Optimal Resource Allocation for Parallel Gaussian Broadcast Channels: Minimum Rate Constraints and Sum Power Minimization

A system consisting of $K$ parallel Gaussian broadcast channels over which a transmitter communicates with $M$ receivers is considered. Assuming perfect channel state information, we study the problem of maximizing a weighted sum of rates under a sum power constraint with additional receiver-specific rate constraints. This problem formulation occurs frequently, e.g., in the context of scheduling for cellular downlink systems. Two algorithms are proposed which of one is based on a modified water-filling procedure. This algorithm is also suited to solve the minimum sum power problem.