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Light propagation in random media is a subject of interest to the optics community at large, with applications ranging from imaging to communication and sensing. However, real-time characterization of wavefront distortion in random media remains a major challenge. Compounding the difficulties, for many applications such as imaging (e.g., endoscopy) and focusing through random media, we only have single-ended access. In this work, we propose to represent wavefronts as superpositions of spatial modes. Within this framework, random media can be represented as a coupled multimode transmission channel. Once the distributed coherent transfer matrix of the channel is characterized, wavefront distortions along the path can be obtained. Fortunately, backreflections almost always accompany mode coupling and wavefront distortions. Therefore, we further propose to utilize backreflections to perform single-ended characterization of the coherent transfer matrix. We first develop the general framework for single-ended characterization of the coherent transfer matrix of coupled multimode transmission channels. Then, we apply this framework to the case of a two-mode channel, a single-mode fiber, which supports two randomly coupled polarization modes, to provide a proof-of-concept demonstration. Furthermore, as one of the main applications of coherent channel estimation, a polarization imaging system through single-mode fibers is implemented. We envision that the proposed method can be applied to both guided and free-space channels with a multitude of applications.