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OFDMA_Part19

# OFDMA_Part19 - up the optimization problem such that the...

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19 of the loop iteration, the algorithm increases the water level by a bit and rechecks the if condition. Also N is the total number of channels that are available. A graphical illustration with one user and three channels is shown in Figure 6 below. Figure 6. Water-Filling For One User and Three Parallel Channels 3.2 Convex Optimization This section briefly discusses Convex Optimization. The following equations and concepts have been adapted from the book titled Convex Optimization by Boyd and Vandenberghe [22]. Several resource allocation problems are set up in the form of an optimization problem, such as maximizing the sum of data rates or minimizing the sum of powers. Often, researchers try to set
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Unformatted text preview: up the optimization problem such that the function being minimized or maximized is convex. This is done because convex functions can be optimized very easily by using the theory of Convex Optimization. Furthermore, several fast and efficient Convex Optimization packages exist for languages such as MATLAB. All these benefits make Convex Optimization the tool of choice in the field of resource allocation. [22] defines the convex optimization problem as follows: Minimize the target function f ( x ) subject to the constraints f i ( x ) ≤ b i for i = 1,…,N …(E11) The target function f ( x ) and the constraint functions f i ( x ) are convex and have the following properties:...
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