MIMO capacity for deterministic channel models: sublinear growth

TL;DR

This paper develops a deterministic model for MIMO channel transfer matrices based on Maxwell equations and demonstrates that the system capacity grows sublinearly with the number of antennas, challenging linear growth assumptions.

Contribution

The authors derive a deterministic transfer matrix model from Maxwell equations and prove that MIMO capacity exhibits sublinear growth with increasing antennas.

Findings

Capacity grows much slower than linearly with the number of antennas.

Results support previous heuristic predictions of sublinear capacity growth.

Model provides a physics-based understanding of MIMO channel behavior.

Abstract

This is the second paper of the authors in a series concerned with the development of a deterministic model for the transfer matrix of a MIMO system. Starting from the Maxwell equations, we have described in \cite{BCFM} the generic structure of such a deterministic transfer matrix. In the current paper we apply the results of \cite{BCFM} in order to study the (Shannon-Foschini) capacity behavior of a MIMO system as a function of the deterministic spread function of the environment, and the number of transmitting and receiving antennas. The antennas are assumed to fill in a given, fixed volume. Under some generic assumptions, we prove that the capacity grows much more slowly than linearly with the number of antennas. These results reinforce previous heuristic results obtained from statistical models of the transfer matrix, which also predict a sublinear behavior.