Capacity of the Class of MIMO Channels With Incomplete CDI-Properties of Mutual Information for a Class of Channels

• Published in: IEEE transactions on information theory 2009-08, Vol.55 (8), p.3725-3734
• Main Authors: Charalambous, C.D., Denic, S.Z., Constantinou, C.
• Format: Article
• Language: English
• Subjects: Applied sciences; Channel capacity; Compound channel; Covariance matrix; Data transmission; Entropy; Exact sciences and technology; Gaussian channels; Information theory; Information, signal and communications theory; Matrix; MIMO; multiple-input multiple- output (MIMO) Gaussian channel; Multiplexers; Mutual information; power allocation; Probability distribution; Radiocommunications; Rayleigh channels; relative entropy constraint; robustness; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; Uncertainty; Wireless networks
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2023716

This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropy D (middot||middot) such that D (p||p nom ) les d , d ges 0, where d is the distance from the so-called nominal channel matrix distribution p nom (H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution p nom (H) and parameter d . A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect to d is shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.