Abstract

Optimal Linear Precoding for Multiple-Input Multiple-Output Gaussian Channels with Arbitrary Inputs

We investigate the linear precoding policy that maximizes 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. The optimal linear precoder can be computed by means of a fixed-point equation as a function of the channel and the input constellation. We show that diagonalizing the channel matrix does not maximize the information transmission rate for nonGaussian inputs. A non-diagonal precoding matrix in general increases the information transmission rate, even for parallel non-interacting channels. Finally, we also investigate the use of correlated input distributions, which further increase the transmission rate for low and medium-snr ranges.

Estimation of Information Theoretic Measures for Continuous Random Variables

We analyze the estimation of information theoretic measures of continuous random variables such as: differential entropy, mutual information or Kullback-Leibler divergence. The objective of this paper is two-fold. First, we prove that the information theoretic measure estimates using the k-nearest-neighbor density estimation with fixed k converge almost surely, even though the k-nearest-neighbor density estimation with fixed k does not converge to its true measure. Second, we show that the information theoretic measure estimates do not converge for k growing linearly with the number of samples. Nevertheless, these nonconvergent estimates can be used for solving the two-sample problem and assessing if two random variables are independent. We show that the two-sample and independence tests based on these nonconvergent estimates compare favorably with the maximum mean discrepancy test and the Hilbert Schmidt independence criterion, respectively.