### Energy Efficient Power Allocation for OFDM-Based Cognitive Radio Systems with Partial Intersystem CSI

"... This paper investigates energy efficient power allocation for orthogonal frequency division multiplexing-(OFDM-) based cognitive radio (CR) systems with partial intersystem channel state information (CSI) available. The goal is to maximize energy efficiency (EE) while ensuring the minimum rate of s ..."

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This paper investigates energy efficient power allocation for orthogonal frequency division multiplexing-(OFDM-) based cognitive radio (CR) systems with partial intersystem channel state information (CSI) available. The goal is to maximize energy efficiency (EE) while ensuring the minimum rate of secondary user (SU) and keeping the average interference power (AIP) introduced to primary user (PU) within a target probability level. We propose a suboptimal algorithm to solve this optimization problem based on classic water-filling (WF) technique. Moreover, we first address the relation between EE and water level. In order to reduce complexity, a simplified algorithm with closed-form solution is also proposed. Numerical results are provided to corroborate our theoretical analysis and to demonstrate the effectiveness of the proposed schemes.

### Nonstationary Resource Sharing with Imperfect Binary Feedback: An Optimal Design Framework for Cost Minimization

"... Abstract-We develop a novel design framework for decentralized resource sharing among self-interested users, who adjust their resource usage levels to minimize the costs of resource usage (e.g. energy consumption or payment) while fulfilling minimum payoff (e.g. throughput) requirements. We model t ..."

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Abstract-We develop a novel design framework for decentralized resource sharing among self-interested users, who adjust their resource usage levels to minimize the costs of resource usage (e.g. energy consumption or payment) while fulfilling minimum payoff (e.g. throughput) requirements. We model the users' interaction as a repeated resource sharing game with imperfect monitoring, which captures the following features of the considered interaction. First, the users are decentralized and self-interested, i.e. they aim to minimize their own costs based on their locally available information and will not "blindly" follow the prescribed resource sharing rules unless it is in their self-interests to do so. Second, the users coexist in the system for some time and interact with each other repeatedly. Finally, the players receive a binary feedback informing them about the imperfectly measured interference/congestion level. The key feature of our proposed policy is that it is nonstationary, namely the users choose time-varying resource usage levels. This is in contrast with all existing policies, which are stationary and dictate users to choose constant resource usage levels. The proposed nonstationary policy is also deviation-proof, in that the self-interested users find it in their self-interests to comply with the policy, and it can be constructed by a low-complexity online algorithm that is run by each user in a distributed fashion. Moreover, our proposed policy only requires the users to have imperfect binary feedback, as opposed to existing solutions based on repeated game models which require a large amount of feedback. The proposed design framework applies to many resource sharing systems, such as power control, medium access control (MAC), and flow control. As a motivating example, we investigate the performance improvement of our nonstationary policy over state-of-the-art policies in power control, and show that significant performance gain (up to 90% energy saving) can be achieved.

### unknown title

, 2012

"... The price of re-establishing perfect, almost perfect or public monitoring in games with arbitrary monitoring ..."

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The price of re-establishing perfect, almost perfect or public monitoring in games with arbitrary monitoring

### Author manuscript, published in "International Sympotsium on Comunications, Control and Signal Processing, Cyprus (2010)" Implicit cooperation in distributed energy-efficient networks

, 2010

"... Abstract—We consider the problem of cooperation in distributed wireless networks of selfish and free transmitters aiming at maximizing their energy-efficiency. The strategy of each transmitter consists in choosing his power control (PC) policy. Two scenarios are considered: the case where transmitte ..."

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Abstract—We consider the problem of cooperation in distributed wireless networks of selfish and free transmitters aiming at maximizing their energy-efficiency. The strategy of each transmitter consists in choosing his power control (PC) policy. Two scenarios are considered: the case where transmitters can update their power levels within time intervals less than the channel coherence time (fast PC) and the case where it is updated only once per time interval (slow PC). One of our objectives is to show how cooperation can be stimulated without assuming cooperation links between the transmitters but only by repeating the corresponding PC game and by signals from the receiver. In order to design efficient PC policies, standard and stochastic repeated games are respectively exploited to analyze the fast and slow PC problems. In the first case a cooperation plan between transmitters, that is both efficient and relies on mild information assumptions, is proposed. In the second case, the region of equilibrium utilities is derived from very recent and powerful results in game theory. I.

### (2012)" Mean Field Energy Games in Wireless Networks

, 2013

"... Abstract—This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a state given by the available energy and/or the indivi ..."

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Abstract—This work tackles the problem of energy-efficient distributed power control in wireless networks with a large number of transmitters. The problem is modeled by a dynamic game. Each transmitter-receiver communication is characterized by a state given by the available energy and/or the individual channel state and whose evolution is governed by certain dynamics. Since equilibrium analysis in such a (stochastic) game is generally difficult and even impossible, the problem is approximated by exploiting the large system assumption. Under an appropriate exchangeability assumption, the corresponding mean field game is well defined and studied in detail for special cases. The main contribution of this work is to show how mean field games can be applied to the problem under investigation and provide illustrative numerical results. Our results indicate that this approach can lead to significant gains in terms of energyefficiency at the resulting equilibrium. I.

### Distributed Cross-layer Power Control in Pre-equalized Dwnlink of a MC-CDMA System

"... The main purpose of this elaboration is to determine the optimal powers of mobile users in a multi-carrier CDMA (MC-CDMA) system receiving data from a base station (BS). The downlink transmission is pre-equalized and the utility function is a generalized energy efficiency (EE) based on a cross-layer ..."

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The main purpose of this elaboration is to determine the optimal powers of mobile users in a multi-carrier CDMA (MC-CDMA) system receiving data from a base station (BS). The downlink transmission is pre-equalized and the utility function is a generalized energy efficiency (EE) based on a cross-layer approach and taking into account the presence of a queue. We rely on game theory as a mathematical tool by considering a non-cooperative game whose equilibrium point is called Nash equilibrium (NE) defining the optimal powers. Accordingly, we developed a distributed algorithm aiming at determining this equilibrium. When the subcarriers number increases, important interference is then introduced. In such case, we showed that the social welfare (sum of utilities of all users) decreases while powers at NE increase. In addition, we deduced that a good choice of the consumed power leads to minimize the individual power and maximize the utility at the NE. Moreover, we noticed that when the packet arrival rate increases, the considered generalized EE can be maximized compared to the conventional EE approach while the power at the NE can be minimized. Therefore, we contribute to improve globally the system performances in terms of social welfare, individual utility function and individual power. General Terms: power control, game theory, non-cooperative game

### Repeated Inter-Session Network Coding Games: Efficiency and Min-Max Bargaining Solution

"... Abstract — Recent results have shown that selfish users do not have an incentive to participate in inter-session network coding in a static non-cooperative game setting. Because of this, the worst-case network efficiency (i.e., the price-of-anarchy) can be as low as 20%. In this paper, we show that ..."

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Abstract — Recent results have shown that selfish users do not have an incentive to participate in inter-session network coding in a static non-cooperative game setting. Because of this, the worst-case network efficiency (i.e., the price-of-anarchy) can be as low as 20%. In this paper, we show that if the same game is played repeatedly, then the price-of-anarchy can be improved to 36%. We design a grim-trigger strategy that encourages users to cooperate and participate in the inter-session network coding. A key challenge is to determine a common cooperative coding rate that the users should mutually agree on. We resolve the conflict of interest among the users through a bargaining process, and obtain tight upper bounds for the price-of-anarchy which are valid for any possible bargaining scheme. Moreover, we propose a simple and efficient min-max bargaining solution that can achieve these upper bounds, as confirmed through simulation studies. The co-existence of multiple selfish network coding sessions as well as the co-existence of selfish network coding and routing sessions are also investigated. Our results represent a first step towards designing practical inter-session network coding schemes which achieve reasonable performance for selfish users. I.