The Impact of Channel Estimation on the Number of Active User with Rayleigh Fading Broadcast Channels

It has already been shown that in the rate-constrained broadcast channels, under the assumption of independent Rayleigh fading channels for different receivers, the user capacity (i.e. the maximum number of users that can be activated simultaneously) scales with ln(Plnn)/Rmin where P is transmit power, Rmin represents the minimum rate required for each receiver to be activated, and n denotes the total number of receivers in the system. However, to meet the aforementioned result, it is assumed that channel state information (CSI) is perfectly known to the receivers. In practical situations, the receivers do not have access to the true CSI and they only know estimated channels. In this paper, the effects of channel estimation are analyzed on the user capacity of rate-constrained broadcast channels. In particular, the Minimum Mean Square Error (MMSE) channel estimation scheme is considered and the effects of this estimation method on the user capacity are investigated. Under the assumption of independent Rayleigh fading channels for different receivers, the user capacity scales with is shown where denotes the variance of estimated channels and is determined by the MMSE channel estimation algorithm. As the received signal model is linear with respect to the fading channels, it is shown that the user capacity scaling law is unchanged and the difference is only a constant factor depending on the channel estimation scheme.