By Ian Wong, Brian Evans
This ebook proposes a unified algorithmic framework in response to twin optimization options that experience complexities which are linear within the variety of subcarriers and clients, and that in attaining negligible optimality gaps in standards-based numerical simulations. Adaptive algorithms in response to stochastic approximation concepts also are proposed, that are proven to accomplish comparable functionality with even a lot reduce complexity. all of the algorithms proposed are essentially awarded in concise block diagrams permitting the reader to enforce those algorithms within the software program in their selection. This publication is an obtainable reference for researchers and practitioners alike.
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Proportional fairness can be attained by setting the user weights as the reciprocal of the user’s average rate so far [55]). We formulate the problem considering ergodic rates for both continuous (capacity-based) and discrete (adaptive modulation and coding ) rates. Note that a similar ergodic formulation for continuous rate maximization has been considered in [38], but they limited their study to the case of maximizing the unweighted sum capacity, and they did not propose efficient algorithms to solve the problem.
Although the focus of this book is primarily on the physical layer transmit optimization, it is important to discuss our assumptions on the cross-layer PHY-MAC interactions in order to see how one can apply the results in PHY-MAC cross-layer optimization discussed in Sec. 4. Specifically, we assume that the upper MAC layer passes the following information to the physical layer optimization routine: • Set of active users M: The MAC layer performs the necessary admission and congestion control to determine which are the active users at a particular time • Priority for the active users wm or φm for all m ∈ M: Depending on queue back-logs and information on the average data rate for each user, the MAC layer sets the appropriate user weights wm in the weighted-sum rate maximization formulations, or the user proportionality values φm in the proportional rate formulations.
Duality, are founded on general geometrical concepts, and are thus also applicable to this infinite dimensional space [64]. Thus, using variational calculus techniques [65], we can extend concepts familiar to deterministic optimization like gradients, subgradients, and Lagrangian duality to this infinite dimensional space. 1) is concave, but the constraint space P is highly non-convex (it is in fact a discrete space), and is in general very difficult to solve. 1) is separable across the subcarriers , and is tied together only by the power constraint.