Tightness of Jensen’s Bounds and Applications to MIMO Communications

Jide Yuan, Michail Matthaiou, Shi Jin, Feifei Gao

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
526 Downloads (Pure)


Due to the difficulty in manipulating the distribution of Wishart random matrices, the performance analysis of multiple-input-multiple-output (MIMO) channels has mainly focused on deriving capacity bounds via Jensen’s inequality. However, to the best of our knowledge, the tightness of Jensen’s bounds1 has not yet been rigorously quantified in the general MIMO context. This paper proposes a new methodology for measuring the tightness of Jensen’s bounds via the sandwich theorem. In particular, we first compare the tightness of two different pairs of upper/lower bounds for a general class of MIMO channels based on the unordered eigenvalue of the instantaneous correlation matrix and for arbitrary numbers of antennas. The tightness of Jensen’s bounds in different channel scenarios is investigated including multiuser MIMO with maximal ratio combining. Our analysis is facilitated by deriving some new results for finite-dimensional Wishart matrices, i.e., for the arbitrary moments of the unordered eigenvalue of central and non-central Wishart matrices. Our results provide very interesting insights into the implications of the system parameters, such as the number of antennas, and signal-to-noise ratio, on the tightness of Jensen’s bounds, and showcase the suitability and limitations of Jensen’s bounds.
Original languageEnglish
Pages (from-to)579-593
Number of pages15
JournalIEEE Transactions on Communications
Issue number2
Early online date20 Nov 2016
Publication statusPublished - Feb 2017


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