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Several important design problems in signal processing for communications can be cast as optimization problems in which the objective is a function of the subspaces spanned by tall complex matrix variables with orthonormal columns. Such problems can be viewed as optimization problems on the complex Grassmann manifold, and an effective means for performing this optimization is to use a Grassmannian...
In many half-duplex cooperative systems, the direct formulation of the problem of finding the jointly optimal power and channel resource allocation that maximizes a weighted sum of the achievable rates can be difficult to solve. In this paper, we provide an efficient algorithm to solve this problem for a class of systems with convex achievable rate regions. For those systems, we show that the weighted-sum-rate...
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