Modelling of Path Arrival Rate for In-Room Radio Channels with Directive Antennas

TL;DR

This paper derives an exact expression for the mean path arrival rate in in-room radio channels with directive antennas, revealing how antenna directivity influences delay spread and channel characteristics.

Contribution

It provides a novel, exact formula for the mean arrival rate considering antenna directivity and room geometry, enhancing understanding of in-room radio channel behavior.

Findings

The mean arrival rate is quadratic in delay and inversely proportional to room volume.

A 'mixing time' is defined to characterize the onset of diffuse reverberation.

Antenna directivity affects delay spread but not the power-delay spectrum.

Abstract

We analyze the path arrival rate for an inroom radio channel with directive antennas. The impulse response of this channel exhibits a transition from early separate components followed by a diffuse reverberation tail. Under the assumption that the transmitter's (or receiver's) position and orientation are picked uniformly at random we derive an exact expression of the mean arrival rate for a rectangular room predicted by the mirror source theory. The rate is quadratic in delay, inversely proportional to the room volume, and proportional to the product of beam coverage fractions of the transmitter and receiver antennas. Making use of the exact formula, we characterize the onset of the diffuse tail by defining a "mixing time" as the point in time where the arrival rate exceeds one component per transmit pulse duration. We also give an approximation for the power-delay spectrum. It turns out that the power-delay spectrum is unaffected by the antenna directivity. However, Monte Carlo simulations show that antenna directivity does indeed play an important role for the distribution of instantaneous mean delay and rms delay spread