Hard fairness versus proportional fairness in wireless communications: The Multiple-Cell Case

We consider the uplink of a cellular communication system with K users per cell and infinite base stations equally spaced on a line. We consider a conventional system that does not make use of joint cell-site processing and compare delay-limited systems and proportional fair scheduling (PFS) systems in terms of the system spectral efficiency C (bit/s/Hz) versus E_b/N₀. PFS performs generally better than the delay-limited system in the regime of low to moderate SNR, but for high SNR the optimal delay-limited system achieves throughput comparable to the PFS system with finite users. The delay-limited system is interference limited. We characterize this limit and validate a commonly made assumption, that outer-cell interference power is equal to a multiplicative factor times the total cell transmit power. In contrast, the spectral efficiency of PFS system can grow without bound if the number of users tends to infinity, thanks to the multiuser diversity effect.