Complexity Analysis of Joint Subcarrier and Power Allocation for the Cellular Downlink OFDMA System

Consider the cellular downlink orthogonal frequency division multiple access (OFDMA) system where a single transmitter transmits signals to multiple receivers on multiple discrete subcarriers. To adapt fast channel fluctuations, the transmitter should be able to dynamically allocate subcarrier and power resources. Assuming perfect channel knowledge, we formulate the joint subcarrier and power allocation problem as two optimization problems: the first is the one of minimizing the total transmission power subject to quality of service constraints, and the second is the one of maximizing a system utility function subject to power budget constraints. In this letter, we show that both the aforementioned formulations of the joint subcarrier and power allocation problem are generally NP-hard. We also identify several subclasses of the problems, which are polynomial time solvable.