Mutual Information Expansion for MIMO Systems and Capacity Formulae at Low SNR

• Published in: IEEE communications letters Vol. 15; no. 3; pp. 329 - 331
• Main Authors: Ioannou, Ioanna, Charalambous, Charalambos D, Denic, Stojan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allocations; Applied sciences; Approximation; Approximation methods; channel capacity; Channels; Coding, codes; Decoding; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Exact sciences and technology; Information, signal and communications theory; low SNR; Lower bounds; Mathematical analysis; MIMO; Mutual information; Mutual information expansion; Radiocommunications; Receivers; Resource management; Signal and communications theory; Signal to noise ratio; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; Upper bound; MIMO system; Lower bound; Second order; Parameter estimation; Channel capacity; Transmitter; Decoding; low SNR; Power allocation; Asymptotic expansion; Channel estimation; First order; Mutual information expansion; Series expansion; Mutual information; Least mean squares methods; Signal to noise ratio
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2011.012511.102277

The paper introduces a new asymptotic series expansion for the mutual information of multiple-input multiple-output (MIMO) channels. The expansion approaches mutual information from below, and for low signal to noise ratio (SNR) first and second order terms give a tight lower bound. The low SNR approximation is used to derive a new water-filling power allocation at the transmitter for the case when the receiver and the transmitter have perfect channel state information. The low SNR approximation is also compared against existing approximations, while the new water-filling policy is related to minimum mean square decoding subject to power constraint.