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We derive exact closed-form expressions for the system-level theoretical spectral efficiency of cellular radio systems that use channel-aware schedulers and operate in the presence of co-channel interference and noise. The co-channel interferers are not identically distributed, as is the case in typical cellular layouts. Accounting for non-identical interferers avoids the loose spectral efficiency bounds in the literature that only look at the worst case and best case locations of identical co-channel interferers. It also enables including the effect of second-tier interferers in the cellular layout, and leads to analytical results that are in excellent agreement with the simulation results. The spectral efficiencies of the greedy Max-SINR and the fair round-robin scheduler are compared. The detrimental effect of using small modulation alphabet sizes, as is the case in second and third generation cellular standards, is also quantified.