Modeling of Path Arrival Rate for In-Room Radio Channels With Directive Antennas

We analyze the path arrival rate for an in-room 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 coverages 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.