Resource Allocation in D2D-Aided High-Speed Railway Wireless Communication Systems: A Matching Theory Approach

Meilin Gao, Bo Ai,＊, Yong Niu, Zhewei Zhang, Yanqing Xu, Dapeng Li

1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

2 School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China

3 ZTE Corporation, Shenzhen, Guangdong, 518057, China

I. INTRODUCTION

Recently high-speed railway (HSR) enjoys the most remarkable reputations for the efficient convenience of facilitating travelling with less energy consumption and air pollution compared to cars and airplanes [1]. As an essential element of public transport systems, HSR and rail intelligent transportation system have been basking in a great boom [2] [3]. Recent demands for operation efficiency and safe reliability prompt railway services to evolve from voice dispatching and critical signaling services to various high-data rate services.For instance, applications of multimedia dispatching video streams, onboard and wayside high definition video surveillance, Internet of Things for Railway (IoT-R) and onboard passenger-oriented broadband services are highly desired with a deluge of bandwidth demand [4]. However, the contradiction between the surging data demand and finite frequency spectrum needs to be relieved. To date, researches on this issue have been widely studied, and novel network architectures with emerging building blocks are remained as hot topics [5] [6] [7].

To meet the demands for amusement and comfort, a dedicated onboard social network service system (SNS) can be regarded as a collection of proximal information exchange for passengers [8]. Specifically, integrated applications consist of file transfer, live chat,video sharing, interactive gaming, etc. These are anticipated to be supported by the onboard SNS, which derives from traditional SNS [9][10]. Although great achievements have been exploited in SNS so far, there is still an open issue in the onboard SNS specified for HSR,faced with typical high-mobility features.According to [8], the imagination of SNS in HSR has been put forward, which includes not only the passenger internal communications but also the rail traffic applications. [11] proposed the virtual crew services including the environmental information of train, the useful local information and the emergency alerts which are provided in a dynamic SNS in HSR.However, more technology implementation needs to be explored.

In this paper, the latest progress in HSR network architectures and technology building blocks are discussed to enable the implementation of the SNS.

In this case, a promising concept termed as device-to-device (D2D) communication is proposed to enable direct transmission in the point-to-point style between closely located user pairs [12]. To achieve intelligent resource allocation of the shared cellular resources,D2D communications should be motived to work on different uplinks and aggregate them.Much efforts have been done by concerning the above issues [13][14][15]. While most of these studies are oriented for low-mobility users, the onboard SNS are faced with severe challenges owing to the penetration loss, the frequent handovers, and the doppler shift.Coo perated economical techniques such as auction mechanism[16][17] is preeminent considering fairness, efficiency and valuation independence. In addition, matching game theory [18] [19] [20] provide a set of mathematical tools to solve resource allocation problems.

Fig. 1 A layered network architecture for onboard SNS wireless communication in HSR

In this paper, a new model composed of a dual-hop wireless intranet system is designed.And we propose a novel approach to allocate resources for the onboard SNS using the many-to-many matching game (M2MG) solved by the swap-matching procedures. Numerous simulation results validate the excellent performance of proposed algorithm and designed implementation for the onboard SNS in HSR.

The rest of the paper is organized as follows. In Section II, we introduce the network architecture and system model dedicated for the onboard SNS in HSR. In Section III, dynamic resource allocation for the onboard SNS can be solved by a many-to-many matching game with the two-sided stable theory. Numerical results are discussed to verify the model efficiency in Section IV. Finally conclusions are drawn in Section V.

II. NETWORK ARCHITECTURE AND SYSTEM MODEL

2.1 Network architecture

2.1.1 Propagation features under HSR scenarios

Particu lar propagation scenarios, high moving speeds over 300 km/h, higher requirements of quality of service (QoS), harsh electromagnetic environments, as well as severe interference are the main features for the rail mobile communications. When compared with the general public land mobile communications, some differences are summarized as following [21]:

1) With the increase of high speed for HSR, the wireless channel exhibits rapidly time-varying and nonstationary.

2) Doppler frequency shift brings harm to the orthogonality of sub-carriers of OFDM signals and introduces inter-carrier interference (ICI).

3) Frequent handoff leads to more handover failures and higher transmission errors along with the increasing velocity.

4) Significant penetration loss is brought when radio signals propagate through the train body covered by stainless steel.

As mentioned above, a potential communication network architecture for high speed railway communication (HSRC) is designed in figure 1, which is layered and composed of a dual-hop architecture. distribute base station(DBS) system is deployed alongside the railway, combined with the mobile relay (MR)adopted in the train, which acts an effective solution in this paper.

Note that when considering the DBS, the baseband unit (BBU) is used to process the baseband signal, and the radio remote unit(RRU) is used to process the radio frequency signal, which can be placed outside along the tracks flexibly. Optical fibers are used to transmit baseband signals between a BBU and several connected RRUs. Furthermore, each MR system comprises a MR placed outside the train, and some access points (AP) installed inside each wagon, among them there is a cable associated with each other through wire transmission. This network architecture is custom designed for the onboard SNS with the consideration of typical features of HSR.

2.1.2 Technology building blocks for HSRC The demands for bandwidth from passengers in HSR is regarded as a great motivation to the following technologies:

1) Half duplex (HD) communication prevails in recent times, which separating the transmit and receive signals with differentiated subchannels. However, when facing short supply of spectrum in HSR, full duplex (FD)technology tends to conquer this plight by allowing simultaneous transmission and reception on the same frequency band [22]. To enable higher spectrum efficiency, the MR in this context will be operated in FD mode with multiple antennas.

2) Stemming from researches that blossomed at the end of the 20thcentury, MIMO communication came into public consciousness and were put into use in the early 21stcentury. MIMO system contributes to the HSR wireless communication by embodying the spatial dimension, providing diverse gains and utilizing the multiplicity of antennas [23].

3) Invoked by the social resources to be shared, the onboard SNS system is proposed with D2D due to the characteristics of proximal interactions. For this scenario, there is no need to connect back to a control and dispatch centre, on the basis of that the onboard SNS can be regarded as a collection of social interactions among proximal members inside wagons.

Based on the above analysis, the information transfer between the train and the DBS can depend on the FD MIMO techniques. As for the inside-train transmission, D2D underlying cellular network is to be implemented.

2.2 System model

In this paper, we focus on the uplink transmission in a single cell of RRU. As illustrated in figure 1, dual-hop links comprise the access network for HSRC. They are connected from user equipment to AP in the inner-hop referring to transmission inside the wagon, and from the MR to RRU in the outer-hop indicating the communication outside the train. All the passengers’ terminal can be categorized into two types, i.e., the traditional cellular user equipment (TUE), and the D2D user equipment (DUE), which is underlying the cellular system by sharing uplink radio resources of TUEs. For clarity, the whole system model can be constructed as the implementation of the onboard SNS, supported by the dual-hop transmission for TUEs.

2.2.1 The transmission for TUE

We consider a high-speed train consisting of some TUEs and DUEs inside the train randomly distributed over the train wagons,denoted as T={1,…,M} and D={1,…,N}.For simplicity, the transmit power of each passenger is assigned a fixed value and equally divided. The available spectrum is divided into K sub-channels with the total bandwidth denoted by B. Each UE is equipped with a single antenna, while the MR and RRU are equipped with multiple antennas. During the inner-hop,Ti∈T will transmit signals to the MR in SIMO mode over orthogonal sub-channels. In the outer-hop, the MR is operated in the FD SIMO model, receiving data from TUEs with a single antenna, while transmitting these data flows to RRU with Ntantennas simultaneously.The related RRU is placed where the vertical distance from the track denoted by d0, and the distance from RRU to the MR is set as dtvarying with time and space.

As for the multi-stream beamforming with multiple antennas, the received SINR at the RRU can be expressed as:

Accordingly, the achievable rates of the MR and the RRU can be denoted as:

The capacity of the entire network assisted by the decode-and-forward relay depends on the minimum of the two-link data rates as. Generally, the wireless communication between the ground and the train turns to be the bottleneck. To ensure that the information will be safely sent to the target, the capacity constraint deriving from the FD mode should satisfy

2.2.2 The Implementation of the onboard SNS

In this section, we present detailed descriptions on the onboard SNS from a perspective of protocol layers, including physical (PHY)layer, media access control (MAC) layer and transport layer.

1) Capacity-Based PHY Layer Model

To highlight quantitatively the efficient use of the rare spectrum, the reuse model is adopted by DUEs inside the train by sharing the sub-channels of TUEs. If the sub-channel allocated to Tiis still available to Dj∈D,then the binary indicator αi,jis set to be 1 indicating the matching between Tiand Dj,otherwise αi,j= 0. To ensure better performance, multiple D2D pairs may match with a same TUE, and one D2D pair is permitted to match with several TUEs when condition allows. Note that, one D2D pair contains a D2D transmitter (DTx) and a D2D receiver (DRx).

Given the effect of channel reusing brought by the onboard SNS, the received SINR and achievable data rate of the MR from Ti∈T need to be updated from previously formulated demonstrations in (1) (5) as :

co-channel interference (CI) from Dj∈D which reuses the sub-channel belonging to Ti,and hj,MRindicates the channel gain from Djto the MR. Thus, the data rate constraint relationship in the uplink TUE information transmission updates as

2) Queue-Based MAC Layer Model

Assuming the packet generation process for Djcan be modelled as the M/G/1 priority queuing system, where the traffic requests are satisfied according to the context dependent priorities. Thus, the average packet delay for the s-th priority stream of Djis given by the P-K formula in [27] as:

where E(Ts) andare first two moments of service time of s-th class stream, ρj,lrepresents the utilization factor for the l-th class stream of Dj, anddenotes the total wireless delay.

3) PER-Based Transport Layer Model

The packet error rate during the transmission inside a D2D pair can be expressed as a function of the received SINR concerning a certain target threshold. For some given modulation and coding scheme, this packet error rate is given by [28]

In this regard, the aim of the system design is to maximize the total utility of all DUEs in the onboard SNS and meanwhile, guarantee the cross-layer QoS requirements. Then the problem can be formulated as:ment of the DUE, n is the coding mode index,and both anand gnare mode-dependent. For simplicity, n can be empirically defined as a pre-defined variable.

With all considerations above, we propose the following utility function for DUE Dj∈D over the sub-channel belonging to TUE Ti∈T as:

subject to

Constraints (14a)-(14b) ensure that each DUE or TUE can satisfy the basic SINR requirements, and (14c)-(14d) ensure the basic PER and delay requirements for DUE. (14e)indicates the binary indicator should be either 0 or 1. As for (14f) and (14g), the quota of matching relationship for TUE and DUE is set.

Here we remark that the non-convex optimization problem (14) is challenging to solve,mainly due to the binary constraint in (14e)and the existence of the interference term in the objective function. To conquer the maximization problem, some efficient methods should be available to solve this problem avoiding combinatorial complexity. While in this paper,we turn to the matching theory referring to the model of college admissions and the stability of marriage [29].

III. DYNAMIC RESOURCE MANAGEMENT AND MANY-TO-MANY MATCHING GAME

For deriving a distributed algorithm that can maximize the utility of DUEs in the onboard SNS, a dynamic resource allocation is modelled as a many-to-many matching game(M2MG) with quotas [30]. We will consider the set of DUEs and the set of TUEs, as two disjoint sets of selfish and rational players aiming to maximize their own benefits. Each player can exchange information with one another without extra signalling cost, since the Channel State Information (CSI) is known to the DBS, i.e., the players have complete information about one another.

3.1 Preliminary knowledge

A matching is defined as an interactive assignment of TUEs in T among DUEs in D, more formally:

Definition 1.Given two disjoint sets,D and T , a many-to-many matching Ψ is a mapping from the set D∪∪ {0} into the set of all subsets of D∪∪ {0} such that for every Dj∈DandTi∈T :

Condition 1) indicates that each Ti∈T can find its matching result Ψ(Ti) coming from a subset of D, similarly, each Dj∈D can connect to a subset of T acting as its matching partnersΨ(Dj). Condition 2) defines the quota allocated to each passenger in view of the channel quality and system complexity. At most Qtbest-qualified DUEs can be allocated to each TUE and Qdbest-qualified TUEs with corresponding sub-channels can be allocated to each DUE.

Peer effects are observed as common results of underlying intricate connections,which are suitable for the proposed model in the onboard SNS with the matching theory.Due to the co-channel interference, strong interdependence among D2D pairs sharing with a sub-channel belong to the same TUE in this situation is termed as peer effects [31], one kind of externalities thriving in economics. For the DUE-TUE association problem using the many-to-many matching, peer effects do play an important role in this paper. The strategy of any DUE not only concerns the information available for itself, but also cares about others who are matched to the same TUE with the presence of peer effects. A preference relationin M2MG is defined to better describe the dynamic interaction features, each element inhas a preference relation specified by giving a utility function [32]. To better describe the interactive behaviours, for any Dj∈D, its preferenceover the set of T is depicted as:

Similarly, for any TUE Ti∈T, the preference relation depends on the CI brought by companion DUEs in the descending order:

where Dj,Dj'∈D are two different partners under the matching Ψ and Ψ' withThe CI from Djto the signal transmitted by Tiis denoted by.Which means the less interference, the better matching relationship.

Definition 2. Given a matching Ψ withandA swap matchingis defined as:whereThus, a new matching pattern has been brought asand.

In other words, a swap matching enables different players to exchange their matched partners through swap operations while keeping other players stable. Also, the existence of such a swap operation is only on the condition that some benefits can be created.

Definition 3.Given a matching Ψ and a pairthere existsForandthen (Dj, Dj’) is called swap-blocked if and only if

Note that this definition discloses the qualifications for a swap operation when swapblocked pairs exist. Condition 1) implies that no players will turn unfavourable through a swap operation, and condition 2) guarantees that at least one player can achieve a strict increment in utility from this operation.

Definition 4.A matching Ψ is two-sided exchange stable (2ES) if and only if there does not exist any pairs being swap-blocked any more.

In such settings, it is vital that current matchings are ‘stable’ in the sense that agents have no incentives to change assignments after being matched [33]. As a result of peer effects,we restrict to considering swaps of players with counterparts’ actions. Both the constraints above guarantee the necessity as well as the efficiency through swap operations.

3.2 Algorithm description

With the definition of M2MG and 2ES, we introduce a DUE-TUE matching algorithm to obtain the optimal system performance for the onboard SNS. The key idea is to keep efficient-swapping iteratively among the players until this system reaches a 2ES matching. As is shown in Table 1 is the proposed algorithm.The key idea of the algorithm can be portioned into two stages. The first stage focuses initialization which is an extension of the deferred-acceptance algorithm [34], and the second step targets on swap-matching process based on the efficient swap operations.

In initialization stage, we assume that all the sub-channels have been allocated to appropriate TUEs already, and no D2D pair has been assigned to any TUE so far. To begin with, according to the explored CSI by DUE and TUE, they construct their own preference list by (14) and (15). Then each D2D pair proposes to his top-ranked choice. Based on these proposals, each TUE will make decision to keep some D2D pairs in a waiting queue based on the Qtmost-wanted matching pairs while under the SINR conditions simultaneously, and reject other proposals. Updating preference lists by removing the TUE which has already rejected the proposal, D2D pairs will repeat proposing until preference lists run empty. Then each TUE will make decisions to choose their most wanted QtD2D pairs from the waiting queue. In swap-matching stage,D2D pair will try to swap matching TUEs with a swap-blocked pair through finite iterations.

It attempts to conclude a random initialization is inferior to the method making the as-signments in accordance with the given preference. Continuing the process of swap-matching, once there exist a swap-blocked pair, strict increment on utility needs assortment. Multiple iterations empowering the swap operations under the condition of SINR requirements of both DUE and TUE would terminate to reach a 2ES result finally.

3.3 Efficiency of stable matchings

Given our model of peer effects, the focus of this section is then on characterizing the sets of 2ES matchings, as defined in Section 3.1.Our results concern (i) the existence of 2ES matchings; (ii) the efficiency of exchange-stable matchings (in terms of personal as well as system utility); (iii) the computation complexity of the proposed algorithm.

Firstly, we begin by focusing on both stability and existence of our proposed algorithm oriented for SNS system in HSR.

Proposition 1: Starting from the initialization, all the players in the TUE and DUE sets can always converge to a final matching Ψ*which comprises iterative mutual matchings.

Proof: We make the proof by contradiction.According to the swap-matching algorithm as shown in Table 1, the swap operations occur only when total utilities of players are strictly improved. The total number of swap-matching operations is a finite number, when the numbers of TUE and DUE are finite with the given quotas of them. We assume that within the given iteration numbers, the swap-matching phase will terminate and there does not exist any swap-blocked pairs in Ψ*. Otherwise further swap- matching needs to be executed, and further increase the utilities for players in both sides of the current matching can be achieved,meaning Ψ* is not the final matching. Based on the discussions above, we conclude the proposed algorithm can always converge to a two-sided exchange stable state.

With respect to the existence of two-sided exchange-stable matchings, our focus will be on the efficiency due to the stability in the matching market for SNG system in HSR communication.

Proposition 2: The SNG system utility of all passengers including TUE and DUE will increase with the evolutions by swap-matching rules.

Proof: During some round of the swap-matching operations, suppose a swapblocked pair (Dj, Dj’) would result in a new swap operation from Ψlto Ψl+1with the original matching TUEs, for instance (Ti, Ti’) .Abided by the rules set in Definition 3, the total utilities of DUE and TUE over all the sub-channels strictly increase over the exchange matchings. Without loss of generality,we can deduce that each DUE passenger gains benefits from the 2ES matching result, in additions, to consider the peer effects brought by other DUE passengers who sharing the same sub-channel from a certain TUE.

Given the influence to convergence due to the number of user equipment, the complex-ity of the proposed algorithm as depicted in Table 1 is to be discussed as follows. For the deferred-acceptance (DA) based initialization,there are several iterations during which each D2D pair will make new proposal to its most preferred TUE in their current preference lists,thus about O(M) times of D2D applications can be reached up to. After all the application iterations, each TUE will make decisions to accept at most QtD2D pairs after sorting the waiting queues, and at the most O(N) times maybe occurred. As for the swap-matching process, each D2D pair attempts to exchange its matched TUEs with other D2D pairs’matched TUEs. Then maximum swap-blocked D2D pairs can be enumerated as, and all the exchangeable TUEs matched to a swapblocked pair reach. In all, the computational complexity of the whole proposed algorithm can be presented asand further be approximated as

We can deduce the many-to-many matching game represents not only the outcome of the mutual matching for D2D pairs and TUE underlying the cellular system, but also the solution of the joint cross-layer performance optimization for the onboard SNS in some sense. What’s more, the dual-hop communication really has a lot to do with the performance of SNS due to the upper bound constraint on the capacity of the FD relay channel. Further analysis can be deduced that the running speed and location of the HSR do relate to the onboard SNS.

IV. NUMERICAL RESULTS

In this section, we evaluate the performance of the stability and low-complexity as well as efficiency of the proposed M2MG algorithm.For comparison, we introduce some other resource allocation methods, namely the DA algorithm and the baseline random algorithm.We set the maximum number of TUE that a D2D pair could access concurrently as Qd= 3,and the maximum number of D2D pairs that a TUE can match with simultaneously as Qt= 2.

Figure 2 presents the number of swap operations at different number of DUE with the range from 6 to 20 (the number of D2D pairs,to be accurate), with the number of TUE fixed as 10 and 20 for comparison. With different settings of TUE, the number of swap operations grows as D2D pairs increase. It is not surprising to see that the swap operations will increase when the number of TUE is 20 are abundant for D2D pairs compared with only 10 TUEs. Due to the limited TUEs, the total matching scheme will reach the upper bound in the long run. When the number of TUE turns insufficient with D2D pairs increasing,a stable and fast convergence can be observed in our proposed algorithm. Moreover, we find that the M2MG algorithm yields a fastest convergence performance among all the considered allocation algorithms with giant gaps.Specifically, Random Algorithm is featured as easy deployment but high complexity, leading to the maximum iterations and low convergence speeds. Furthermore, the DA method achieve a compromise between above two methods.

Similar analysis could be concluded for figure 3 when the number of swap operation increases with different settings of the number of TUE ranging from 10 to 28, while the number of D2D pair is set fixed as 10 and 20 in contrast. Configured with some certain TUE numbers, the more DUEs there are, then more swap iterations will happen during the allocation process. From another perspective,the DA algorithm can achieve nearly 46.3%improvement in saving superfluous swaps in comparison with the random allocation algo-rithm under the 20-D2D pairs scenario. What’s more, almost 70.2% performance improvement is reflected under the same D2D configurations in the proposed algorithm compared with the random algorithm.

Table II Simulation Parameters

Fig. 2 Number of swap operations vs. number of DUE

Fig. 3 Number of swap operations vs. number of TUE

Fig. 4 CDF of the number of swap operations vs. the number of D2D pairs

Also, the cumulative distribution function(CDF) of the number of swap operations is displayed in figure 4 and figure 5 which are based on the same condition as in figure 2 and figure 3, respectively. In all, the efficiency and stability can be deduced from the simulation results of iteration times and CDF of swap operation.

Figure 6 demonstrates the achievable total utility comparison of the proposed M2MG method, DA method and random method with different numbers of the D2D pairs. We can observe that the proposed algorithm achieve the best performance on the total utility of DUE in onboard SNS, the DA strategy can also achieve good performances while the random algorithm seems the worst. As the number of TUE increases, the total utility of the DUE also improves, especially when the number of DUE becomes larger. However, the total utility improvement becomes less effective and reaches the upper bound when the number of TUE lifts and exceeds at some break point.Specially, the break point depends on both the numbers of D2D pairs and the quotas of passengers. Obviously, the more DUE, the higher upper bound for total utility of the onboard SNS under the same assumption of the TUE.Therefore, for the proposed scheme, the maximum utility can be improved when compared with the ordinary random method.

Figure 7 shows the throughput of D2D pairs in onboard SNS varying with the number of TUE under different D2D pair settings. As can be seen from this figure, with the same number of active D2D pairs, the more available TUE can bring more efficient channel capacity due to the more abundant sub-channels. With the increase number of TUE, the throughput of onboard SNS improves with a considerable slow-down growth rate. Specially, when the available TUEs exceed the maximum matching pair that D2D pairs can form, system throughput will reach a upper bound due to the quotas constraint.

V. CONCLUSIONS

In this work, we have solved the resource allocation problem in the onboard SNS for HSR wireless network by maximizing the system total utility. By formulating the sub-channel assignment problem as a many-to-many matching game with peer effects, we have proposed a two-stage algorithm: the first stage for initialization is based on the DA algorithm,and the second stage adopts a swap matching process enabling each user to exchange matching pairs when possible. Properties of the proposed algorithm have been discussed including convergence, stability, complexity and efficiency. When c ompared with some other allocation algorithms, not only the stability and low-complexity represented by the number of swap operations can be observed in the simulation results, but also implying the high-efficient and optimality expressed by the total utility as well as the system capacity of the onboard SNS. The simulation results have demonstrated that the proposed M2MG algorithm outperforms the existing strategies with giant gaps, thus making it a promising candidate for supporting the functionality of the HSR onboard SNS.

ACKNOWLEDGEMENTS

We gra tefully acknowledge anonymous reviewers who read drafts and made many helpful suggestions. This work is supported by the National Key Research and Development Program Under Grant 2016YFB 1200102-04,Natural Science Foundation of China under Grant U1334202. This work is also supported in part by the National S&T Major Project 2016ZX03001021-003, the Fundamental Research Funds for the Central Universities under Grant 2016RC056, in part by the State Key Laboratory of Rail Traffic Control and Safety， Beijing Jiaotong University, under Contract RCS2017ZT009, and in part by the China Postdoctoral Science Foundation under Grant 2017M610040.

Fig. 5 CDF of the number of swap operations vs.the number of TUE

Fig. 6 Total utility of DUE vs. the number of TUE

Fig. 7 Throughput of D2D pairs vs. number of TUE

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