Spectrum Allocation, Power Control, Routing, and Congestion Control for Wireless Networks with Duplexing Constraints

We develop distributed algorithms to allocate resources in multi-hop wireless networks so as to minimize the total cost. In order to observe the fundamental duplexing constraint, we first devise a spectrum allocation scheme that divides the whole spectrum into multiple sub-bands and activates conflict- free links on each sub-band. We show that the minimum number of required sub-bands grows asymptotically at a logarithmic rate with the chromatic number of network connectivity graph. A simple distributed and asynchronous algorithm is developed to feasibly activate links on the available sub-bands. We then develop node-based distributed algorithms for optimally controlling the transmission powers on active links for each sub-band, jointly with traffic routes and user input rates in response to channel states and traffic demands. We show that the algorithms asymptotically converge to the optimal operating point.