Stochastic optimization based on the Laplace transform order with applications to precoder designs

Stochastic optimization arising from precoding in a multi-antenna fading channel with channel mean feedback to maximize data rates is important but challenging. The use of relaying further complicates the situation, as it may induce a nonconvex structure in the objective function, thereby excluding the use of existing approaches which re quire convexity or concavity. To deal with challenges as such, this paper presents a new framework for solving a class of stochastic optimization problems. The analysis here involves the comparison of two nonnegative random variables in the Laplace transform order. Our framework is particularized to optimal precoding for maximum ergodic or effective capacity in multi-antenna channels with or with out relaying assuming channel mean feedback, where the objectives may or may not have convexity or concavity. The application to stochastic power allocation is also discussed.