Resource Allocation for Millimeter Wave Self-Backhaul Network Using Markov Approximation

Millimeter wave (mmW) self-backhaul has been regarded as a high-capacity and low-cost solution to deploy dense small cell networks but its performance depends on a resource allocation strategy, which can effectively reduce interference (including co-tier interference, cross-tier interference, and self-interference). Taking the use of beamforming and the advantage of mmW short-range communication into account, this paper formulates a resource allocation problem in which sub-channels can be shared among low-interference links while orthogonal sub-channels can be used at the links that suffer high-level interference among them. The objective is to maximize the sum data rates of all users while ensuring the data rate of backhaul link at each small cell base station is greater than or equal to the sum data rates of all its served users in the access links. Besides, the data rate of each user should achieve its minimum traffic demand. The optimization problem is a combinatorial integer programming problem with a series of inequality constraints, which is difficult to solve. By introducing penalty function and penalty factors into it, the problem is transferred to an equivalent problem without any inequality, and then it can be addressed by the Markov approximation method. First, by leveraging the log-sum-exp method to approximate the equivalent problem, we deduce the near optimal solution. However, it is difficult to calculate the deduced solution since that it needs all possible solution information, and thus a Markov chain is then utilized to converge to the near optimal solution. The numerical results are shown to verify the performance of the proposed algorithm.