This paper addresses the channel estimation and precoding challenges in millimeter wave (mmWave) cellular systems, which are crucial for achieving high data rates. The authors propose an adaptive algorithm to estimate mmWave channel parameters, leveraging the sparse nature of the channel. A novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths, enabling efficient channel estimation. For single-path channels, an upper bound on the estimation error probability is derived, and insights into the efficient allocation of training power are provided. The adaptive channel estimation algorithm is extended to multi-path channels using the sparse property of the channel. A hybrid analog/digital precoding algorithm is proposed to overcome hardware constraints and approach the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains to exhaustive search methods, and the proposed channel estimation and precoding algorithms can approach the coverage probability achieved with perfect channel knowledge, even in the presence of interference.This paper addresses the channel estimation and precoding challenges in millimeter wave (mmWave) cellular systems, which are crucial for achieving high data rates. The authors propose an adaptive algorithm to estimate mmWave channel parameters, leveraging the sparse nature of the channel. A novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths, enabling efficient channel estimation. For single-path channels, an upper bound on the estimation error probability is derived, and insights into the efficient allocation of training power are provided. The adaptive channel estimation algorithm is extended to multi-path channels using the sparse property of the channel. A hybrid analog/digital precoding algorithm is proposed to overcome hardware constraints and approach the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains to exhaustive search methods, and the proposed channel estimation and precoding algorithms can approach the coverage probability achieved with perfect channel knowledge, even in the presence of interference.