The number of wireless devices connected to the cellular wireless network is anticipated to increase heavily in the next few years, eventually reaching tens of billions. Thus, there is a need for a new cellular wireless network, which is able to handle tens of billions of wireless devices. This phenomenon has an associated effect in terms of a huge increase in traffic. A number of means is under investigation to respond to that need. Among several alternatives, the category of massive multiple input multiple output (MIMO) systems is a great candidate for this purpose. Because of the large number of antennas in massive MIMO, there is a need to reduce the dimension of the MIMO channel effectively to decrease the complexity by considering the sparsity in the channel in terms of angle of arrival and delay, as introduced by the technique of Joint Spatial Division and Multiplexing. This can be achieved effectively by using a particular statistical pre-beamforming technique introduced recently. In this paper, different adaptive algorithms for estimating the channel vector coefficient and their performance, based on this recent pre-beamforming technique, are studied. Different approaches are used in order to find the best algorithm based on the channel estimation accuracy and the complexity of the algorithm. As a byproduct, with the help of the provided analysis, in single-carrier time-varying massive MIMO channels, the optimal number of RF chains (required spatial dimensions) can be determined in hybrid beamforming in terms of the achievable information rate by taking the estimation accuracy of different adaptive acquisition algorithms into account.