Stochastic Optimization and Its Applications in Multihop Wireless MIMO Networks

In this paper, an algorithm is devised to solve a general mathematical problem of optimizing an expected average cost criterion subject to constraints on both 1) instantaneous resource allocation decisions and 2) the long-term average resource allocation requirements. The construction of the algorithm does not require knowledge about the statistics of the underlying process, yet the performance of this algorithm, under mild mixing conditions on the underlying stochastic process, is shown to converge asymptotically to the optimal under causal observations. This general result is applied to the case of joint power-rate allocation in MIMO wireless multi-hop networks, in which nodes can form broadcast clusters in an attempt to take advantage of dirty paper coding. A distributed implementation of the algorithm is presented for the applied case. The numerical results shows that using dirty paper coding within each broadcast cluster provides a significant improvement over traditional link-based techniques. October 1, 2008 DRAFT