A geometrical investigation of the rank-1 Ricean MIMO channel at high SNR


Jan Hansen and Helmut Bölcskei


Proc. of IEEE International Symposium on Information Theory (ISIT), Chicago, IL, USA, pp. 64, June 2004.

DOI: 10.1109/ISIT.2004.1365101

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We investigate the high-SNR mutual information (MI) of the Ricean MIMO channel for i.i.d. gaussian code books, no channel state information (CSI) at the transmitter, perfect CSI at the receiver, and the case where the channel's deterministic component has rank 1. Our main results can be summarized as follows: 1) Using an illustrative geometrical technique, we decompose the MI into the sum of the MIs of one single-input single-output (SISO) Ricean channel and several SISO Rayleigh fading channels with different diversity orders. 2) We derive an analytical approximation for the probability density function (pdf) of the MI that reveals the gaussian nature of MI both in the Rayleigh and the rank-1 Ricean cases. 3) We provide accurate approximations for the mean and the variance of the MI which allow to analytically quantify the impact of the K-factor on capacity.


MIMO, Ricean fading, capacity, parallelotope

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