Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

Lozano Solsona, Angel; Tulino, Antonia M.; Verdú, Sergio

doi:http://dx.doi.org/10.1109/TIT.2006.876220

Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

Citation

Lozano A, Tulino A M, Verdu S. Optimum power allocation for parallel Gaussian channels with arbitrary input distributions. IEEE Transactions on Information Theory. 2006; 52(7): 3033-3051. DOI 10.1109/TIT.2006.876220

Abstract

The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signalling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc) are used in lieu of the ideal Gaussian /nsignals. This paper gives the power allocation policy that maximizes the mutual information /nover parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error proves key to solving the power allocation problem.