Signal quality pricing: Decomposition for spectrum scheduling and system configuration

Who gets to use radio spectrum, and when, where, and how? Many problems in traditional radio communication, wireless networking, and cognitive radio are variants of this question. Optimization decomposition based on Lagrangian relaxation of signal quality requirements provides a mathematical framework for solving this type of combined problem. This paper demonstrates the technique as a solution to optimal spatial reuse time-division multiple access (STDMA) scheduling with reconfigurable antennas. The joint beam steering and scheduling (JBSS) problem offers both a challenging mathematical structure and significant practical value. We present algorithms for JBSS and describe an implemented system based on these algorithms. We achieve up to 600% of the throughput of TDMA with a mean of 234% in our experiments. The decomposition approach leads to a working distributed protocol which is provably equivalent to our original problem statement while also producing optimal solutions in an amount of time that is at worst linear in the size of the input. This is, to the best of our knowledge, the first actually implemented wireless scheduling system based on dual decomposition. We identify and briefly address some of the challenges that arise in taking such a system from theory to reality.