Millimeter wave (mmWave) communication, currently used in the IEEE 802.11ad standard and 5G, can support high data rates at mm wave frequencies. mmWave systems typically use large antenna arrays and directional beams to achieve such high data rates. Beamforming is a key enabling technique which compensates the high path losses of the mm waves, by employing highly directional signal transmission and reception. In this research, we explore the cell discovery and channel estimation problems in mm wave systems. Cell Discovery is the process of finding at-least one accessible directional path to a base station. Channel estimation is a more complex problem, in which the user estimates the entire channel itself. However, the probability of detection of the accessible path and quality of the channel estimate depends on the beamforming vectors used at transmitter and receiver. Over the past few years, many beamforming algorithms are developed. The widely used exhaustive beam search scans all possible directions and results in large training overhead. On the other hand, hierarchical search suffers from low SNR prior to beamforming and is susceptible to multipath interference within a sector. In our work, we develop specialized training beams that can achieve fast cell discovery with a receiver algorithm of lower complexity, capable of identifying the accessible paths without user feedback. ­­



Our proposed training vectors are developed based on the mutually unbiased bases (MUB) from quantum information theory and the beamforming scheme is called as MUBB method. The scheme supports three-dimensional beam training using uniform planar arrays and can be realized with hybrid beamforming architecture. Unlike the existing random beamforming method, MUBB method allows the deterministic construction of training beams, resulting in a sensing matrix of low mutual coherence which determines the accuracy of base station identification. We validate this result by characterizing the relationship between the probability of detecting at least one base station and the mutual coherence. Our proposed receiver algorithm based on Orthogonal Matching Pursuit harnesses this lower mutual coherence property of the sensing matrix and can be implemented easily. We also include design parameters to provide flexibility over training duration and beam width. We substantiate the superior performance of MUBB method over the other training schemes through comprehensive simulations based on practical millimeter wave channels generated using NYUSIM simulator in terms of probability of detecting the correct base station, the achievable post-cell discovery beamforming gain and required training overhead.

Later we extend the proposed training schemes and receiver algorithms to solve the mmWave channel estimation problem. For the cases considered, we observe lower channel estimation error, better beamforming gain, and asymptotic spectral efficiency for MUBB based method with lesser training overhead.