Summary |
In this thesis, we investigate the problem of resource management for two-hop interference channels from a game-theoretic perspective. Our focus is on designing simple and distributed resource allocation schemes that can achieve near-optimal network-wide performance. To achieve this goal, we start by considering the two-hop interference channel with two users using decode-and-forward (DF) relaying. It is shown the problem admits a natural non-cooperative game-theoretic formulation, where Nash equilibrium (NE) is derived in closed-form and proved to be always unique. We further show that this unique NE achieves sum-rate optimality when the crosstalks coefficients of the network are small, characterized explicitly by a sufficient condition. To guide the self-interested players towards the equilibrium point, we propose a simple and distributed algorithm that converges to the NE from an arbitrary starting point, even in the presence of asynchronism between the systems. We then relax the assumption for DF relaying by allowing the relaying nodes to select between DF relaying and amplify-and-forward (AF) relaying, which we shall refer to as the general relaying problem. We show that the techniques used for DF relaying are not applicable in this general setting. A key contribution is made here by showing the possibility of a unified treatment for this general relaying problem through the framework of standard function. This successful treatment is accomplished by a game scalarization technique followed by a selection technique of the single-dimensional strategy, both of which are instrumental in establishing the properties of NE. We prove that the general relaying game still possesses a unique NE, which can be achieved through a simple distributed procedure initiated from an arbitrary starting point. Furthermore, for the case when both links adopt DF relaying, we prove that the NE is globally stable in the interference-limited regime. Finally, we discuss, through extensive numerical results, the impacts of system topology and relaying combinations on the system sum rate. For the two-hop interference channel with two users or systems, an important point is whether the game-theoretic approach proposed for the two-user model is generalizable to a network with more than two systems. We prove that this is indeed the case. The proofs tackle the following non-trivial extension as well: Incorporation of both total power constraints (for each system) and peak power constraints (for each transmitter). The properties of the N-player AF game, when all the players adopt AF relaying, is shown to admit a similar treatment as the two-player case in a non-trivial manner. The N-player DF game, on the other hand, is shown to possess multiple NE, among which we define and study two particular NEs: the aggressive NE and the conservative NE. A contribution is made here by proving the uniqueness of the aggressive NE through an implicit characterization of the BR. It is shown that the NE can be reached through iterative best response (BR) updated and implemented in a distributed fashion. Numerical results show similar findings as those of the two-player network. Intuitively, when the network is interference-limited, the competitive design will result in performance degradation. To improve the efficiency of the NE in interference-limited scenarios and obtain Pareto-improvement, we will consider two different solutions: 1) randomization approach; and 2) pricing approach. Both approaches share a common underlying principle which tries to create opportunities for orthogonal usages of the shared frequency resource. The randomized power control approach allows the systems to transmit probabilistically and enhances the sum rate through interference avoidance. The pricing approach, on the other hand, functions by inducing a pricing cost proportional to the transmit power, which performs interference regularization by shutting down interferers of high significance. We show that both approaches admit a unique NE in practical scenarios, which boosts up the sum rate significantly in interference-limited scenarios. |