Power Control and Scheduling For Low SNR Region in the Uplink of Two Cell Networks

In this paper we investigate the sub-channel assignment and power control to maximize the total sum rate in the uplink of two-cell network. It is assumed that there are some sub-channels in each cell which should be allocated among some users. Also, each user is subjected to a power constraint.
The underlying problem is a non-convex mixed integer non-linear optimization problem which does not have a trivial solution. To solve the problem, having fixed the consumed power of each user, and assuming low co-channel interference region, the sub-channel allocation problem is reformulated into a more mathematically tractable problem which is shown it can be tackled through the so-called Hungarian algorithm.
Then, the consumed power of each user is reformulated as a quadratic fractional problem which can be numerically derived. Numerical results demonstrate the superiority of the proposed method in low SNR region as compared to existing works addressed in the literature.