In this paper we present a graph-based resource allocation scheme for
sidelink broadcast V2V communications. Harnessing available information on
geographical position of vehicles and spectrum resources utilization, eNodeBs
are capable of allotting the same set of sidelink resources to different
vehicles distributed among several communications clusters. Within a
communications cluster, it is crucial to prevent time-domain allocation
conflicts since vehicles cannot transmit and receive simultaneously, i.e., they
must transmit in orthogonal time resources. In this research, we present a
solution based on a bipartite graph, where vehicles and spectrum resources are
represented by vertices whereas the edges represent the achievable rate in each
resource based on the SINR that each vehicle perceives. The aforementioned time
orthogonality constraint can be approached by aggregating conflicting vertices
into macro-vertices which, in addition, reduces the search complexity. We show
mathematically and through simulations that the proposed approach yields an
optimal solution. In addition, we provide simulations showing that the proposed
method outperforms other competing approaches, specially in scenarios with high
vehicular density.Comment: arXiv admin note: substantial text overlap with arXiv:1805.0655

Abanto-Leon, Luis F.

de Groot, Sonia Heemstra

Koppelaar, Arie

English

arXiv

In this paper we present a graph-based resource allocation scheme for sidelink broadcast V2V communications. Harnessing available information on geographical position of vehicles and spectrum resources utilization, eNodeBs are capable of allotting the same set of sidelink resources to different vehicles distributed among several communications clusters. Within a communications cluster, it is crucial to prevent time-domain allocation conflicts since vehicles cannot transmit and receive simultaneously, i.e., they must transmit in orthogonal time resources. In this research, we present a solution based on a bipartite graph, where vehicles and spectrum resources are represented by vertices whereas the edges represent the achievable rate in each resource based on the SINR that each vehicle perceives. The a forementioned time orthogonality constraint can be approached by aggregating conflicting vertices into macro-vertices which, in addition, reduces the search complexity. We show mathematically and through simulations that the proposed approach yields an optimal solution. In addition, we provide simulations showing that the proposed method outperforms other competing approaches, specially in scenarios with high vehicular density.</p

De Groot, Sonia Heemstra

Pure OAI Repository

 PosterCitation for published version (APA):Abanto-Leon, L. F., Koppelaar, A., & De Groot, S. H. (2017). Poster: Resource allocation with conflict resolutionfor vehicular sidelink broadcast communications. In MobiCom 2017 - Proceedings of the 23rd AnnualInternational Conference on Mobile Computing and Networking (Vol. Part F131210, pp. 525-527). Associationfor Computing Machinery, Inc. https://doi.org/0.1145/3117811.3131260Document license:CC BYDOI:0.1145/3117811.3131260Document status and date:Published: 04/10/2017Document Version:Accepted manuscript including changes made at the peer-review stagePlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 04. Oct. 2023Poster: Resource Allocation with Conflict Resolution forVehicular Sidelink Broadcast CommunicationsLuis F. Abanto-LeonEindhoven University ofTechnologyEindhoven, Netherlandsl.f.abanto@tue.nlArie KoppelaarNXP SemiconductorsEindhoven, Netherlandsarie.koppelaar@nxp.comSonia Heemstra de GrootEindhoven University ofTechnologyEindhoven, Netherlandssheemstradegroot@tue.nlABSTRACTIn this paper we present a graph-based resource allocationscheme for sidelink broadcast V2V communications. Harness-ing available information on geographical position of vehiclesand spectrum resources utilization, eNodeBs are capable ofallotting the same set of sidelink resources to different vehiclesdistributed among several communications clusters. Within acommunications cluster, it is crucial to prevent time-domainallocation conflicts since vehicles cannot transmit and receivesimultaneously, i.e., they must transmit in orthogonal timeresources. In this research, we present a solution based ona bipartite graph, where vehicles and spectrum resourcesare represented by vertices whereas the edges represent theachievable rate in each resource based on the SINR thateach vehicle perceives. The aforementioned time orthogonal-ity constraint can be approached by aggregating conflictingvertices into macro-vertices which, in addition, reduces thesearch complexity. We show mathematically and throughsimulations that the proposed approach yields an optimalsolution. In addition, we provide simulations showing that theproposed method outperforms other competing approaches,specially in scenarios with high vehicular density.KEYWORDSresource allocation; vehicular communications; sidelink1 INTRODUCTIONVehicle–to–vehicle (V2V) communications is one of the noveluse cases in 5G and has attracted much interest, specially forsafety applications, since connected vehicles may have thepotential to prevent accidents [1].In V2V Mode 3, eNodeBs assign resources to vehicles forthem to periodically broadcast CAM messages [2]. Oncethe allocation has been accomplished, data is disseminateddirectly between vehicles. Conversely, in conventional cel-lular communications, data traverse the eNodeB via up-link/downlink before it can be forwarded. Thus, since dataPermission to make digital or hard copies of part or all of this workfor personal or classroom use is granted without fee provided thatcopies are not made or distributed for profit or commercial advantageand that copies bear this notice and the full citation on the first page.Copyrights for third-party components of this work must be honored.For all other uses, contact the owner/author(s).MobiCom ’17, October 16–20, 2017, Snowbird, UT, USA© 2017 Copyright held by the owner/author(s).ACM ISBN 978-1-4503-4916-1/17/10.https://doi.org/10.1145/3117811.3131260Figure 1: V2V Broadcast Communications via Sidelinktraffic is controlled by the eNodeB, users can be allocated inthe same time resource but different frequency subchannels.Nevertheless, in V2V Mode 3 the flow of data is not con-trolled, thus it is fundamental to guarantee that vehicles willtransmit in orthogonal time resources to prevent conflicts.On the other hand, assignment problems can be representedas weighted bipartite graphs, where the objective is to finda maximal matching. This classical problem is called hereinunconstrained weighted graph matching. Resource allocationfor V2V communications has a time orthogonality constraintwhich cannot be handled by the mentioned method. We havetherefore envisaged a solution called constrained weightedgraph matching, which incorporates the mentioned constraint.The objective of this paper is two-fold:(︀𝑖)︀prove that anoptimal solution for the constrained weighted graph matchingproblem exists and(︀𝑖𝑖)︀discuss the suitability of such an ap-proach for avoiding resource allocation conflicts in broadcastvehicular communications.2 MOTIVATION AND CONTRIBUTIONSOur motivation is to develop an approach capable of(︀𝑎)︀preventing allocation conflicts—by enforcing constraints—and(︀𝑏)︀maximizing the sum-rate capacity of the system. Forinstance, in one of the clusters of Fig. 1, a resource conflictcan be observed between vehicles 𝑉8 and 𝑉10 since they havebeen allotted resources in the same time subframe.The contributions of our work are summarized:∙ Kuhn-Munkres [3] is a computationally efficient methodfor solving matching problems in bipartite graphs. How-ever, due to additional time orthogonality constraints,the resultant problem is not directly approachable by it.In our solution, vertices conflicting among each other𝑣1𝑣2...𝑣𝑁𝑟1𝑟2...𝑟𝐾𝑟𝐾+1𝑟𝐾+2...𝑟2𝐾...𝑟𝐾𝑁−1+1𝑟𝐾𝑁−1+2...𝑟𝐾𝑁macro-macro-macro-vertexℛ1vertexℛ2vertexℛ𝑁𝒱VehiclesℛResourcesFigure 2: Constrained Weighted Bipartite Graphhave been aggregated into macro-vertices yielding aresultant graph which is solvable by Kuhn-Munkres.∙ Vertex aggregation cuts down the number of effectivevertices and therefore narrows the amount of potentialsolutions, without affecting optimality.∙ We show through simulations that our approach is ca-pable of providing fairness among all vehicles, especiallyin scenarios with high vehicle density.3 PROPOSED APPROACHLet 𝐺 =(︀𝒱, ℛ, ℰ)︀be a bipartite graph such that |ℛ| =𝐾|𝒱| = 𝐾𝑁 , as depicted in Fig. 2. In this scheme, the 𝐾𝑁vertices in ℛ are clustered into 𝑁 disjoint groups {ℛ𝛼}𝑁𝛼=1called macro-vertices, such that ℛ = ∪𝑁𝛼=1ℛ𝛼, ℛ𝛼 ∩ ℛ𝛼′ = ∅,∀𝛼 , 𝛼′. Each macro-vertex ℛ𝛼 is an aggregation of 𝐾 ver-tices, i.e., |ℛ𝛼| = 𝐾. The target is to find a vertex–to–vertex(or vehicle–to–resource) matching with maximum sum ofweights such that no two vertices in 𝒱 are matched to anytwo vertices in the same macro-vertex ℛ𝛼. This conditionmust be satisfied as it depicts the time orthogonality require-ment that prevents allocation conflicts. We will show thatthe optimal solution is tantamount to finding the maximumvertex–to–macro-vertex matching.In Fig. 2, vertices 𝑣𝑖 represent the vehicles in cluster 𝒱whereas vertices 𝑟𝑗 represent the allotable resources managedby the eNodeB. 𝐾 represents the number of resources persubframe. 𝑁 represents the amount of available subframesin which the resource allocation task can be accomplished.The problem is formulated by (1)max c𝑇 xsubject to[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⏟                         ⏞                         A⊗11×𝐾 x = 1 (1)where ⊗ represents the tensor product operator, c ∈ R𝑀 , x ∈B𝑀 with 𝑀 = 𝐾𝑁2. The solution and weight vectors are x =[︀𝑥1,1, . . . , 𝑥𝑁,𝑁]︀𝑇 and c = [︀𝑐1,1, . . . , 𝑐𝑁,𝑁 ]︀𝑇 , respectively.Also, 𝑐𝑖𝑗 = 𝐵 log2(︀1+SINR𝑖𝑗)︀. Because x exists on the binarysubspace, the cost function can be equivalently expressedas c𝑇 x = x𝑇 𝑑𝑖𝑎𝑔(︀c)︀x without affecting optimality. Also,we can add zero-valued terms 𝑐𝑖𝑗𝑥𝑖𝑗𝑥𝑖𝑘 (with 𝑟𝑗 , 𝑟𝑘 ∈ ℛ𝛼)to the cost function without affecting the solution. A moregeneralized expression is given by x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×𝐾 −I𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x = 0.Now, the augmented cost function can be recast asc𝑇 x= x𝑇 𝑑𝑖𝑎𝑔(︀c)︀x + x𝑇(︀I𝑀×𝑀 ⊗[︀1 − I]︀𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 I𝑀×𝑀 ⊗ 1𝐾×111×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×1)︀⏟                           ⏞                           y𝑇(︀I𝑀×𝑀 ⊗ 11×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x⏟                                      ⏞                                      d(2)From (2), we obtain that d =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀xand y =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀x. Similarly, we obtain that x =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀†y. In the following, we use the previousrelations to simplify the constraint in (1),(︂[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⊗ 11×𝐾)︂ (︀I𝑀×𝑀 ⊗ 1†1×𝐾)︀y = 1=(︂[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂I𝑀×𝑀)︂⊗(︀11×𝐾1†1×𝐾)︀⏟                ⏞                1y = 1=[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂y = 1(3)Thus, the problem in (3) can be recast as (4)max d𝑇 ysubject to[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⏟                         ⏞                         Ay = 1. (4)Fig.3 shows the transformation process from (1) to (4). Wenotice that d depends on x which is not desirable. In orderto eliminate this dependency, we state without a proof—dueto space limitations—thatd = lim𝛽→∞1𝛽∘log{I𝑀×𝑀 ⊗ 11×𝐾e∘𝛽c} (5)where∘log{·} and e∘{·} are the element-wise natural logarithmand Hadamard exponential [4], respectively.I𝑀×𝑀 ⊗ 11×𝐾I𝑀×𝑀 ⊗ 11×𝐾×𝑑𝑖𝑎𝑔·xcydFigure 3: Transformation Process4 SIMULATIONSWe consider a 10 MHz channel which is divided into severalresource chunks, each with an extent of 1ms in time and1.26 MHz in frequency. To wit, 1.26 MHz corresponds to 7resource blocks (RBs), each consisting of data (5RBs) andcontrol information (2RBs) [5]. In our model, we consider thatclusters are independent from each other. Thus, resourcesused in a certain cluster can be repurposed by vehicles inother clusters. Since we consider a message rate of 10 Hz,the resource allocation task is carried out every 0.1 s andtherefore the maximum number of allotable subframes is 100.We also assume that the sidelink channel conditions of eachvehicle are reported to the eNodeB via uplink. The resourceallocation is broadcasted to vehicles via downlink. Notice thatsidelink resources are exclusively used for communications.In Fig. 4, we compare 4 different algorithms in base of theaverage over 1000 simulations. We have considered 𝑁 = 100vehicles in each cluster. Through simulations, we show thatour scheme is optimal since it achieves the same performanceas exhaustive search. The greedy algorithm performs as goodas the proposed approach when we examine the highest-ratevehicle only. This is logical as the premise of the greedy algo-rithm is to assign the best resources on first-come first-servedbasis. Considering the system average rate, our proposedapproach has an advantage over the greedy algorithm. Also,when considering the worst-rate vehicle, our proposal excelsas it is capable of providing a higher level of fairness. In allcases, the random allocation algorithm is outperformed bythe other approaches. Fig. 5 shows the achievable rate forHighest-Rate VehicleWorst-RateVehicleSystemAverageRateSystem RateStandardDeviation02468108.977.128.221.168.977.128.221.168.915.858.021.257.631.764.521.67Rate[Mbits/s/resource]Exhaustive Search Graph-based AlgorithmGreedy Algoritm Random AlgorithmFigure 4: Vehicles Data Ratethe worst-rate vehicle. The proposed graph-based algorithmattains the same performance as the exhaustive search. Weobserve that when the vehicle density per cluster is low, thegreedy approach attains near optimal solutions as there arefar more resources than vehicles to serve. However, as thedensity increases, especially near the overload state, its per-formance drops. The random allocation algorithm performsworse than the other approaches.20 40 60 80 1002345678Number of VehiclesRate[Mbits/s/resource]Graph-based AlgorithmExhaustive SearchGreedy AlgoritmRandom AlgorithmFigure 5: Worst-rate Vehicle2 4 6 8 100.10.40.71Ratex [bits / s / Hz]Pr(︀ Rate<Rate x)︀ Graph-based AlgorithmExhaustive SearchGreedy AlgoritmRandom AlgorithmExhaustive Searchw/o constraintsFigure 6: Cumulative Distribution FunctionFig. 6 shows the CDF of the achievable rates. We observethat the proposed approach outperforms the other two ap-proaches. For the sake of comparison, we have included theresults of the unconstrained system, which does not takesinto account conflict avoidance constraints. This is of coursenot desirable but it serves as a comparison bound.5 CONCLUSIONWe have presented a novel resource allocation algorithm forV2V communications considering conflict constraints. Wewere able to transform the original problem into a simplifiedform. In our future work, we will consider (𝑖) power controland (𝑖𝑖) the assumption that a subset of vehicles may belongto more than one cluster simultaneously.REFERENCES[1] Crash data analyses for vehicle-to-infrastructure communicationsfor safety applications. Technical Report FHWA-HRT-11-040, U.S.Department of Transportation, November 2012.[2] Intelligent transport systems (its); stdma recommended parametersand settings for cooperative its; access layer part. Technical ReportETSI TR 102 861, ETSI, January 2012.[3] J. Munkres. Algorithms for the assignment and transportationproblems. SIAM J Appl Math, 5(1):32–38, March 1957.[4] Fumio Hiai. Monotonicity for entrywise functions of matrices.Journal of Linear Algebra and its Applications, 431(8):1125–1146,September 2009.[5] Technical specification group radio access network; evolved uni-versal terrestrial radio access (e-utra); physical layer procedures;(release 14) v14.2.0. Technical Report 3GPP TS 36.213, 3GPP,March 2017.

Poster:Resource allocation with conflict resolution for vehicular sidelink broadcast communications

 PosterCitation for published version (APA):Abanto-Leon, L. F., Koppelaar, A., & De Groot, S. H. (2017). Poster: Resource allocation with conflict resolutionfor vehicular sidelink broadcast communications. In MobiCom 2017 - Proceedings of the 23rd AnnualInternational Conference on Mobile Computing and Networking (Vol. Part F131210, pp. 525-527). Associationfor Computing Machinery, Inc. https://doi.org/0.1145/3117811.3131260Document license:CC BYDOI:0.1145/3117811.3131260Document status and date:Published: 04/10/2017Document Version:Accepted manuscript including changes made at the peer-review stagePlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 05. Oct. 2023Poster: Resource Allocation with Conflict Resolution forVehicular Sidelink Broadcast CommunicationsLuis F. Abanto-LeonEindhoven University ofTechnologyEindhoven, Netherlandsl.f.abanto@tue.nlArie KoppelaarNXP SemiconductorsEindhoven, Netherlandsarie.koppelaar@nxp.comSonia Heemstra de GrootEindhoven University ofTechnologyEindhoven, Netherlandssheemstradegroot@tue.nlABSTRACTIn this paper we present a graph-based resource allocationscheme for sidelink broadcast V2V communications. Harness-ing available information on geographical position of vehiclesand spectrum resources utilization, eNodeBs are capable ofallotting the same set of sidelink resources to different vehiclesdistributed among several communications clusters. Within acommunications cluster, it is crucial to prevent time-domainallocation conflicts since vehicles cannot transmit and receivesimultaneously, i.e., they must transmit in orthogonal timeresources. In this research, we present a solution based ona bipartite graph, where vehicles and spectrum resourcesare represented by vertices whereas the edges represent theachievable rate in each resource based on the SINR thateach vehicle perceives. The aforementioned time orthogonal-ity constraint can be approached by aggregating conflictingvertices into macro-vertices which, in addition, reduces thesearch complexity. We show mathematically and throughsimulations that the proposed approach yields an optimalsolution. In addition, we provide simulations showing that theproposed method outperforms other competing approaches,specially in scenarios with high vehicular density.KEYWORDSresource allocation; vehicular communications; sidelink1 INTRODUCTIONVehicle–to–vehicle (V2V) communications is one of the noveluse cases in 5G and has attracted much interest, specially forsafety applications, since connected vehicles may have thepotential to prevent accidents [1].In V2V Mode 3, eNodeBs assign resources to vehicles forthem to periodically broadcast CAM messages [2]. Oncethe allocation has been accomplished, data is disseminateddirectly between vehicles. Conversely, in conventional cel-lular communications, data traverse the eNodeB via up-link/downlink before it can be forwarded. Thus, since dataPermission to make digital or hard copies of part or all of this workfor personal or classroom use is granted without fee provided thatcopies are not made or distributed for profit or commercial advantageand that copies bear this notice and the full citation on the first page.Copyrights for third-party components of this work must be honored.For all other uses, contact the owner/author(s).MobiCom ’17, October 16–20, 2017, Snowbird, UT, USA© 2017 Copyright held by the owner/author(s).ACM ISBN 978-1-4503-4916-1/17/10.https://doi.org/10.1145/3117811.3131260Figure 1: V2V Broadcast Communications via Sidelinktraffic is controlled by the eNodeB, users can be allocated inthe same time resource but different frequency subchannels.Nevertheless, in V2V Mode 3 the flow of data is not con-trolled, thus it is fundamental to guarantee that vehicles willtransmit in orthogonal time resources to prevent conflicts.On the other hand, assignment problems can be representedas weighted bipartite graphs, where the objective is to finda maximal matching. This classical problem is called hereinunconstrained weighted graph matching. Resource allocationfor V2V communications has a time orthogonality constraintwhich cannot be handled by the mentioned method. We havetherefore envisaged a solution called constrained weightedgraph matching, which incorporates the mentioned constraint.The objective of this paper is two-fold:(︀𝑖)︀prove that anoptimal solution for the constrained weighted graph matchingproblem exists and(︀𝑖𝑖)︀discuss the suitability of such an ap-proach for avoiding resource allocation conflicts in broadcastvehicular communications.2 MOTIVATION AND CONTRIBUTIONSOur motivation is to develop an approach capable of(︀𝑎)︀preventing allocation conflicts—by enforcing constraints—and(︀𝑏)︀maximizing the sum-rate capacity of the system. Forinstance, in one of the clusters of Fig. 1, a resource conflictcan be observed between vehicles 𝑉8 and 𝑉10 since they havebeen allotted resources in the same time subframe.The contributions of our work are summarized:∙ Kuhn-Munkres [3] is a computationally efficient methodfor solving matching problems in bipartite graphs. How-ever, due to additional time orthogonality constraints,the resultant problem is not directly approachable by it.In our solution, vertices conflicting among each other𝑣1𝑣2...𝑣𝑁𝑟1𝑟2...𝑟𝐾𝑟𝐾+1𝑟𝐾+2...𝑟2𝐾...𝑟𝐾𝑁−1+1𝑟𝐾𝑁−1+2...𝑟𝐾𝑁macro-macro-macro-vertexℛ1vertexℛ2vertexℛ𝑁𝒱VehiclesℛResourcesFigure 2: Constrained Weighted Bipartite Graphhave been aggregated into macro-vertices yielding aresultant graph which is solvable by Kuhn-Munkres.∙ Vertex aggregation cuts down the number of effectivevertices and therefore narrows the amount of potentialsolutions, without affecting optimality.∙ We show through simulations that our approach is ca-pable of providing fairness among all vehicles, especiallyin scenarios with high vehicle density.3 PROPOSED APPROACHLet 𝐺 =(︀𝒱, ℛ, ℰ)︀be a bipartite graph such that |ℛ| =𝐾|𝒱| = 𝐾𝑁 , as depicted in Fig. 2. In this scheme, the 𝐾𝑁vertices in ℛ are clustered into 𝑁 disjoint groups {ℛ𝛼}𝑁𝛼=1called macro-vertices, such that ℛ = ∪𝑁𝛼=1ℛ𝛼, ℛ𝛼 ∩ ℛ𝛼′ = ∅,∀𝛼 , 𝛼′. Each macro-vertex ℛ𝛼 is an aggregation of 𝐾 ver-tices, i.e., |ℛ𝛼| = 𝐾. The target is to find a vertex–to–vertex(or vehicle–to–resource) matching with maximum sum ofweights such that no two vertices in 𝒱 are matched to anytwo vertices in the same macro-vertex ℛ𝛼. This conditionmust be satisfied as it depicts the time orthogonality require-ment that prevents allocation conflicts. We will show thatthe optimal solution is tantamount to finding the maximumvertex–to–macro-vertex matching.In Fig. 2, vertices 𝑣𝑖 represent the vehicles in cluster 𝒱whereas vertices 𝑟𝑗 represent the allotable resources managedby the eNodeB. 𝐾 represents the number of resources persubframe. 𝑁 represents the amount of available subframesin which the resource allocation task can be accomplished.The problem is formulated by (1)max c𝑇 xsubject to[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⏟                         ⏞                         A⊗11×𝐾 x = 1 (1)where ⊗ represents the tensor product operator, c ∈ R𝑀 , x ∈B𝑀 with 𝑀 = 𝐾𝑁2. The solution and weight vectors are x =[︀𝑥1,1, . . . , 𝑥𝑁,𝑁]︀𝑇 and c = [︀𝑐1,1, . . . , 𝑐𝑁,𝑁 ]︀𝑇 , respectively.Also, 𝑐𝑖𝑗 = 𝐵 log2(︀1+SINR𝑖𝑗)︀. Because x exists on the binarysubspace, the cost function can be equivalently expressedas c𝑇 x = x𝑇 𝑑𝑖𝑎𝑔(︀c)︀x without affecting optimality. Also,we can add zero-valued terms 𝑐𝑖𝑗𝑥𝑖𝑗𝑥𝑖𝑘 (with 𝑟𝑗 , 𝑟𝑘 ∈ ℛ𝛼)to the cost function without affecting the solution. A moregeneralized expression is given by x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×𝐾 −I𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x = 0.Now, the augmented cost function can be recast asc𝑇 x= x𝑇 𝑑𝑖𝑎𝑔(︀c)︀x + x𝑇(︀I𝑀×𝑀 ⊗[︀1 − I]︀𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 I𝑀×𝑀 ⊗ 1𝐾×111×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x= x𝑇(︀I𝑀×𝑀 ⊗ 1𝐾×1)︀⏟                           ⏞                           y𝑇(︀I𝑀×𝑀 ⊗ 11×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀x⏟                                      ⏞                                      d(2)From (2), we obtain that d =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀𝑑𝑖𝑎𝑔(︀c)︀xand y =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀x. Similarly, we obtain that x =(︀I𝑀×𝑀 ⊗ 11×𝐾)︀†y. In the following, we use the previousrelations to simplify the constraint in (1),(︂[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⊗ 11×𝐾)︂ (︀I𝑀×𝑀 ⊗ 1†1×𝐾)︀y = 1=(︂[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂I𝑀×𝑀)︂⊗(︀11×𝐾1†1×𝐾)︀⏟                ⏞                1y = 1=[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂y = 1(3)Thus, the problem in (3) can be recast as (4)max d𝑇 ysubject to[︂I𝑁×𝑁 ⊗ 11×𝑁11×𝑁 ⊗ I𝑁×𝑁]︂⏟                         ⏞                         Ay = 1. (4)Fig.3 shows the transformation process from (1) to (4). Wenotice that d depends on x which is not desirable. In orderto eliminate this dependency, we state without a proof—dueto space limitations—thatd = lim𝛽→∞1𝛽∘log{I𝑀×𝑀 ⊗ 11×𝐾e∘𝛽c} (5)where∘log{·} and e∘{·} are the element-wise natural logarithmand Hadamard exponential [4], respectively.I𝑀×𝑀 ⊗ 11×𝐾I𝑀×𝑀 ⊗ 11×𝐾×𝑑𝑖𝑎𝑔·xcydFigure 3: Transformation Process4 SIMULATIONSWe consider a 10 MHz channel which is divided into severalresource chunks, each with an extent of 1ms in time and1.26 MHz in frequency. To wit, 1.26 MHz corresponds to 7resource blocks (RBs), each consisting of data (5RBs) andcontrol information (2RBs) [5]. In our model, we consider thatclusters are independent from each other. Thus, resourcesused in a certain cluster can be repurposed by vehicles inother clusters. Since we consider a message rate of 10 Hz,the resource allocation task is carried out every 0.1 s andtherefore the maximum number of allotable subframes is 100.We also assume that the sidelink channel conditions of eachvehicle are reported to the eNodeB via uplink. The resourceallocation is broadcasted to vehicles via downlink. Notice thatsidelink resources are exclusively used for communications.In Fig. 4, we compare 4 different algorithms in base of theaverage over 1000 simulations. We have considered 𝑁 = 100vehicles in each cluster. Through simulations, we show thatour scheme is optimal since it achieves the same performanceas exhaustive search. The greedy algorithm performs as goodas the proposed approach when we examine the highest-ratevehicle only. This is logical as the premise of the greedy algo-rithm is to assign the best resources on first-come first-servedbasis. Considering the system average rate, our proposedapproach has an advantage over the greedy algorithm. Also,when considering the worst-rate vehicle, our proposal excelsas it is capable of providing a higher level of fairness. In allcases, the random allocation algorithm is outperformed bythe other approaches. Fig. 5 shows the achievable rate forHighest-Rate VehicleWorst-RateVehicleSystemAverageRateSystem RateStandardDeviation02468108.977.128.221.168.977.128.221.168.915.858.021.257.631.764.521.67Rate[Mbits/s/resource]Exhaustive Search Graph-based AlgorithmGreedy Algoritm Random AlgorithmFigure 4: Vehicles Data Ratethe worst-rate vehicle. The proposed graph-based algorithmattains the same performance as the exhaustive search. Weobserve that when the vehicle density per cluster is low, thegreedy approach attains near optimal solutions as there arefar more resources than vehicles to serve. However, as thedensity increases, especially near the overload state, its per-formance drops. The random allocation algorithm performsworse than the other approaches.20 40 60 80 1002345678Number of VehiclesRate[Mbits/s/resource]Graph-based AlgorithmExhaustive SearchGreedy AlgoritmRandom AlgorithmFigure 5: Worst-rate Vehicle2 4 6 8 100.10.40.71Ratex [bits / s / Hz]Pr(︀ Rate<Rate x)︀ Graph-based AlgorithmExhaustive SearchGreedy AlgoritmRandom AlgorithmExhaustive Searchw/o constraintsFigure 6: Cumulative Distribution FunctionFig. 6 shows the CDF of the achievable rates. We observethat the proposed approach outperforms the other two ap-proaches. For the sake of comparison, we have included theresults of the unconstrained system, which does not takesinto account conflict avoidance constraints. This is of coursenot desirable but it serves as a comparison bound.5 CONCLUSIONWe have presented a novel resource allocation algorithm forV2V communications considering conflict constraints. Wewere able to transform the original problem into a simplifiedform. In our future work, we will consider (𝑖) power controland (𝑖𝑖) the assumption that a subset of vehicles may belongto more than one cluster simultaneously.REFERENCES[1] Crash data analyses for vehicle-to-infrastructure communicationsfor safety applications. Technical Report FHWA-HRT-11-040, U.S.Department of Transportation, November 2012.[2] Intelligent transport systems (its); stdma recommended parametersand settings for cooperative its; access layer part. Technical ReportETSI TR 102 861, ETSI, January 2012.[3] J. Munkres. Algorithms for the assignment and transportationproblems. SIAM J Appl Math, 5(1):32–38, March 1957.[4] Fumio Hiai. Monotonicity for entrywise functions of matrices.Journal of Linear Algebra and its Applications, 431(8):1125–1146,September 2009.[5] Technical specification group radio access network; evolved uni-versal terrestrial radio access (e-utra); physical layer procedures;(release 14) v14.2.0. Technical Report 3GPP TS 36.213, 3GPP,March 2017.

In this paper we present a graph-based resource allocation scheme for sidelink broadcast V2V communications. Harnessing available information on geographical position of vehicles and spectrum resources utilization, eNodeBs are capable of allotting the same set of sidelink resources to different vehicles distributed among several communications clusters. Within a communications cluster, it is crucial to prevent time-domain allocation conflicts since vehicles cannot transmit and receive simultaneously, i.e., they must transmit in orthogonal time resources. In this research, we present a solution based on a bipartite graph, where vehicles and spectrum resources are represented by vertices whereas the edges represent the achievable rate in each resource based on the SINR that each vehicle perceives. The a forementioned time orthogonality constraint can be approached by aggregating conflicting vertices into macro-vertices which, in addition, reduces the search complexity. We show mathematically and through simulations that the proposed approach yields an optimal solution. In addition, we provide simulations showing that the proposed method outperforms other competing approaches, specially in scenarios with high vehicular density

NARCIS 

Poster: Resource allocation with conflict resolution for vehicular sidelink broadcast communications

https://pure.tue.nl/ws/files/74178530/MOBICOM_ACM_2017.pdf

Poster: Resource Allocation with Conflict Resolution for Vehicular Sidelink Broadcast Communications

Abstract

Similar works

Full text

Available Versions

Pure OAI Repository

Pure OAI Repository

NARCIS