We address the problem of distributed power control in a two-tier cellular network, where full-duplex small cells underlay a macro cell in a co-channel deployment scenario. We first formulate the distributed power control problem as a non-cooperative game and then extend it to a repeated game with imperfect public monitoring. The repeated game formulation prevents deceitful small cells from deviating from the social optimal solution for their own benefit. We establish the existence and uniqueness of the Nash equilibrium in the formulated non-cooperative game. We also characterize the set of public perfect equilibrium for the repeated game. A two-phase distributed algorithm is proposed to achieve and enforce a Pareto optimal transmit power profile. The solution obtained by this algorithm is also social optimal. Phase 1 of the algorithm is a fully distributed learning phase based on perturbed Markov chains, where each base station individually learns a Pareto optimal operating point. Phase 2 is composed of two rules: 1) a detection rule based on Page-Hinckley test to detect cheating and 2) a punishment rule to motivate cheating base stations to cooperate. Through theoretical analysis, we prove that the proposed distributed power control mechanism achieves a public perfect equilibrium point of the formulated repeated game. The power control algorithm is also cheat-proof and needs only a small amount of information exchange among network nodes. The effectiveness of the algorithm is shown through numerical analysis. Our proposed model, algorithm, and analysis are also valid for a half-duplex system as a special case.

Device-to-device (D2D) communications can enhance spectrum and energy efficiency due to direct proximity communication and frequency reuse. However, such performance enhancement is limited by mutual interference and energy availability, especially when the deployment of D2D links is ultra-dense. In this paper, we present a distributed power control method for ultra-dense D2D communications underlying cellular communications. In this power control method, in addition to the remaining battery energy of the D2D transmitter, we consider the effects of both the interference caused by the generic D2D transmitter to others and the interference from all others caused to the generic D2D receiver. We formulate a mean-field game (MFG) theoretic framework with the interference mean-field approximation. We design the cost function combining both the performance of the D2D communication and cost for transmit power at the D2D transmitter. Within the MFG framework, we derive the related Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations. Then, a novel energy and interference aware power control policy is proposed, which is based on the Lax-Friedrichs scheme and the Lagrange relaxation. The numerical results are presented to demonstrate the spectrum and energy efficiency performances of our proposed approach.

Distributed resource allocation is considered as a significant feature of future self-organizing wireless networks. On the other hand, full-duplex transmission is an emerging technology which can theoretically double the data rate. and hence enhance the performance of wireless networks significantly. In this work, we address the problem of distributed power control in a two-tier network with full-duplex small cells underlaying one macro cell in a co-channel deployment scenario. We first formulate the corresponding distributed power control problem as a non-cooperative game and then extend it to a repeated game with imperfect public monitoring. The repeated game setting is used as it can withstand cheating. We show the existence and uniqueness of the Nash equilibrium of the formulated non-cooperative game and characterize the set of perfect public equilibrium for the repeated game. A two phase distributed algorithm is then proposed to achieve a power profile which is also a perfect public equilibrium. The power control algorithm is cheat-proof and needs only a small amount of information exchange among network nodes. The effectiveness of the algorithm is shown using numerical results. Our proposed algorithm and analysis are also valid for a half-duplex system as it is a special case of the full-duplex model presented in the paper.

A novel distributed power control paradigm is proposed for dense small cell networks co-existing with a traditional macrocellular network. The power control problem is first modeled as a stochastic game and the existence of the Nash Equilibrium is proven. Then, we extend the formulated stochastic game to a mean field game (MFG) considering a highly dense network. An MFG is a special type of differential game which is ideal for modeling the interactions among a large number of entities. We analyze the performance of two different cost functions for the mean field game formulation. Both of these cost functions are designed using stochastic geometry analysis in such a way that the cost functions are valid for the MFG setting. A finite difference algorithm is then developed based on the Lax-Friedrichs scheme and Lagrange relaxation to solve the corresponding MFG. Each small cell base station can independently execute the proposed algorithm offline, i.e., prior to data transmission. The output of the algorithm shows how each small cell base station should adjust its transmit power in order to minimize the cost over a predefined period of time. Moreover, sufficient conditions for the uniqueness of the mean field equilibrium for a generic cost function are also given. The effectiveness of the proposed algorithm is demonstrated via numerical results.

We propose an evolutionary game theory (EGT)-based distributed resource allocation scheme for small cells underlaying a macro cellular network. EGT is a suitable tool to address the problem of resource allocation in self-organizing small cells since it allows the players with bounded-rationality to learn from the environment and take individual decisions for attaining the equilibrium with minimum information exchange. EGT-based resource allocation can also provide fairness among users. We show how EGT can be used for distributed subcarrier and power allocation in orthogonal frequency-division multiple access (OFDMA)-based small cell networks while limiting interference to the macrocell users below given thresholds. Two game models are considered, where the utility of each small cell depends on average achievable signal-to-interference-plus-noise ratio (SINR) and data rate, respectively. Forthe proposed distributed resource allocation method, the average SINR and data rate are obtained based on a stochastic geometry analysis. Replicator dynamics is used to model the strategy adaptation process of the small cell base stations and an evolutionary equilibrium is obtained as the solution. Based on the results obtained using stochastic geometry, the stability of the equilibrium is analyzed. We also extend the formulation by considering information exchange delay and investigate its impact on the convergence of the algorithm. Numerical results are presented to validate ourtheoretical findings and to show the effectiveness of the proposed scheme in comparison to a centralized resource allocation scheme.