Solar scintillation effects can be significant for deep-space telecommunication links at small Sun-Earth-Probe (SEP) angles. Severe scintillation can make the telecommunication link unavailable. The physical characteristics of solar conjunction and scintillation are presented, the Rician channel model is set up, and the Gaussian approaches of communications channel are obtained once Rician factor exceeds 10\,dB in deep space exploration due to weak solar scintillation. At last, we simulated the weak scintillation effects on telemetry signals at both X-band and Ka-band by the model.