On the Mutual Information and Power Allocation for Vector Gaussian Channels with Finite Discrete Inputs

In this paper, the mutual information and power allocation are discussed for vector Gaussian channels with finite discrete inputs. It is shown that the classic waterfilling and mercury-waterfilling policies, which are allocating power to a bank of independent parallel channels, may lead to significant loss compared to the original system without power allocation for finite discrete inputs. A generalized linear precoder, which is a non-diagonal and non-unitary matrix, is proposed for cross-channel power allocation to maximize the mutual information for vector channels. Numerical examples show that the new precoding-based power allocation provides significant gain for a broad region of signal-to-noise ratios.