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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.