  Capacity is one of the most important performance metrics for wireless
communication networks. It describes the maximum rate at which the information
can be transmitted of a wireless communication system. To support the growing
demand for wireless traffic, wireless networks are becoming more dense and
complicated, leading to a higher difficulty to derive the capacity.
Unfortunately, most existing methods for the capacity calculation take a
polynomial time complexity. This will become unaffordable for future
ultra-dense networks, where both the number of base stations (BSs) and the
number of users are extremely large. In this paper, we propose a fast algorithm
TOSE to estimate the capacity for ultra-dense wireless networks. Based on the
spiked model of random matrix theory (RMT), our algorithm can avoid the exact
eigenvalue derivations of large dimensional matrices, which are complicated and
inevitable in conventional capacity calculation methods. Instead, fast
eigenvalue estimations can be realized based on the spike approximations in our
TOSE algorithm. Our simulation results show that TOSE is an accurate and fast
capacity approximation algorithm. Its estimation error is below 5%, and it runs
in linear time, which is much lower than the polynomial time complexity of
existing methods. In addition, TOSE has superior generality, since it is
independent of the distributions of BSs and users, and the shape of network
areas.
