  In this paper, a framework of beamspace channel estimation in millimeter wave
(mmWave) massive MIMO system is proposed. The framework includes the design of
hybrid precoding and combining matrix as well as the search method for the
largest entry of over-sampled beamspace receiving matrix. Then based on the
framework, three channel estimation schemes including identity matrix
approximation (IA)-based scheme, scattered zero off-diagonal (SZO)-based scheme
and concentrated zero off-diagonal (CZO)-based scheme are proposed. These
schemes together with the existing channel estimation schemes are compared in
terms of computational complexity, estimation error and total time slots for
channel training. Simulation results show that the proposed schemes outperform
the existing schemes and can approach the performance of the ideal case. In
particular, total time slots for channel training can be substantially reduced.
