Codebook-based beamforming is used in millimeter wave communications to alleviate the difficuity of obtaining accurate channel state information (CSI) for large antenna arrays. However, the required codebook size is usually large thus codebook search becomes computationally prohibitive due to its exponential growth. To address this, we propose a direct search technique with the concept of tracking the strong beam stream based on the recently proposed global direct search (GDS) optimization method. Simulation results show that our beam training technique achieves a near-optimal performance (about 97% as that of the exhaustive search) at much lower complexity levels.
