Effects of channel estimation on the optimal number of active users in multi-user channels with Rayleigh fading

It has already been shown that in rate-constrained multi-user channels, under the assumption of independent Rayleigh fading channels for different terminals, the number of active users (i.e. the user capacity) scales with double logarithmically with the total number of users. However, to achieve the aforementioned result, it is assumed that channel state information (CSI) is perfectly known to the receivers. Due to this fact that the gain channel is time variant, CSI can be estimated by empirical algorithms of the channel estimation like Minimum Mean Square Error (MMSE). Considering the errors stemmed from the channel estimation, this paper intends to assess the role of the channel estimator in the analysis of the number of the active users.