Abstract

A large body of optimization problems abound in the telecommunications field, particularly enticing ones relating to resource optimization in communication systems. In this talk, we will consider power allocation optimization problems in multiple-input multiple-output (MIMO) Gaussian channels with arbitrary discrete inputs, that represent a large number of relevant communications scenarios such as multiple antenna systems, code division multiple access (CDMA) systems or digital subscriber line (DSL) systems.

We capitalize on the recently discovered relationship between mutual information and minimum mean-squared error (MMSE) to determine the power allocation strategy that maximizes the mutual information between the system input and output. We also put forth a novel mercury-waterfilling interpretation of the optimal power allocation procedure that generalizes the conventional waterfilling interpretation applicable to parallel independent Gaussian channels with Gaussian inputs as well as the conventional mercury-waterfilling interpretation applicable to parallel independent Gaussian channels with arbitrary inputs. Subsequently, we exploit the mutual information-MMSE relationship to specialize the optimal power allocation strategy to the asymptotic regimes of low- and high-SNR.

Of particular relevance, we demonstrate that in the high-power regime the power allocation strategy that maximizes mutual information also maximizes the minimum distance of the output lattice, hence minimizes the error probability. We also investigate the form of the optimal precoding policy for MIMO channels with arbitrary discrete inputs.

Finally, we show that the techniques have the potential to significantly increase the transmission rate of current systems, namely Gigabit DSL systems.

This represents joint work with Fernando Perez-Cruz and Sergio Verdú of Princeton University.