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

‎It has already been shown that in 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 (P \ln n)/R_{\min} where P is transmit power‎, ‎R_{\min} represents the minimum rate required for each receiver to be activated‎, ‎and n denotes the total number of receivers in the system‎. ‎However‎, ‎to achieve 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 is 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 is investigated‎. ‎Under the assumption of independent Rayleigh fading channels for different receivers‎, ‎it is shown that the user capacity scales with \ln (\hat{\sigma}^۲ P \ln n)/R_{\min} where \hat{\sigma}^۲ 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.

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