Influence of Time-Varying Atmospheric Channel on Time Reversal Spatial Power Combination of Sparse Array on Ground

The spatial power combination based on the time reversal (TR) technique is severely affected by the time-varying characteristics of channels. In this paper, a mathematical model of TR power combination in the slowly time-varying atmospheric channel and the concept of channel time-varying factor are proposed to study the feasibility of this technique for spatial power combination in incompletely reciprocal channels. Combining the theoretical analysis and Monte Carlo simulations, we analyze the relationship between the power combination efficiency and the permittivity of the time-varying atmospheric channel, which follows a normal distribution. The results indicate that the power combination efficiency of the TR technique will be lower than that of the completely reciprocal channel if the atmospheric channel is slowly varied, and the faster the channel changes, the lower the efficiency becomes. In order to keep the power combination efficiency above 50%, the channel time-varying factor needs to be less than about 54.3% of the signal period. And when it takes more than 90%, the signals radiated by each antenna have been completely incoherent at target point. Different from the short-distance power combination, when the target point is far away and at a high altitude, the time-variability of the atmosphere over such a huge area is not negligible, so the power combination efficiency will be also severely affected. The mathematical model and results of this study can provide a theoretical basis for further research of long-distance spatial power combination based on the TR technology and error estimation in related engineering design.