  In this paper, we show that there exists an arbitrary number of power
allocation schemes that achieve capacity in systems operating in parallel
channels comprised of single-input multiple-output (SIMO) Nakagami-m fading
subchannels when the number of degrees of freedom L (e.g., the number of
receive antennas) tends to infinity. Statistical waterfilling -- i.e.,
waterfilling using channel statistics rather than instantaneous channel
knowledge -- is one such scheme. We further prove that the convergence of
statistical waterfilling to the optimal power loading scheme is at least O(1/(L
log(L))), whereas convergence of other schemes is at worst O(1/log(L)). To
validate and demonstrate the practical use of our findings, we evaluate the
mutual information of example SIMO parallel channels using simulations as well
as new measured ultrawideband channel data.
