  Design of energy efficient protocols for modern wireless systems has become
an important area of research. In this paper, we propose a distributed
optimization algorithm for the channel assignment problem for multiple
interfering transceiver pairs that cannot communicate with each other. We first
modify the auction algorithm for maximal energy efficiency and show that the
problem can be solved without explicit message passing using the carrier sense
multiple access (CSMA) protocols. We then develop a novel scheme by converting
the channel assignment problem into perfect matchings on bipartite graphs. The
proposed scheme improves the energy efficiency and does not require any
explicit message passing or a shared memory between the users. We derive bounds
on the convergence rate and show that the proposed algorithm converges faster
than the distributed auction algorithm and achieves near-optimal performance
under Rayleigh fading channels. We also present an asymptotic performance
analysis of the fast matching algorithm for energy efficient resource
allocation and prove the optimality for large enough number of users and number
of channels. Finally, we provide numerical assessments that confirm the energy
efficiency gains compared to the state of the art.
