On Optimal Relay Placement and Sleep Control to Improve Energy Efficiency in Cellular Networks

We consider the joint optimization of relay station (RS) placement and RS sleep/active probability to enhance the energy efficiency of a one-dimensional cellular network. When the RSs are always active, conditions for optimal RS placement that minimizes transmission power are derived, based on which closed-form solution is obtained with path-loss exponent being two, and a simple numerical method for general values of path-loss exponent is proposed. When the circuit power consumption of active RSs is considered, RSs should enter sleep mode appropriately to save power. An algorithm based on projected Newton method is proposed to jointly optimize the RS placement and sleep/active probability. It is shown via numerical examples that the benefit of implementing RSs and optimizing RS placement is substantial and increases with the path-loss exponent. We also justify the interaction between RS placement and RS sleep control, which is effectively tackled by the proposed algorithm to minimize the total power consumption.