Elements of information theory
Elements of information theory
Convex Optimization
Approximation Bounds for Quadratic Optimization with Homogeneous Quadratic Constraints
SIAM Journal on Optimization
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
IEEE Transactions on Signal Processing
Spectral efficiency in the wideband regime
IEEE Transactions on Information Theory
Mutual information and minimum mean-square error in Gaussian channels
IEEE Transactions on Information Theory
Gradient of mutual information in linear vector Gaussian channels
IEEE Transactions on Information Theory
Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
IEEE Transactions on Information Theory
Robust MMSE precoding in MIMO channels with pre-fixed receivers
IEEE Transactions on Signal Processing
Differential feedback of MIMO channel gram matrices based on geodesic curves
IEEE Transactions on Wireless Communications
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The design of the precoder the maximizes the mutual information in linear vector Gaussian channels with an arbitrary input distribution is studied. Precisely, the precoder optimal left singular vectors and singular values are derived. The characterization of the right singular vectors is left, in general, as an open problem whose computational complexity is then studied in three cases: Gaussian signaling, low SNR, and high SNR. For the Gaussian signaling case and the low SNR regime, the dependence of the mutual information on the right singular vectors vanishes, making the optimal precoder design problem easy to solve. In the high SNR regime, however, the dependence on the right singular vectors cannot be avoided and we show the difficulty of computing the optimal precoder through an NP-hardness analysis.