Angular Properties for Power from a Spatial Cluster

A spatial cluster of scatterers, which forms a link between a transmitter and a receiver, behaves as a random array that passively relays the radio signal. The statistical properties of the antenna pattern for this random array are derived in the far field. The analysis is performed for circularly symmetric clusters with independent and uniformly distributed phases for the scattering events. The average lobe width, the average notch width, and the number of level crossings for the antenna pattern are derived for a Gaussian spatial cluster. The simulation of the cluster properties coincides with the analytical results.