Spatial modeling of three-dimensional multipath wireless channels

Abstract

The wireless communication channel is charactarized by multipath propagation mechanism due to scattering by objects surrounding the communicating nodes. Unmitigated multipath propagation can be harmful due to the introduced distortion by superimposing multiple signal replicas. On the other hand, the multipath propagation can be beneficial in providing implicit diversity, as the propagation paths can be used as multiple communication channels. This dissertation thesis presents a simple method for spatial modeling of narrowband multipath channels. It presents results that have stemmed from a new approach in channel characterization - deriving the second-order fading statistics like level-crossing rate, average fade duration, and coherence distance and time from the multipath angular power distribution (APD) at the receiver antenna. First, a new method is presented for characterizing the three-dimensional angular spread of the received multipath in terms of the zeroth- and first-degree spherical harmonic coefficients of the APD, and the dependence of the average spatial correlation of the received signal envelope on that angular spread is derived. Second, the derivation of the average second-order fading channel statistics in terms of the angular spread is extended for characterizing the angular variability of the second-order fading statistics in a local area and local volume. This characterization is obtained in terms of the so-called three-dimensional multipath shape factors - an extension of an earlier work on horizontal propagation. The multipath shape factors in this work are defined in terms of the zeroth-, first- and second-degree spherical harmonic coefficients of the APD. Third, the shape factor theory has been extended for modeling mobile-to-mobile multipath channels through the joint APD at both wireless link ends. For this purpose, joint multipath shape factors have been defined in terms of the double Fourier coefficients of the joint biazimuthal APD for the two-dimensional model, or the double spherical harmonic coefficients of the joint bispherical APD for the three-dimensional model.