Analysis of Joint Angular Distribution for Nonreciprocal Beams via the Mixture of Gaussian Distribution Based on Ray-Tracing

Multiple-input and multiple-output (MIMO) technology can not only provide huge data rates but also overcome the severe propagation attenuation effect, especially in millimeter-wave (mmWave) bands by utilizing beamforming. The nonreciprocal beam is a novel transmission pattern, which indicates that transceivers adopt asymmetrical beamwidths. Such a special pattern can achieve fast beam alignment and alleviate equipment costs. Thorough knowledge of the corresponding wireless channel is pivotal to the system design and optimization, which remains to be investigated. In this paper, we first propose a 3-dimensional (3-D) channel model based on ray-tracing, which is capable of reflection simulation. Based on this model, the ray-based beamforming mechanism is illustrated. The angular distribution is pivotal to beam channel modeling and characterization since transceiver beams filter rays in the angular domain. Then, we conduct an omnidirectional antenna-based channel simulation in an urban macro-cell scenario via the ray-tracing platform. On this basis, we focus on the distribution of the quasiangles, i.e., angles between departure/arrival reflected rays and the line-of-sight (LoS) path. We find that gamma distribution is a better option to fit the quasiarrival angular distribution than the von Mises distribution. Furthermore, to characterize the relationship between quasiangles of departure (AoD) and quasiangles of arrival (AoA), the Gaussian mixture model (GMM) is adopted and the expectation-maximization (EM) algorithm is used to estimate the unknown parameters of GMM. Our findings provide useful insights to beam channel modeling, which should take the joint angular distribution into consideration.