  MIMO technology is one of the most significant advances in the past decade to
increase channel capacity and has a great potential to improve network capacity
for mesh networks. In a MIMO-based mesh network, the links outgoing from each
node sharing the common communication spectrum can be modeled as a Gaussian
vector broadcast channel. Recently, researchers showed that ``dirty paper
coding'' (DPC) is the optimal transmission strategy for Gaussian vector
broadcast channels. So far, there has been little study on how this fundamental
result will impact the cross-layer design for MIMO-based mesh networks. To fill
this gap, we consider the problem of jointly optimizing DPC power allocation in
the link layer at each node and multihop/multipath routing in a MIMO-based mesh
networks. It turns out that this optimization problem is a very challenging
non-convex problem. To address this difficulty, we transform the original
problem to an equivalent problem by exploiting the channel duality. For the
transformed problem, we develop an efficient solution procedure that integrates
Lagrangian dual decomposition method, conjugate gradient projection method
based on matrix differential calculus, cutting-plane method, and subgradient
method. In our numerical example, it is shown that we can achieve a network
performance gain of 34.4% by using DPC.
