We derive analytical expressions for the probability density function (pdf) of the random mutual information between transmitted and received vector signals of a random space-time independent and identically distributed (i.i.d.) multiple-input multiple-output (MIMO) channel, assuming that the transmitted signals from the multiple antennas are Gaussian i.i.d.. We show that this pdf can be well approximated by a Gaussian distribution, and such a Gaussian approximation is based on expressions for the given pdfs mean and variance that we derive. We prove that at high signal-to-noise ratio (SNR), every factor of 2 increase in SNR leads to an increase in outage rate in the amount of min(M, N) bits, where M and N denote the number of transmit and receive antennas, respectively. A simple expression for the moment generating function (MGF) of the mutual information pdf is also provided, based on which we establish normality of the pdf, when both M and N are large, and the SNR is large.
Bibliographical noteFunding Information:
Manuscript received July 11, 2002; revised November 21, 2003. This work was supported by the National Science Foundation under Grant CCR-0105612 and by the ARL/CTA under Grant DAAD 19-01-2-011. The material in this correspondence was presented in part at the 40th Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2002. Z. Wang is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: email@example.com). G. B. Giannakis is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: firstname.lastname@example.org). Communicated by ˙. E. Telatar, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2004.825029
- Multiple-input multiple-output (MIMO)
- Mutual information