On the transfer matrix of a MIMO system

Abstract

We develop a deterministic ab-initio model for the input-output relationship of a multiple-input multiple-output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's Law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple-element arrays affect the properties of a MIMO channel, e.g. its capacity and its number of degrees of freedom.Comment: Accepted for publication in Mathematical Methods in the Applied Science

MIMO capacity for deterministic channel models: sublinear growth

“…where M T is the number of T X antennas, M R is the number of RX antennas, I MR is the M R ×M R identity matrix, E T is the average total energy transmitted by the T X antennas, N 0 is the variance of the noise, H is the M R × M T channel transfer matrix which establishes the linear relationship between the signals at RX antennas and the signals at the T X antennas. Starting from the Maxwell equations, we have shown in [1] what is the generic structure of such a transfer matrix (see below (1.2)). In the present paper we apply the formula obtained in [1] and study the behavior of the MIMO capacity as a function of M T , M R and of the deterministic spread function of the environment.…”

“…The antennas are assumed to fill in a given, fixed volume. According to [1], under certain conditions the transfer matrix can be well approximated by:…”

“…In contrast with the probabilistic models where the correlations between antennas are introduced rather arbitrarily, in [1] we developped a deterministic ab-initio model for the channel transfer matrix (see (1.2)) which implicitely takes into account these correlations, through the matrices a T and a R which completely describe the radiation patterns of the transmitting and receiving arrays, while the spread function s(Ω, Ω ′ ) describes the scattering environment. The mathematical technical assumptions in Theorem 1.1 are physically natural, thus our results confirm that the capacity of a system in a realistic environment grows more slowly than linearly.…”

“…

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 [1] the generic structure of such a deterministic transfer matrix. In the current paper we apply the results of [1] 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.

…”

“…Starting from the Maxwell equations, we have described in [1] the generic structure of such a deterministic transfer matrix. In the current paper we apply the results of [1] 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.…”