We consider multiuser multicarrier systems, where each non-symmetrically distributed user reports only partial indices of subcarriers whose normalized SNRs exceed the predetermined threshold so that only partial feedback information is available at the base station. To accommodate both efficiency and fairness, the base station is assumed to perform the normalized SNR based proportional fair scheduling (PFS). Using the simple and quite well matched approximation of the ordered channel capacity, the approximated ergodic capacity of the full SNR feedback scheme is derived as well as the exact expression of the ergodic capacity of the partial index feedback scheme. Their asymptotic behaviors as the number of users and average SNR increase are also derived. An important finding through the performance analysis and numerical examples in this paper is that, also in the non-symmetrical multiuser distributed multicarrier system performing the PFS with limited feedback, the ergodic capacity of the optimal asymptotic growth rate can be achieved, keeping the average feedback overhead bounded regardless of the number of users.