Hard Fairness versus Proportional Fairness in Wireless Communications: the Single-Cell Case

Abstract—We consider the uplink and the downlink of a mul-tiuser wireless system with one base station and K user terminals (single-cell case). Each user is affected by a position-dependent path loss, fixed in time, and by a slowly time-varying frequency-selective fading channel modeled as M parallel block-fading channels. We study the system throughput (sum rate) versus Eb/N0 under hard fairness and proportional fairness constraints. We obtain closed-form expressions for the throughput in the limit of a large number of users, as well as for the asymptotics in the low and high SNR regions. I