First-and second-order statistics that can be attained at a practical receiver via maximum-ratio combining (MRC) reception across correlated Nakagami-m branches are studied in this paper. A lump sum of the branch weight squares is employed in the conventional analysis of the MRC reception. The conventional MRC reception whose first-and second-order statistics were only derived on a noise-free condition can never be achieved in practice because the branches, which are smeared by crosscorrelation and are corrupted by noise, can only be statistically specified and they must be considered of as stochastic processes at the receiver, instead of deterministic time functions. The proposed method, in fact, considers the branch weights as stochastic processes and effectively restores diversity by the assistance from a linear transformation. Significant component selection combining (SCSC) can hence be applied not only to simplify the inner receiver but also to reduce the estimation error and the thermal noise. The MRC reception is then conducted with assistance from estimates of the decorrelated branches that are selected by the SCSC methods. The performance merit figures, i.e., first-and second-order statistics, must be redefined in the post-inner-receiving sense to provide sufficient and accurate information required for the design or the derivations of the outer receiving techniques or algorithms. The first-and second-order statistics of the MRC reception over the significant decorrelated diversity branches were verified by computer simulations.