Stochastic Integral Operator Model for IS, US and WSSUS Channels

TL;DR

This paper introduces a stochastic integral operator model for IS, US, and WSSUS channels, providing a mathematical framework that decomposes channels into independent components with specific stochastic properties.

Contribution

It establishes that WSSUS channels can be modeled as stochastic integrals and characterizes the kernel as an additive process under independence assumptions.

Findings

WSSUS channels can be represented as stochastic integrals.

Channels with independent scattering decompose into deterministic and stochastic components.

The stochastic kernel can be described by Levy measures.

Abstract

In this article, we proved that, under weak and natural requirements, uncorrelated scattering (in particular WSSUS) channels can be modeled as stochastic integrals. Moreover, if we assume (not only uncorrelated but also) independent scattering, then the stochastic integral kernel is an additive stochastic process. This allows us to decompose an IS channel into a sum of independent channels; one deterministic, one with a Gaussian kernel, and two others described by the Levy measure of the additive process.