Total Power Minimization for High Rate Communication in Multi-channel Multi-user Wireless Networks

A key challenge in wireless networks is to control and minimize power. In this paper, we study a total power minimization problem subject to power and Signal-to-Interference-plus-Noise Ratio (SINR) constraints in wireless networks with multiple independent channels. The objective is to minimize the total transmission power of the system while the sum rate targets of channels are satisfied. However, this problem is non-convex and thus is hard to solve. Through the Shannon capacity formula, we establish a connection between power and rate, and get an equivalent transformation of this optimization problem. We transfer the original problem from power domain into rate domain, which plays an important role in using convex approximation next and algorithm design. Then, leveraging the Perron-Frobenius theorem, we reformulate the problem with spectral radius constraint. Finally we obtain an approximated convex problem with rate as variable of the initial optimization problem. Further, we propose a corresponding convex approximation algorithm to get the approximation value. Simulation results evaluate that our algorithm can achieve efficient power and rate allocations.