Self-interference cancellation plays a crucial role in achieving reliable full-duplex communications. In general, it is essential to cancel the self-interference signal below the thermal noise level, which necessitates accurate reconstruction of the self-interference signal. In this paper, we propose a high-precision channel estimation method specifically designed for sub-noise self-interference cancellation. Exploiting the fact that all transmitted symbols are known to their respective receivers, our method utilizes all transmitted symbols for self-interference channel estimation. Through analytical derivations and numerical simulations, we validate the effectiveness of the proposed method. The results demonstrate the superior performance of our approach in achieving sub-noise self-interference cancellation.