Channel State Information at the Transmitter (CSIR) is downlink CSI known at the receiver. CSIR can be estimated usually by demodulating pilot signals at each user.

The observed pilot signal is given by[1][2]

$ \mathbf{s}_k = \sqrt{ \frac{T_1 P}{N_t}} \mathbf{h}_k + \mathbf{z}_k $

where $ \mathbf{z}_k \sim CN(0, N_0 \mathbf{I}) $. Using the MMSE estimation method, the variance of the estimated channel error for each element is given by

$ \frac{1}{1 + \frac{T_1}{N_t} \rho} $

where $ \rho = \frac{P}{N_0} $ is the normalized average SNR of both uplink and downlink channels.

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