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We develop distributed algorithms to allocate resources in multi-hop wirelessnetworks with the aim of minimizing total cost. In order to observe thefundamental duplexing constraint that co-located transmitters and receiverscannot operate simultaneously on the same frequency band, we first devise aspectrum allocation scheme that divides the whole spectrum into multiplesub-bands and activates conflict-free links on each sub-band. We show that theminimum number of required sub-bands grows asymptotically at a logarithmic ratewith the chromatic number of network connectivity graph. A simple distributedand asynchronous algorithm is developed to feasibly activate links on theavailable sub-bands. Given a feasible spectrum allocation, we then designnode-based distributed algorithms for optimally controlling the transmissionpowers on active links for each sub-band, jointly with traffic routes and userinput rates in response to channel states and traffic demands. We show thatunder specified conditions, the algorithms asymptotically converge to theoptimal operating point.

Distributed Algorithms for Spectrum Allocation, Power Control, Routing, and Congestion Control in Wireless Networks