  This paper derives the asymptotic distribution of the normalized $k$-th
maximum order statistics of a sequence of non-central chi-square random
variables with non-identical non-centrality parameter. We demonstrate the
utility of these results in characterizing the signal to noise ratio in three
different applications in wireless communication systems where the statistics
of the $k$-th maximum channel power over Rician fading links are of interest.
Furthermore, we derive simple expressions for the asymptotic outage
probability, average throughput, achievable throughput, and the average bit
error probability. The proposed results are validated via extensive Monte Carlo
simulations.
