An approach to the second-order statistics of maximum-ratio combining-like reception over independent Nakagami channels

A statistical approach facilitating performance assessment in maximum-ratio combining (MRC)-like reception over independent nonidentically distributed (INID) Nakagami-m fading channels was investigated. Using the proposed method, generalized simple closed-form second-order statistics, i.e., level-crossing rate (LCR) and average fade duration (AFD), can be readily formulated. These second-order statistics can be classified as generalized because multiple (i.e., not limited to two) identically or nonidentically distributed diversity branches can be incorporated. These closed formulations can be accurately applied in various practical environments where nonidentically distributed branches are presented, e.g., single-user single-input-multiple-output (SU-SIMO) applications, relay networks, and macrodiversity reception in wideband code-division multiple access (W-CDMA) communications. The analytic formulations derived in this work were comprehensively verified in computer simulations. The derived closed forms were also carefully verified by comparison with those obtained using the true MRC in the degenerate scenarios, i.e., those in which only two diversity branches exist or where identically distributed diversity branches can be assumed. The derived closed formulations of the second-order statistics were shown to be generalized, accurate, easily evaluated, and clearly insightful with respect to their physical interpretation although they are approximate to those of the true MRC.