Network-Assisted Resource Allocation with Quality and Conflict Constraints for V2V Communications

1 Network-Assisted Resource Allocation with Quality and Conflict Constraints for V2V Communications Luis F . Abanto-Leon, Arie K oppelaar , Sonia Heemstra de Groot Abstract The 3rd Generation Partnership Project (3GPP) has recently established in Rel. 14 a network- assisted resource allocation scheme for vehicular broadcast communications. Such no vel paradigm is known as v ehicle–to–vehicle (V2V) mode-3 and consists in eNodeBs engaging only in the distribution of sidelink subchannels among vehicles in cov erage. Thereupon, without further intervention of the former , vehicles will broadcast their respecti ve signals directly to their counterparts. Because the allotment of subchannels takes place intermittently to reduce signaling, it must primarily be conflict-free in order not to jeopardize the reception of signals. W e hav e identified four piv otal types of allocation requirements that must be guaranteed: one quality of service (QoS) requirement and three conflict conditions which must be precluded in order to preserve reception reliability . The underlying problem is formulated as a maximization of the system sum-capacity with four types of constraints that must be enforced. In addition, we propose a three-stage suboptimal approach that is cast as multiple independent knapsack problems (MIKPs). W e compare the two approaches through simulations and sho w that the latter formulation can attain acceptable performance at lesser complexity . Index T erms subchannel allocation, broadcast vehicular communications, quality of service I . I N T RO D U C T I O N The 3rd Generation Partnership Project has recently proposed in Release 14 two new resource allocation concepts for vehicle–to–v ehicle (V2V) communications, namely V2V mode-3 and V2V mode-4 . The latter one, is intended for supporting scenarios wherein network coverage is not av ailable. Thus, vehicles will be required to sense the occupancy of subchannels and reserve a subset for their o wn transmission. Each vehicle reserves subchannels in a semi-persistent 2 manner while attempting not degrade the link conditions of their counterparts [1]. On the other hand, in V2V mode-3 eNodeBs only provide support in the apportionment of subchannels but do not intervene in traffic control as occurs with mainstream cellular communications. Thus, once subchannels hav e been distributed, v ehicles will broadcast their signals in turns over the designated resources until a ne w allocation is processed [2]. Because the assignment of subchannels does not take place frequently (e.g. once ev ery few hundred milliseconds or more) to reduce signaling information, it must be ( i ) conflict-free and ( ii ) provide suf ficient capacity to satisfy the differentiated quality of service (QoS) requirements for each v ehicle. In this work, we pro vide a formulation for the described subchannel allocation problem in V2V mode-3 . The objectiv e is to maximize the sum-capacity of the system—consisting of several vehicles distributed ov er a number of clusters—while enforcing the fulfillment of four types of requirements which are described in more detail in the following section. Moreover , we propose a simplified three-stage formulation of the primal problem in terms of multiple independent knapsack problems (MIKPs) [3]. In the initial stage, the clusters are hierarchically sorted based on their cardinality . In the second stage, ev ery vehicles from each cluster is matched with time- domain subframe. In the last stage, vehicles are apportioned specific subchannels from within the assigned subframe such that the QoS requirements are fulfilled. Across all the stages, subchannels are selected such that conflicts of an y type are pre vented. The remaining of the paper is organized as follo ws. In Section II, we enunciate the moti vation of the present work and briefly summarize our contributions. In Section III, the subchannel allocation problem for V2V mode-3 including four types of constraints is formulated. In Section IV , a simplified allocation approach based on MIKPs is described. Section V discusses simulation results and Section VI is dev oted to summarizing our concluding remarks. I I . M OT I V A T I O N A N D C O N T R I B U T I O N S Fig. 1 depicts an scenario with N = 11 vehicles grouped into 3 clusters. It can be ob- served that cluster 1 consists of vehicles { v 1 , v 2 , v 3 , v 4 , v 5 , v 6 } , cluster 2 consists of vehicles { v 5 , v 6 , v 7 , v 8 , v 9 } whereas cluster 3 is constituted by vehicles { v 10 , v 11 } . Moreov er , vehicles { v 5 , v 6 } lie at the intersection of cluster 1 and cluster 2 . Depending on the distribution of vehicles across the clusters, some subchannel assignments might be detrimental since interference could be originated due to subchannel repurposing and thus impinging on communication reliability . 3 Figure 1: V ehicular broadcast communications in V2V mode -3 W e hav e identified four types of conditions that are compulsory for QoS-aware conflict-free allocations in V2V broadcast communications [6]. • T ype I : Each vehicle has a differentiated QoS requirement. W e define QoS in terms of the channel capacity required by a vehicle to con vey the intended signal. For instance, in Fig. 1 vehicles v 8 and v 6 hav e been assigned four and two subchannels, respectiv ely . • T ype II : When two or more vehicles in the same cluster transmit concurrently , they cannot recei ve the signals of the others due to half-duplex PHY . This problem does not af fect other vehicles in the cluster , only those that engaged in simultaneous transmission. An example of this case is depicted by v 10 and v 11 , which hav e been assigned subchannels in the same subframe. • T ype III : In order to support scenarios with high v ehicular density and improv e the utilization of radio resources, the subchannels assigned to a vehicle should preferably be selected from within the same subframe. This problem is depicted by v ehicle v 3 whose allotted subchannels span two subframes. • T ype IV : V ehicles lying at the intersection of clusters may receiv e concurrent signals from other vehicles that are not aware of each other , similarly to the hidden node problem experi- enced in IEEE 802.11p [4]. Thus, signals from dif ferent v ehicles may overlap concurrently in 4 time and frequency; thus becoming undecodable to other vehicles. For example, if vehicles v 1 and v 9 transmit in the same subchannel, vehicles v 5 and v 6 may not be able to correctly decode the receiv ed signals. Considering the requirements abo ve described, we propose a formulation for the subchannel allocation problem in V2V mode-3 . Furthermore, we propose a simplified method consisting of three stages. In the first stage, the clusters 1 are sorted based on their cardinality , from the highest to the lowest. Thus, clusters with a higher number of vehicles will be processed first as these are more complicated to optimize. In the second stage, we perform a matching between vehicles and subframes in a random manner without explicitly allotting specific subchannels to vehicles. This prev ents T ype III conflicts as the subchannels (to be selected in the third stage) will be confined to a single subframe. In addition, all the vehicles that belong to the same cluster must be placed in dif ferent subframes to pre vent T ype II conflicts. In the third stage, a method for attaining the dif ferentiated QoS requirements of T ype I for each vehicle is formulated as multiple independent knapsack problems (MIKPs). Since the allocation of subchannels for the whole system is performed sequentially for each cluster at a time, subchannels that may cause vehicles at the intersection to undergo T ype IV conflicts can be remov ed from the apportionment process. Thus, all the four types of requirements can be fulfilled. W e show through simulations that the proposed approach based on MIKPs can attain acceptable performance when compared to the optimal solution. I I I . P RO B L E M F O R M U L A T I O N W e consider that downlink and uplink spectrum resources are av ailable for periodical signaling between vehicles and the eNodeB. In-cov erage vehicles will report via uplink information on the percei ved quality of subchannels. Based on such information, the eNodeB will assign subchannels to each vehicle. Moreov er, via do wnlink the eNodeB informs the vehicles of the designated subchannels for their use. For the system, we have considered a 10 MHz channel for exclusi ve sidelink broadcast communications between v ehicles. The channelization of spectrum resources into subchannels to serve in sidelink communications [5] is shown in Fig. 2. The number of subframes is denoted by L and each consists of K 1 The clusters are formed based on their similarity in position, speed and direction using an affinity Gaussian kernel as described in [8]. 5 Control Data 4 RBs 10 RBs 1 ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L (ms) Frequency (MHz) 1 ms 1 ms 1 ms r 1 r 2 r K r K +1 r K +2 r 2 K r K L B B B Figure 2: Sidelink subchannels for V2V communications subchannels of duration 1 ms and bandwidth B = 1 . 26 MHz such that K B ≤ 10 MHz. Thus, in each subframe, at most 7 subchannels can be supported. The reason for such granularity is that in safety applications, a single subchannel with the specified dimensions, i.e. 14 resource blocks (RBs) can suf ficiently bear a CAM message. Howe ver , for other types of applications, a larger amount of subchannels might be required. In Fig. 2, r k represents a sidelink subchannel and R l = { r ( l − 1) K +1 , . . . , r lK } is the set of subchannels contained in subframe l , for l = 1 , 2 , . . . , L . Thus, the whole set of subchannels in an allocation window of L ms is giv en by R = ∪ L l =1 R l = { r 1 , r 2 , . . . , r K L } . Also, the total number of vehicles distributed among J clusters in the system is denoted by N . Thus, if V ( j ) denotes a particular cluster j , then V = ∪ j V ( j ) = { v 1 , v 2 , . . . , v N } represents all the vehicles in the system. On the other hand, x ik is a boolean variable that indicates with 1 whether a vehicle v i ∈ V and subchannel r k ∈ R are matched or with 0 otherwise. Also, the achiev able capacity that vehicle v i can attain if it transmits in subchannel r k is represented by c ik = B log 2 (1 + SINR ik ) . Similarly , SINR ik is the signal–to–interference–plus–noise ratio (SINR) that vehicle v i percei ves in subchannel r k 2 . In the forthcoming subsections, the objectiv e function for the subchannel allocation problem is introduced. Then, the four types of assignment requirements are described in detail. A. Objective Function The aim is to maximize the sum-capacity of the system while satisfying the four types of allocation requirements. The objecti ve function is expressed as c T x where x and c are 2 In strict sense, c ik and SINR ik depict metrics between v ehicle v i and some vehicle v u with which v i experiences the weakest link quality . Thus, if the weakest link can be lev eraged, other vehicles receiving signals from v i may experience superior conditions. For the purpose of simplicity , the index u representing vehicle v u has been dropped. 6 vectors containing elements x ik and c ik for all the vehicles v i and subchannels r k , i.e. x = [ x 1 , 1 , . . . , x 1 ,K L , . . . , x N , 1 , . . . , x N ,K L ] T , c = [ c 1 , 1 , . . . , c 1 ,K L , . . . c N , 1 , . . . , c N ,K L ] T B. T ype I: P er-vehicle QoS r equirement For each vehicle v i the required capacity to transmit the intended signal is denoted by q i . Such demand is expressed by P K L k =1 c ik x ik = q i , for i = 1 , 2 , . . . , N . Since fulfillment of the exact requested q i may not be feasible, the condition can be slightly relaxed and cast as q i −  ≤ P K L k =1 c ik x ik ≤ q i +  . Thus, for all the N vehicles in the system, the set of constraints can be expressed as q N × 1 −  ≤ ( I N × N ⊗ 1 1 × K L )( c ◦ x ) ≤ q N × 1 +  (1) where q = [ q 1 , q 2 , . . . , q N ] T and  =  · ( 1 N × 1 ) , ∃  ≥ 0 . The symbols ⊗ and ◦ represent the Kronecker and Hadamard product, respecti vely . C. T ype II: Intra-cluster subframe allocation conflicts When two or more intra-cluster vehicles transmit in subchannels that belong to the same subframe, they will not able to recei ve each other’ s signals due to half-duplex PHY assumption. This, ho wev er , will not af fect other vehicles. If we can guarantee that no pair of intra-cluster vehicles will transmit concurrently in subchannels of the same subframe, this kind of conflict can be a voided. Let v y and v z denote two different vehicles in the same cluster , thus when the condition  P k 1 x y k 1   P k 2 x z k 2  = 0 holds, conflicts do not occur . The indexes k 1 and k 2 represent two subchannels r k 1 and r k 2 belonging to the same subframe R l 0 , for l 0 = 1 , 2 , . . . , L . The equality is non-zero only when both vehicles transmit on at least one subchannel of R l 0 . More generally , for N vehicles, a compact form of e xpressing these constraints is gi ven by [( G + P × N ⊗ I L × L ) x s ] ◦ [( G − P × N ⊗ I L × L ) x s ] = 0 P L × 1 (2) where x s = ( I N L × N L ⊗ 1 1 × K ) x . The total number of intra-cluster vehicle pairs in the whole system is denoted by P . The boolean matrices G + and G − hav e a strong relation with the topology of the scenario and the distribution of vehicles across the clusters. These matrices also collect information on the restricted allocations that lead to this kind of conflict. 7 D. T ype III: Minimal time-dispersion of subc hannels When the subchannels apportioned to a vehicle span over sev eral subframes, the signal duration ov er the air persists longer . And because signals broadcasted by vehicles are of periodic nature, this implies that less time will remain for other vehicles (in the same cluster) to transmit. Therefore, if a vehicle has high QoS requirements, subchannels should be selected from within the same subframe since this will allow to maximize the number of served vehicles. Moreover , considering the described channelization, v ehicles can be assigned up to K subchannels from any subframe. For any v ehicle v i , to guarantee that the allotted subchannels will be confined to a single subframe, the follo wing must hold ( P u ∈R l x iu )( P u 0 ∈R l 0 x iu 0 ) = 0 , for l 6 = l 0 ∀ l , l 0 = 1 , 2 , . . . , L . Notice that the equality does not hold when vehicle v i transmits in any two subchannels r u and r u 0 that are in different subframes l and l 0 , respectiv ely . In a more general manner , for N vehicles, this can be e xpressed as [( I N × N ⊗ Q + L × L ) x s ] ◦ [( I N × N ⊗ Q − L × L ) x s ] = 0 N L × 1 . (3) The matrices Q + and Q − are boolean and contain significant information about the admissible and prohibited configurations regarding the time-dispersion of subchannels. E. T ype IV : One-hop inter -cluster subchannel conflicts T wo or more vehicles that are not aware of each other may transmit in the same subchannel. Thus, signals coming from these vehicles will merge and possibly become undecodable for other vehicles, specially for those that lie at the intersections of clusters. For any pair of vehicles v i ∈ V ( j ) and v i 0 ∈ V ( j 0 ) located in dif ferent intersecting clusters but not at the intersection, the follo wing must hold x ik x i 0 k = 0 ∀ r k ∈ R to prevent this kind of conflict. More generally , for N vehicles these conditions can e xpressed as [( H + U × N ⊗ I K L × K L ) x ] ◦ [( H − U × N ⊗ I K L × K L ) x ] = 0 U × 1 (4) where U is the number of vehicle pairs within one hop, e.g. v 1 and v 9 in Fig. 1. The matrices H + and H − collect general knowledge of the vehicles that are within one-hop range that could potentially originate conflicts. The complete formulation of the problem is gi ven by (5). Furthermore, to provide a better understanding of the matrices G − , G + , Q − , Q + , H − and H + , consider the following. 8 max c T x (5a) sub ject to q N × 1 −  ≤ ( I N × N ⊗ 1 1 × K L )( c N K L × 1 ◦ x N K L × 1 ) ≤ q N × 1 +  (5b) [( G + P × N ⊗ I L × L )( I N L × N L ⊗ 1 1 × K ) x ] ◦ [( G − P × N ⊗ I L × L )( I N L × N L ⊗ 1 1 × K ) x ] = 0 P L × 1 (5c) [( I N × N ⊗ Q + L × L )( I N L × N L ⊗ 1 1 × K ) x ] ◦ [( I N × N ⊗ Q − L × L )( I N L × N L ⊗ 1 1 × K ) x ] = 0 N L × 1 (5d) [( H + U × N ⊗ I K L × K L ) x ] ◦ [( H − U × N ⊗ I K L × K L ) x ] = 0 U × 1 . (5e) Example: Consider N = 4 vehicles distributed into J = 2 clusters, such that V (1) = { v 1 , v 2 , v 3 } and V (2) = { v 1 , v 2 , v 4 } with V (1) ∩ V (2) = { v 1 , v 2 } . Also, K = 3 and L = 3 . Thus, the matrices for this scenario are: G − =           1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0           G + =           0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1           H − =        0 0 1 0        H + =        0 0 0 1        Q − =     0 0 0 1 0 0 0 1 1     Q + =     1 0 0 1 0 0 0 1 0     Q = [ Q − ] T Q + =     0 0 0 1 0 0 1 1 0     The dimensions of G − and G + are 5 × 4 because there are N = 4 vehicles and P = 5 pairs of intra-cluster vehicles: v 1 − v 2 , v 1 − v 3 , v 1 − v 4 , v 2 − v 3 and v 2 − v 4 . For instance, if v 1 and v 2 transmit concurrently , a T ype II conflict will arise as they belong to the same cluster . This case is considered in row one of both matrices (first pair of vehicles), i.e., [ G − ] 11 = 1 and [ G + ] 12 = 1 . Ho wev er , v 3 and v 4 are in different clusters and the condition (2) is not violated. For this reason a ro w p with such a combination where [ G − ] p 3 = 1 and [ G + ] p 4 = 1 does not exist. The square matrices Q − and Q + hav e dimensions 3 × 3 since there are L = 3 subframes. The influence of these matrices can be best understood examining the product Q . There are three combinations that lead to T ype III conflicts, i.e. when any vehicle transmits in subframes 1 and 2 ([ Q ] 21 = 1) , or 1 and 3 ([ Q ] 31 = 1) , or 2 and 3 ([ Q ] 32 = 1) disregarding permutations. The square matrices H − and H + hav e dimensions 4 × 1 because there are N = 4 vehicles. T ype IV conflicts will manifest when two vehicles that are at one hop distance transmit in the same subchannel. Such case happens when v 3 and v 4 transmit concurrently in time and frequency , i.e. [ H − ] 31 = 1 and [ H + ] 41 = 1 . 9 I V . P R O P O S E D S U B C H A N N E L A L L O C A T I O N A P P R OA C H In this section, we realize the allocation of subchannels to vehicles following a three-stage process as depicted in Algorithm 1. Stage 1: The clusters are sorted hierarchically based on their cardinality such that |V ( j ) |≥ |V ( j +1) | . This means that clusters with a larger number of vehicles will be processed first. The intuiti ve reasoning is that larger clusters might be more difficult to optimize in terms of efficiently distributing the av ailable subchannels among vehicles. Stage 2: Every v ehicle in cluster V ( j ) is randomly matched to some subframe without explicitly specifying the allocated subchannels. The only requirement is that each vehicle in V ( j ) has to Algorithm 1: Subchannel Allocation Algorithm based on Multiple Independent Knapsack Problems (MIKPs) begin Stage 1: Sort the clusters in descending order of cardinality . for j = 1 : J do Stage 2: Assign randomly to each vehicle v i ∈ V ( j ) some subframe l k i without placing more than one vehicle in each subframe. Stage 3: Solve a knapsack problem for each vehicle v i ∈ V ( j ) max X s = { a | r a ∈R k i } c is subject to X s = { a | r a ∈R k i } c is ≤ q i where R k i is the set of subchannels in subframe l k i . 10 A verage Maximum Minimum Std. Dev . 0 10 20 30 12 . 18 13 . 15 10 . 76 0 . 72 11 . 31 13 . 15 6 . 59 1 . 13 Rate [Mbps] Exact Formulation MIKP-based Approach Figure 3: Group of vehicles with target QoS = 12 Mbps and admissible range [10.4 - 13.6] Mbps A verage Maximum Minimum Std. Dev . 0 10 20 9 . 54 10 . 17 7 . 78 0 . 59 9 . 07 10 . 17 5 . 41 1 . 02 Rate [Mbps] Exact Formulation MIKP-based Approach Figure 4: Group of vehicles with target QoS = 9 Mbps and admissible range [7.4 - 10.6] Mbps be assigned exactly one subframe to prevent T ype III conflicts 3 . In addition, no more than one vehicle in V ( j ) can be placed in the same subframe to prev ent T ype II conflicts. Thus, a vehicle v i will broadcast over a set of subchannels located in some subframe l k i . Step 3: Since vehicles hav e already been assigned to a specific subframe, a knapsack problem has to be solved to find which subchannels fulfill the QoS demands of the vehicle 4 . The subchannel allocations that may cause vehicles to undergo T ype IV conflicts are remov ed. Such information can be readily obtained from matrices H − and H + . V . S I M U L A T I O N S By means of 1000 simulations, the performance of (5) and Algorithm 1 are e valuated using Matlab programming en vironment. W e consider an scenario with N = 40 vehicles distrib uted ov er J = 4 clusters wherein |V (1) | = 16 , |V (2) | = 16 , |V (3) | = 16 , |V (4) | = 8 , and |V (1) ∩ V (2) ∩ V (3) | = 8 , |V (1) ∩ V (4) | = ∅ , |V (2) ∩ V (4) | = ∅ , |V (3) ∩ V (4) | = ∅ . Furthermore, we assume that each vehicle 3 A random pairing between vehicles and subframes is not the only possible manner of matching elements of these two groups. For instance, this could have been accomplished following a greedy or ordered criterion. Furthermore, an assignment based on the maximization of the achiev able capacity per subframe could hav e been opted. Nev ertheless, for the sake of simplification, in this work a random distribution was selected. 4 The knapsack problem is solved through dynamic programming allowing to reduce the complexity compared to exhaustiv e search, which tests e very possible combination of subchannels. In exchange of saving computation time, the knapsack problem requires a modest memory space to store previously computed partial combinations. The knapsack problem in this work is a special case known as the subset sum problem [3] [7]. 11 A verage Maximum Minimum Std. Dev . 0 5 10 15 6 . 19 7 . 18 4 . 82 0 . 71 6 . 09 7 . 18 3 . 95 0 . 82 Rate [Mbps] Exact Formulation MIKP-based Approach Figure 5: Group of v ehicles with target QoS = 6 Mbps and admissible range [4.4 - 7.6] Mbps A verage Maximum Minimum Std. Dev . 0 5 10 3 . 79 4 . 24 2 . 08 0 . 49 3 . 89 5 . 99 1 . 23 0 . 69 Rate [Mbps] Exact Formulation MIKP-based Approach Figure 6: Group of v ehicles with target QoS = 3 Mbps and admissible range [1.4 - 4.6] Mbps requires an y of the follo wing QoS v alues { 12 , 9 , 6 , 3 } Mbps and there are 10 vehicles of each kind spread across the clusters. The number of subframes is L = 16 and the number of subchannels per subframe is K = 3 . Also, we consider  = 1 . 6 Mbps and the rate ranges are therefore [10 . 4 − 13 . 6] Mbps, [7 . 4 − 10 . 6] Mbps, [4 . 4 − 7 . 6] Mbps and [1 . 4 − 4 . 6] Mbps. From Fig. 3 to Fig. 6 the achiev ed data rates for each group of vehicles are shown. F our criteria are emplo yed to assess the performance of the two approaches. Although both approaches can in average pro vide the required QoS, it is critical to e valuate their performance in terms of the de viation from the target values. Thus, in the case of the MIKP-based approach, the target QoS is mostly not attained as the achie ved rate v alues fall out of the admissible ranges. On the other hand, the exact formulation can guarantee the tar get QoS v alues in a tighter manner without se vere de viation. Nev ertheless, the disadvantage of the e xact formulation is that a feasible solution may not be obtained if the requirements are not satisfied for all the vehicles. For the described setup, in 8% of the cases a feasible solution was not found. This effect is not shown in the figures as only the successful allocations were considered. In practical situations, the parameter  can be increased and thus the QoS requirements be relaxed for the algorithm to be ex ecuted again. Ho we ver , this will depend on the particular scenario and whether the eNodeBs can afford to repeat the process. Although the proposed approach exhibits a simpler formulation and provides looser solutions, it can in 100% of the cases provide at least a minimum operational le vel of service to all the vehicles. For this reason, under the criterion minimum , the algorithm does not perform as good as the exact formulation since ev ery obtained solution contemplates that 12 all in-co verage v ehicles are always being served. Furthermore, the criterion standard deviation depicts ho w dif ferent the attained QoS v alues are among vehicles with the same requirements. Thus, the proposed approach is less restricti ve in this sense and the provided QoS might v ary in a wider range. In both cases, no conflicts were originated although this outcome might change when the number of subchannels is scarcer . V I . C O N C L U D I N G R E M A R K S W e presented a formulation for subchannel allocation in V2V mode-3 with four types of constrains. In addition, we proposed a simpler scheme using an extension of the knapsack problem in order to approach the initial formulation. Although the latter scheme is suboptimal, it does not fail in servicing and providing vehicles with subchannels because the QoS constraints are not as tight as in the original formulation. R E F E R E N C E S [1] ”3GPP TR 36.885; T echnical Specification Group Radio Access Network; Study on L TE-based V2X Services; (Release 14) v14.0.0, ” June 2016. [2] L.F . Abanto-Leon, A. Koppelaar , and S. M. 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