Abstract-Demand-side management, together with the integration of distributed energy generation and storage, are considered increasingly essential elements for implementing the smart grid concept and balancing massive energy production from renewable sources. We focus on a smart grid in which the demand-side comprises traditional users as well as users owning some kind of distributed energy sources and/or energy storage devices. By means of a day-ahead optimization process regulated by an independent central unit, the latter users intend to reduce their monetary energy expense by producing or storing energy rather than just purchasing their energy needs from the grid. In this paper, we formulate the resulting grid optimization problem as a noncooperative game and analyze the existence of optimal strategies. Furthermore, we present a distributed algorithm to be run on the users' smart meters, which provides the optimal production and/or storage strategies, while preserving the privacy of the users and minimizing the required signaling with the central unit. Finally, the proposed day-ahead optimization is tested in a realistic situation.

Abstract-Many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure; the classical example is the capacity-achieving solution for a frequency-selective channel. For simple waterfilling solutions with a single waterlevel and a single constraint (typically, a power constraint), some algorithms have been proposed in the literature to compute the solutions numerically. However, some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints. For such cases, it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure. In addition, a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing.The purpose of this paper is twofold. On the one hand, it overviews the waterfilling results existing in the literature from a unified viewpoint. On the other hand, it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice; to be more precise, it provides a practical algorithm to evaluate numerically a general waterfilling solution, which includes the currently existing waterfilling solutions and others that may possibly appear in future problems.

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Abstract-This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high 0 . Index Terms-Correlated fading, free probability, multipleinput multiple-output (MIMO) capacity, random matrix theory.

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