = [ 𝑥 ( 𝑗 ) 1 , 1 , . . . , 𝑥 ( 𝑗 ) 𝐿,𝐾 𝐿 ] 𝑇 and c 𝑗 = [ 𝑐 ( 𝑗 ) 1 , 1 , . . . , 𝑐 ( 𝑗 ) 𝐿,𝐾 𝐿 ] 𝑇 . Also, w e claim without a pro of due to space limitations, that (2) can b e recast as (3) without affecting optimality . max d 𝑇 𝑗 y 𝑗 sub ject to  I 𝐿 × 𝐿 ⊗ 1 1 × 𝐿 1 1 × 𝐿 ⊗ I 𝐿 × 𝐿  y 𝑗 = 1 . (3) where d 𝑗 = lim 𝛽 →∞ 1 𝛽 ∘ log { I 𝑀 × 𝑀 ⊗ 1 1 × 𝐾 e ∘ 𝛽 c 𝑗 } with ∘ log {·} and e ∘{·} represen ting the element-wise natural logarithm and Hadamard exp onential [ 3 ], respectively . Note that y 𝑗 is of low er dimensionality than x 𝑗 and therefore it can b e solv ed with less complexity . 3 SIMULA TIONS W e consider a 10 MHz channel whic h is divided into sub- c hannels, eac h with dimensions of 1ms in time and 1.26 MHz in frequency [ 4 ]. In our model, we assume a CAM message rate of 10 Hz. In Fig. 3, w e compare 4 different algorithms in base of the av erage o ver 1000 sim ulations. W e considered b oth ov erlapping and non-ov erlapping clusters, each with at most 𝑁 = 100 vehicles. Through sim ulations, w e sho w that our scheme can attain near-optimalit y as its p erformance is similar to exhaustive searc h. Considering the system aver- age r ate criterion, our approach has an adv antage ov er the Highest- Rate V ehicle System A verage Rate W orst-Rate V ehicle Rate Standard Deviation 0 5 10 8 . 97 8 . 24 7 . 14 0 . 48 8 . 97 8 . 11 6 . 94 0 . 55 8 . 97 7 . 88 5 . 35 0 . 65 8 . 17 4 . 55 1 . 43 1 . 21 Rate [Mbits / s / sub channel] Exhaustive Search Proposed Algorithm Greedy Algoritm Random Algorithm Figure 3: V ehicles data rate 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 Number of vehicles ( 𝑁 ) Rate [Mbits / s / sub channel] Exhaustive Search Proposed Algorithm Greedy Algoritm Random Algorithm Figure 4: W orst-rate v ehicle greedy algorithm. Also, when considering the worst-r ate vehi- cle , our prop osal excels as it is capable of providing a higher lev el of fairness. In all cases, the random allocation algo- rithm is outp erformed by the other approaches. Fig. 4 shows the achiev able rate for the worst-r ate vehicle . W e observe that when the v ehicle densit y per cluster is low, the greedy approac h attains near optimal solutions as there are more sub c hannels than v ehicles to serve. How ever, as the densit y increases, esp ecially near the o verload state, its p erformance dramatically drops. Nev ertheless, our approach can pro vide a fair allocation ev en in high vehicle density scenarios. 4 CONCLUSION W e hav e presented a nov el hierarchical sub channel allo cation sc heme for V2V sidelink communications with intra-cluster conflict constraints. The approac h is capable of attaining near-optimalit y at less complexity than exhaustiv e search. REFERENCES [1] Intelligen t transp ort systems (its); stdma recommended parameters and settings for co op erative its; access lay er part. T echnical Rep ort ETSI TR 102 861, ETSI, January 2012. [2] James Munkres. Algorithms for the assignment and transp ortation problems. SIAM J Appl Math , 5(1):32–38, March 1957. [3] F umio Hiai. Monotonicity for entrywise functions of matrices. Journal of Line ar Algebr a and its A pplic ations , 431(8):1125–1146, September 2009. [4] T echnical sp ecification group radio access netw ork; evolved uni- versal terrestrial radio access (e-utra); physical lay er pro cedures; (release 14) v14.2.0. T echnical Report 3GPP TS 36.213, 3GPP , March 2017.