In this letter, the use of adaptive source transmission with amplify-and-forward relaying is proposed. Three different adaptive techniques are considered: (i) optimal simultaneous power and rate adaptation; (ii) constant power with optimal rate adaptation; (iii) channel inversion with fixed rate. The capacity upper bounds of these adaptive protocols are derived for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) Rayleigh fading and non-i.i.d.
Rayleigh fading environments. The capacity analysis is based on an upper bound on the effective received signal-to-noise ratio (SNR). The tightness of the upper bound is validated by the use of a lower bound and by Monte Carlo simulation. It isshown that at high SNR the optimal simultaneous power and rate adaptation and the optimal rate adaptation with constant power provide roughly the same capacity. Channel inversion is shown to suffer from a deterioration in capacity relative to the other adaptive techniques.
We propose a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Each stage models dispatching and transmission decisions that are made on subsequent time periods. Certain generation decisions are made only in the first stage and the second stage realizes the actual renewable generation, where the uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using extra, high marginal-cost power sources that can be tapped in short order. We propose two outer approximation algorithms to solve this nonconvex optimization problem to optimality. We show that under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. Numerical experiments for a variety of parameter settings were carried out to indicate the efficiency and usability of this method of large practical instances.
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