The global shortage of microwave bandwidth has become a critical issue that may inhibit the growth of mobile networks needing to support content-rich applications. For this reason, the underutilized millimeter wave (mmWave) spectrum has attracted significant attention as a medium to support next-generation mobile. Although this spectrum has an abundance of available bandwidth, mmWave wave frequencies also have propagation characteristics that make digital communication very challenging. Due to the signals atmospheric, reflection, and penetration losses, this spectrum suffers from much greater attenuation compared to microwave signals.
To overcome these losses, mmWave systems will need to be equipped with large antenna arrays to enable directionality gains through beamforming. Due to the reduced wavelength of mmWave signals, large arrays can be packed into a small area and are therefore suitable for consumer electronics. However, by simply adopting conventional multiple-input multiple-output (MIMO) electronics with high-rate digital components tied to each antenna, the resulting power drain becomes unpractical for portable devices. To reduce hardware cost, complexity, and power consumption, constrained hardware architectures have been proposed for use in mmWave mobile systems. These consist of a small number of RF chains that are tied to the array of antennas through a network of phase shifters. In these architectures the role of beamforming is split across both the analog and the digital domains, which can make the task of channel estimation difficult and time-consuming. Furthermore, due to heavy signal losses, pilot signals will also need to be beamformed in order to get a clear estimate of the channel. In this thesis, we consider this problem of mmWave channel estimation for a wide range of deployment topologies including; point-to-point, multi-user, and multi-cellular.