Fair Resource Allocation for the Gaussian Broadcast Channel with ISI

We consider fair resource allocation in Gaussian frequency-division broadcast channel with intersymbol interference. The goal is to allocate power and subchannels in a way such that proportional fairness is achieved. We show that the subchannel allocation problem is NP-hard. If multiple users are allowed to time-share a subchannel, the relaxed problem is equivalent to the cake cutting problem and can be efficiently solved. For the joint power and subchannel allocation problem, we propose an iterative method, which solves the power allocation problem and subchannel allocation problem alternately. Simulation results show that its performance is nearly optimal.