Power Spectrum Optimization of Multi-Carrier MIMO Ad Hoc Networks: A Dual Stochastic Approximation Approach

Multi-carrier MIMO (MC-MIMO) has emerged as a promising technology to provide significant capacity gain for broadband wireless ad hoc networks. However, due to the non-convex and large-scale problem structure, little work has been done on power spectrum optimization to harvest MC-MIMO’s capacity gain for broadband ad hoc networks. Our principal goal in this work is to fill this challenging gap. First, we make advance in general non-convex optimization theory by showing a surprising result that the duality gap of a certain class of non-convex optimization problems is zero if they satisfy the “concave perturbation” condition. Further, we show that the power spectrum optimization problem of MC-MIMO ad hoc networks satisfies the concave perturbation condition. This important result allows us to tackle the problem with a much lower complexity in the dual domain, where we design efficient centralized and distributed algorithms based on complete knowledge of channel distribution information (CDI). To further eliminate the requirement of complete CDI knowledge, we devise an online adaptive algorithm by stochastic approximation. We show that, when the feedback of channel state information (CSI) is error free, our proposed subgradient stochastic approximation (SSA) algorithm converges with probability one to the same optimal solution obtained by the off-line algorithm. In the case where there is error in CSI, we show that SSA can still converge with probability one to the same optimal solution if the resultant subgradients are asymptotically unbiased, or is recurrent to some neighborhood of the optimal solution when the resultant subgradients are biased.