MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation

Abstract

Abstract-In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs.Index Terms-Gaussian noise channels, minimum mean-square error (MMSE), multiple-input-multiple-output (MIMO) systems, mutual information, optimum power allocation, precoding, waterfilling.

Mercury-Waterfilling for Generalized Multicarrier Signaling

“…5 shows, how the power is allocated after application of the MFP when the input were Gaussian. Such results are of course in line with the origin results provided in [17][18][19][20] and show how the knowledge about the transmit signal distribution can improve the performance of the system. This performance can be expressed either in the maximum achievable rate or minimum required total transmit power.…”

“…However, the optimality of this approach is conditioned by the assumption that the input data are Gaussian distributed, what in typical communication systems is not valid. It has been showed [17,18,20] …”

“…Due to the matrix representation, the matrix solutions derived for origin MFP [17,20] can be applied.…”

“…the phenomena of possibly strong overlapping of neighboring pulses on TF plane. In this paper the idea of application of the Mercury-Water Filling Principle (MFP) [17][18][19][20] in GMC systems is considered. The rationale of the mercury-filling concept, originally proposed for OFDM systems, is the observation that WaterFilling Principle (WFP) [21], known as the best power allocation strategy for multicarrier systems, is optimal only under the assumption that the input values to the channel are Gaussian distributed.…”

“…QAM symbols) are used. The authors of [17,18,20] have showed the benefits that one can gain from possessing of the knowledge about the character of input data. But, as stated above, the mercury-waterfilling concept have been developed for OFDM systems.…”