Several practical multi-user multi-carrier communication systems arecharacterized by a multi-carrier interference channel system model where theinterference is treated as noise. For these systems, spectrum optimization is apromising means to mitigate interference. This however corresponds to achallenging nonconvex optimization problem. Existing iterative convexapproximation (ICA) methods consist in solving a series of improving convexapproximations and are typically implemented in a per-user iterative approach.However they do not take this typical iterative implementation into account intheir design. This paper proposes a novel class of iterative approximationmethods that focuses explicitly on the per-user iterative implementation, whichallows to relax the problem significantly, dropping joint convexity and evenconvexity requirements for the approximations. A systematic design framework isproposed to construct instances of this novel class, where several newiterative approximation methods are developed with improved per-user convex andnonconvex approximations that are both tighter and simpler to solve (inclosed-form). As a result, these novel methods display a much fasterconvergence speed and require a significantly lower computational cost.Furthermore, a majority of the proposed methods can tackle the issue of gettingstuck in bad locally optimal solutions, and hence improve solution qualitycompared to existing ICA methods.
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