Wireless systems and interference avoidance

Motivated by the emergence of programmable radios, we seek to understand a new class of communication system where pairs of transmitters and receivers can adapt their modulation/demodulation method in the presence of interference to achieve better performance. Using signal to interference ratio as a metric and a general signal space approach, we present a class of iterative distributed algorithms for synchronous systems which results in an ensemble of optimal waveforms for multiple users connected to a common receiver (or colocated independent receivers). That is, the waveform ensemble meets the Welch (1974) bound with equality and, therefore, achieves minimum average interference over the ensemble of signature waveforms. We derive fixed points for a number of scenarios, provide examples, look at ensemble stability under user addition and deletion as well as provide a simplistic comparison to synchronous code-division multiple-access. We close with suggestions for future work.