Spectrum Coordination in Energy Efficient Cognitive Radio Networks

Device coordination in open spectrum systems is a challenging problem, particularly since users experience varying spectrum availability over time and location. In this paper, we propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, we address a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. In particular, we show that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. We also show that when users experience very different channel gains on their two carriers, they may choose to transmit on the same carrier at the Stackelberg equilibrium as this contributes enough energy efficiency to outweigh the interference degradation caused by the mutual transmission. Then, we provide an algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case and the throughput-based-utility systems. Typically, it is shown that the proposed Stackelberg decision approach optimizes the energy efficiency while still maximizing the throughput at the equilibrium.Comment: 12 pages, 10 figures, to appear in IEEE Transactions on Vehicular Technolog

Multi-Leader Multi-Follower Model with Aggregative Uncertainty

We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated

Bilevel optimization of Eco-Industrial parks for the design of sustainable resource networks

This work presents a bilevel programming framework for the design of sustainable resource networks in eco-industrial parks (EIP). First, multiobjective optimization methods are explored in order to manage the multi-criteria nature of EIP network design problems. Then, different case studies are modeled in order to minimize and maintain in equilibrium participating plants operating costs while minimizing resource consumption. Thus, the structure of the model is constituted by a bilevel programming framework where the enterprises’ plants play a Nash game between them while being in a Stackelberg game structure with the authority. This structure defines a model which, in order to be solved, has to be transformed into a MOPEC (Multiple Optimization Problems with Equilibrium Constraints) structure. Regarding the case studies, monocontaminant water networks in EIP are studied first, where the influence of plants operating parameters are studied in order to determine the most important ones to favor the symbiosis between plants. The water network is composed of a fixed number of process and water regeneration units where the maximal inlet and outlet contaminant concentrations are defined a priori. The aim is to determine which processes are interconnected and the water regeneration allocation. Obtained results highlight the benefits of the proposed model structure in comparison with traditional multiobjective approaches, by obtaining equilibrate different plants operating costs (i.e. gains between 12-25%) while maintaining an overall low resource consumption. Then, other case studies are approached by using the bilevel structure to include simultaneously energy networks in a multi-leader-multi-follower formulation where both environmental authorities are assumed to play a noncooperative Nash game. In the first case study, economic gain is proven to be more significant by including energy networks in the EIP structure. The second industrial case study explores a supply-demand utility network model where the environmental authority aims to minimize the total equivalent CO2 emissions in the EIP. In all cases, the enterprises’ plants are encouraged to participate in the EIP by the extremely favorable obtained results