Power Loading in Parallel Diversity Channels Based on Statistical Channel Information

TL;DR

This paper investigates power allocation schemes in SIMO parallel channels with Nakagami-m fading, showing statistical waterfilling approaches optimality as the number of receive antennas grows large, supported by simulations and real data.

Contribution

It proves the convergence rate of statistical waterfilling to the optimal scheme in large antenna systems and compares it with other schemes, providing practical validation.

Findings

Statistical waterfilling converges at O(1/(L log L)) rate.

Other schemes converge at worst at O(1/log L).

Simulations and real ultrawideband data validate the theoretical results.

Abstract

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.