# Channel state information

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Channel state information or channel status information (CSI) is information which represents the state of a communication link from the transmit source(s) to the receiver source(s). CSI is mathematically represented as $h = |h| e^{j\sin(\angle(h))}$, which can be extended to vector or matrix values depending on the number of source and destination elements.

## Channel State Information at the Transmitter (CSIT) Edit

Channel State Information at the Transmitter (CSIT) is downlink CSI known at the transmitter. CSIT can be known by estimating uplink signals in [[time division duplex| time division duplex (TDD) systems] and receiving feedback signaling from users in frequency division duplex|frequency division duplex (FDD) systems]. In the FDD systems, the feedback signal is generated based on the fact that each user estimates the CSI via demodulating pilot signals.

## Channel State Information at the Receiver (CSIR) Edit

Channel State Information at the Receiver (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.

## ReferencesEdit

1. M. Kobayashi, N. Jindal, and G. Caire, Optimized Training and Feedback for MIMO Downlink Channels, IEEE Information Theory Workshop, June 2009.
2. G. Caire, N. Jindal, M. Kobayashi, and N. Ravindran, Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback, Submitted to IEEE Trans. Information Theory, Nov. 2007. (Revised May 2009)