4.3 Cross-Layer Coalitional Game Formulation
4.3.1 Cross-Layer Coalitional Game Overview
In this section, we introduce the proposed CLC game framework to cooperatively cluster D2D pairs, in order to reduce transmission power, increase channel rate, and utilise resources more efficiently. The proposed CLC game combines a mode selection and resource allocation coalitional game (main game), along with a dedi- cated mode resource allocation sub-problem and an interference management sub- problem. Moreover, we outline how the main coalitional game interacts with each sub-problem (and vice versa).
Let N = C ∪ D be the set of players, which consists of all cellular users and D2D pairs within the network. Within the proposed game, D2D pairs aim to form cooperative clusters based on mode selection and resource allocation, where D2D pairs and cellular users form a set F. We assume a fixed cluster structure, where the set of clusters F is a collection of F disjoint clusters. That is, the number of clusters considered, equals the number of orthogonal resource blocks allocated to
4.3 Cross-Layer Coalitional Game Formulation 87
users in the network. A cluster Fπ ∈ F is defined as a subset of N, such that
SR
π=1Fπ = N, where ∀Fπ,Fπ′ ∈ F, if Fπ′ 6= Fπ, then Fπ′ ∩ Fπ = ∅. Moreover,
the set of clusters F can be broken down into smaller subsets based on D2D pair mode selections, i.e., F =DRM ∪ DCM ∪ DDM whereDRM is the set of D2D pairs
selecting reuse mode, DCM is the set of D2D pairs selecting cellular mode, and
DDM is the set of D2D pairs selecting dedicated mode.
Definition 4.3 A cross-layer coalition formation game is defined by GCLC =
(N, v,F), where N is the finite set of players; v is the non-transferable coali- tion value that captures the individual utilities of D2D pairs and cellular users; and F is the set of coalitions.
Initially, cellular users are partitioned into singleton clusters (that is, the BS allocates each cellular user an orthogonal resource block), where all D2D pairs within close proximity (satisfying the threshold distance for direct communication and QoS constraints) are randomly partitioned across all clusters (that is, clustering based on resource sharing). Thus, forming the set DRM, such that SFπ∈DRM Fπ =
C. Any remaining D2D pairs not within close proximity will operate in cellular mode and are partitioned into singleton clusters (that is, the BS allocated D2D pairs in cellular mode an orthogonal resource block). Thus, forming the set DCM ⊂ F.
Fig. 4.2 shows the proposed CLC game framework, and the relationships be- tween the main game (red block) and the sub-problems (blue blocks). Within the CLC game, optimal D2D mode selection is determined in the mode selection and resource allocation coalitional game and the dedicated mode resource allocation sub-problem. Moreover, the coalitional game determines if D2D pairs are to op- erate in reuse mode or cellular mode, and the dedicated mode resource allocation sub-problem determines which D2D pairs in reuse mode will be allocated orthog- onal spectrum.
Firstly the BS checks if there are any idle orthogonal resource blocks available within the network to allocate to D2D pairs in reuse mode (ensuring that there is a sufficient amount of resource blocks available if a cellular user joins the network or if D2D pairs switch to cellular mode). If resource blocks are available, the ded- icated mode resource allocation sub-problem (Section 4.3.3.1) determines suitable D2D pairs operating in reuse mode to allocate an orthogonal resource block to. Thus, D2D pairs switch transmission mode from reuse to dedicated, which directly maps to partitioning D2D pairs into singleton clusters and forming the set of D2D
88 D2D Mode Selection and Resource Allocation in D2D Networks
BS checks for any idle resource blocks to al- locate to D2D pairs operating in reuse mode.
Initial clustering of D2D pairs and cel- lular users: F = DRM ∪ DCM
Dedicated mode resource allocation sub- problem (Section 4.3.3.1) for D2D pairs in
DRM. Update coalition partition F, and DDM.
Interference management sub-problem: D2D pair scheduling (Section 4.3.3.2) for D2D pairs in DRM. Update coalition partition F.
Coalitional game (Section 4.3.2) for D2D pairs in
DRM and DCM. Update coalition partition F.
Interference management sub-problem: Power control (Sec- tion 4.3.3.2) for all D2D pairs and cellular users in coali-
tion Fπ ∈ F,∀Fπ ∈ F. Update coalition partition F.
yes
no
Figure 4.2: Proposed CLC game framework to solve resource utilisation in D2D communications. The red block indicates where the network-assisted or user- assisted schemes are considered.
4.3 Cross-Layer Coalitional Game Formulation 89
pairs operating in dedicated mode DDM ⊂ F. Next, the interference management
sub-problem schedules D2D pairs in reuse mode across all clusters, in order to re- duce intra-cell interference within the network (Section 4.3.3.2). Then, all D2D pairs operating in cellular mode DCM and reuse mode DRM, determine their most
preferred transmission mode or resource sharing cellular user, in the mode selection and resource allocation coalitional game (Section 4.3.2). Finally, the interference management sub-problem also considers a power control sub-game (Section 4.3.3.2), to determine optimal transmit power for each user in cluster Fπ ∈ F, ∀Fπ ∈ F,
while guaranteeing (4.9) and (4.10). Thus, after each game/sub-problem in the proposed CLC game, the coalition partitionF is updated accordingly. The process is repeated for a finite number of stages.
The red block in Fig. 4.2, indicates a different implementation scheme, to ac- commodate for the network-assisted and user-assisted scenarios.
Remark 4.3 There are three types of clusters out of a total of R disjoint clus-
ters, which reflect the three transmission modes for D2D pairs: (i) D2D pair i in dedicated mode forms a singleton set, {i}; (ii) D2D pair i in cellular mode forms a singleton set, {i}; (iii) D2D pair i in reuse mode forms a cluster with a total of
X D2D pairs sharing the same resource block, which makes up the setX,X ⊂ D, plus one cellular user.