Microscopic Analysis for Decoupling Principle of Linear Vector Channel

TL;DR

This paper proves that in large linear vector channels, each individual input element can be modeled as an independent scalar Gaussian channel, extending the decoupling principle beyond collections of elements.

Contribution

It extends the decoupling principle to individual elements of linear vector channels, showing scalar-channel characterization applies at the single-element level in large systems.

Findings

Decoupling principle valid for individual input elements.

Linear vector channels decompose into independent scalar Gaussian channels.

Applicable in large-system limit with fixed input-output ratio.

Abstract

This paper studies the decoupling principle of a linear vector channel, which is an extension of CDMA and MIMO channels. We show that the scalar-channel characterization obtained via the decoupling principle is valid not only for collections of a large number of elements of input vector, as discussed in previous studies, but also for individual elements of input vector, i.e. the linear vector channel for individual elements of channel input vector is decomposed into a bank of independent scalar Gaussian channels in the large-system limit, where dimensions of channel input and output are both sent to infinity while their ratio fixed.