2015/04/03 by Walid Hachem, Aris Moustakas, Aris L. Moustakas +5
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #cs.IT #math-ph #math.IT #math.MP
paper · pdf · doi:10.48550/arxiv.1504.00847
arxiv created 2015/04/03 · openalex publication_date 2015/04/03 · arxiv updated 2015/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a random non-centered multiple antenna radio transmission channel. Assume that the deterministic part of the channel is itself frequency selective, and that the random multipath part is represented by an ergodic stationary vector process. In the Hilbert space l2(\mathbb Z), one can associate to this channel a random ergodic self-adjoint operator having a so-called Integrated Density of States (IDS). Shannon's mutual information per receive antenna of this channel coincides then with the integral of a log function with respect to the IDS. In this paper, it is shown that when the numbers of antennas at the transmitter and at the receiver tend to infinity at the same rate, the mutual information per receive antenna tends to a quantity that can be identified and, in fact, is closely related to that obtained within the random matrix approach. This result can be obtained by analyzing the behavior of the Stieltjes transform of the IDS in the regime of the large numbers of antennas.