Power Optimization on a Random Wireless Network

Consider a wireless network of transmitter-receiver pairs. The transmitters adjust their powers to maintain a particular SINR target at the corresponding receiver in the presence of interference from neighboring transmitters. In this paper we analyze the power vector that achieves this target (and hence is optimal) in the presence of randomness in the network. The randomness is realized by randomly turning off a fraction of transmitter-receiver pairs in a regular lattice. We show that the problem is identical to the so-called Anderson model, which describes the motion of electrons in a dirty metal. We show that traditional random matrix theory is only an approximation that, while accurate in some cases, fails to fully describe the system. We apply the coherent potential approximation (CPA), which is equivalent to random matrix theory, to evaluate the average power vector. We also find that although beyond a certain point the infinite system is infeasible with probability one, any arbitrarily large, but finite system has a typically small probability of becoming infeasible. The CPA framework allows us to calculate this outage probability with exponential accuracy by showing that it is proportional to the tails of the eigenvalue distribution of the system.