Stochastic modelling of LOS double-directional channel in spherical wave domain — Concept, formulation and validation

Double-directional channel is to de-embed antennas from both ends of a MIMO system, and to describe the propagation phenomenon. Double-directional channel model in spherical wave domain [1] is intuitive for antenna de-embedding, and its input of antenna part is simply the coefficients of spherical wave expansion [2] of radiation pattern. Besides, it is antenna-friendly because the truncation of channel model can be determined by antenna size. Empirically, transmission engineers prefer stochastic channel description; there is a need of antenna de-embedded stochastic description, which then enables the performance evaluation of different antennas in certain propagation environment through antenna-channel recombination. This paper provides the concept, formulation and validation of stochastic modelling of double-directional channel in spherical wave domain for LOS scenario where the MIMO channel can be described as the sum of a dominant and fading part. Firstly, the statistical parameters of double-directional channel in spherical wave domain are studied by using the LOS channel model parameters in plane wave domain, based on the explicit relationship of channel model in spherical wave domain and the generating model in plane wave domain [3]. The statistical characteristics of mode-to-mode links [1], i.e. the entries of model, for LOS scenario are summarized, such as the imbalanced average power, the Ricean distributed envelope with different ⁁-factor for different entry, and the correlation of its dominant part and fading part. Secondly, according to the statistical characteristics, a stochastic modelling of LOS double-directional channel in spherical wave domain is proposed, where the model inputs can be derived from samples of channel response. The proposed modelling avoids the use of channel model parameters in plane wave domain, and intends for antenna de-embedding and antenna-channel recombination which are sheer actions in spherical wave domain. Moreover, the appropriate array configuration for antenna de-embedding and antenna-channel recombination is discussed respectively. Finally, the proposed stochastic modelling is validated by simulation. Channel responses embedding spherical array with proposed configuration are obtained by the generating model [3] in the very beginning. The statistical parameters are calculated from antenna de-embedded channel responses, and then double-directional channel model in spherical wave domain is generated by the proposed stochastic model. The de-embedded stochastic double-directional channel models are recombined with spherical and circular array respectively, to obtain the synthesized channel responses. The cumulative distribution functions of large-scale gain, channel capacity, and eigenvalues of synthesized channel responses are compared with that of the referenced responses which can be obtained by the generating model.