Existing work on cross-layer optimization for wireless
networks adopts simple physical-layer models, i.e., treating
interference as noise. In this paper, we adopt a recently proposed deterministic channel which is a simple abstraction of
the physical layer that effectively captures the effect of channel
strength, broadcast and superposition in wireless channels.
Within the Network Utility Maximization (NUM) framework, we
study the cross-layer optimization for wireless networks based
on this deterministic channel model. First, we extend the wellapplied
conflict graph model to capture the flow interactions
over the deterministic channels and characterize the feasible rate
region. Then we study distributed algorithms for general wireless
multi-hop networks. The convergence of algorithms is proved
by Lyapunov stability theorem and stochastic approximation
method. Further, we show the convergence to the bounded
neighborhood of optimal solutions with probability one under
constant steps and constant update intervals. Our numerical
evaluation validates the analytical results.