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We consider the uplink of a cellular communication system with $K$ users percell and infinite base stations equally spaced on a line. The system isconventional, i.e., it does not make use of joint cell-site processing. A hardfairness (HF) system serves all users with the same rate in any channel state.In contrast, a system based on proportional fairness serves the users withvariable instantaneous rates depending on their channel state. We compare thesetwo options in terms of the system spectral efficiency \textsf{C} (bit/s/Hz)versus $E_b/N_0$. Proportional fair scheduling (PFS) performs generally betterthan the more restrictive HF system in the regime of low to moderate SNR, butfor high SNR an optimized HF system achieves throughput comparable to that ofPFS system for finite $K$. The hard-fairness system is interference limited. Wecharacterize this limit and validate a commonly used simplified model thattreats outer cell interference power as proportional to the in-cell total powerand we analytically characterize the proportionality constant. In contrast, thespectral efficiency of PFS can grow unbounded for $K \to \infty$ thanks to themultiuser diversity effect. We also show that partial frequency/time reuse canmitigate the throughput penalty of the HF system, especially at high SNR.

Hard Fairness Versus Proportional Fairness in Wireless Communications: The Multiple-Cell Case