Abstract
In the general model introduced in Chap. 2, the physical layer of a wireless communication system is described by a set of feasible physical layer parameter setups \(\mathcal{X}1\) and a rate function r that assigns a rate vector r(x1) to every feasible parameter setup \(\mathit{x}1 \in \mathcal{X}1\).
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Notes
- 1.
Assuming that P ≥ 0.
- 2.
The rate function is concave if h k = 0 for all but one users. This case is of little interest as it basically corresponds to a single-user system.
- 3.
The following parameters were used to generate the figure: \(P/{\sigma }^{2} = 10\), h 1 = (2, 1), h 2 = (1, 2).
- 4.
Another benefit of using the distance in rate space as convergence criterion is that an examination of the continuity properties of f is not required. The function f is obviously not continuous at β0, and continuity at β > β0 is not obvious.
- 5.
Corollary 4.1.9 requires \(\mathcal{X}D = \mathcal{X}{D}^{{\prime}}\).
- 6.
Here, the term “efficient solution” refers to solution whose computational complexity is practically feasible for large K.
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© 2012 Springer-Verlag Berlin Heidelberg
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Brehmer, J. (2012). Physical Layer Models. In: Utility Maximization in Nonconvex Wireless Systems. Foundations in Signal Processing, Communications and Networking, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17438-4_4
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DOI: https://doi.org/10.1007/978-3-642-17438-4_4
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