Color of interference and joint encoding and medium access in large wireless networks

We address the problem of resource allocation in extended wireless networks in the presence of user dynamics. We first characterized the first two order statistics of the interference in such networks where users arrive according to a spatio-temporal Poisson process where each user has a certain amount of information to transmit, specified by a probability distribution. We show that, user dynamics and single user behavior dominate the auto-covariance function. We then formulated an optimization problem in order to develop a joint power and rate allocation scheme for systems in which users transmit simultaneously up on arrival, without any collision avoidance or scheduling. We then provide an iterative algorithm to solve the optimization problem, thereby obtaining the rate and power allocation strategy, taking into consideration the correlation of interference and the energy constraints. We also observe that our scheme leads to an interference averaging phenomenon as the transmission duration becomes large, which reduces the outages in the packet transmissions. Our scheme is a low overhead and completely asynchronous over users.