Robust Power Allocation for Parallel Gaussian Channels with Approximately Gaussian Input Distributions

In both wired and wireless communication networks, power allocation is an important technique to improve system performance. This paper investigates the power allocation problem for parallel Gaussian channels from an information-theoretic perspective with the aim of maximizing the sum of mutual informations (i.e., an achievable data rate). If all the inputs are Gaussian, it is well-known that the waterfilling policy provides an optimal solution. For arbitrary input distributions, a generalization of waterfilling, so-called mercury/waterfilling, provides an optimal solution in terms of the minimum mean square errors (MMSEs). However, the difficulty of obtaining closed-form analytical expressions of the MMSE often makes computing the mercury/waterfilling solution challenging. This paper proposes a robust waterfilling power allocation (RPA) policy for parallel Gaussian channels when the input distributions are close to Gaussian distributions in the Kullback-Leibler (KL) divergence (relative entropy). First, it is shown that the proposed policy results in water-levels that are close to the optimal ones in a well-defined sense. Second, tight bounds for the loss in mutual information (data rate) are given. This bounded loss property makes the proposed power allocation policy robust and approximately optimal, which is illustrated by means of various simulation setups. Moreover, the RPA policy provides a general framework for solving the power allocation problem for parallel channels, with the classical waterfilling being included as a special case. Finally, the RPA policy is argued to be scalable with the number of users since it inherently uses the classical low complexity waterfilling.