The Capacity of the Amplitude-Constrained Vector Gaussian Channel

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.

[1]  Shlomo Shamai,et al.  Upper and Lower Bounds on the Capacity of Amplitude-Constrained MIMO Channels , 2017, GLOBECOM 2017 - 2017 IEEE Global Communications Conference.

[2]  M. Abramowitz,et al.  Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables , 1966 .

[3]  Shlomo Shamai,et al.  The capacity of average and peak-power-limited quadrature Gaussian channels , 1995, IEEE Trans. Inf. Theory.

[4]  Andrew Thangaraj,et al.  Capacity Bounds for Discrete-Time, Amplitude-Constrained, Additive White Gaussian Noise Channels , 2015, IEEE Transactions on Information Theory.

[5]  Yaming Yu,et al.  On Log-concavity of the Generalized Marcum Q Function , 2011, ArXiv.

[6]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[7]  D. E. Amos,et al.  Computation of modified Bessel functions and their ratios , 1974 .

[8]  H. Vincent Poor,et al.  On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective , 2018, IEEE Transactions on Information Theory.

[9]  Bruno Clerckx,et al.  On the capacity of vector Gaussian channels with bounded inputs , 2014, 2015 IEEE International Conference on Communications (ICC).

[10]  H. Vincent Poor,et al.  The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points , 2019, IEEE Transactions on Information Theory.

[11]  Amos Lapidoth,et al.  Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels , 2003, IEEE Trans. Inf. Theory.

[12]  Luca Barletta,et al.  Capacity Bounds for Amplitude-Constrained AWGN MIMO Channels with Fading , 2020, 2020 IEEE International Symposium on Information Theory (ISIT).

[13]  Richard D. Wesel,et al.  Capacities and Optimal Input Distributions for Particle-Intensity Channels , 2020, IEEE Transactions on Molecular, Biological and Multi-Scale Communications.

[14]  Joel G. Smith,et al.  The Information Capacity of Amplitude- and Variance-Constrained Scalar Gaussian Channels , 1971, Inf. Control..

[15]  Luca Barletta,et al.  On the Capacity of the Oversampled Wiener Phase Noise Channel , 2020, ArXiv.