In wireless communications, channel state information (CSI) refers to known channel properties of a communication link. This information describes how a signal propagates from the transmitter to the receiver and represents the combined effect of, for example, scattering, fading, and power decay with distance. The method is called Channel estimation. The CSI makes it possible to adapt transmissions to current channel conditions, which is crucial for achieving reliable communication with high data rates in multiantenna systems.
Contents
- Different kinds of channel state information
- Mathematical description
- Instantaneous CSI
- Statistical CSI
- Estimation of CSI
- Least square estimation
- MMSE estimation
- Data aided versus blind estimation
- References
CSI needs to be estimated at the receiver and usually quantized and fed back to the transmitter (although reverse-link estimation is possible in TDD systems). Therefore, the transmitter and receiver can have different CSI. The CSI at the transmitter and the CSI at the receiver are sometimes referred to as CSIT and CSIR, respectively.
Different kinds of channel state information
There are basically two levels of CSI, namely instantaneous CSI and statistical CSI.
Instantaneous CSI (or short-term CSI) means that the current channel conditions are known, which can be viewed as knowing the impulse response of a digital filter. This gives an opportunity to adapt the transmitted signal to the impulse response and thereby optimize the received signal for spatial multiplexing or to achieve low bit error rates.
Statistical CSI (or long-term CSI) means that a statistical characterization of the channel is known. This description can include, for example, the type of fading distribution, the average channel gain, the line-of-sight component, and the spatial correlation. As with instantaneous CSI, this information can be used for transmission optimization.
The CSI acquisition is practically limited by how fast the channel conditions are changing. In fast fading systems where channel conditions vary rapidly under the transmission of a single information symbol, only statistical CSI is reasonable. On the other hand, in slow fading systems instantaneous CSI can be estimated with reasonable accuracy and used for transmission adaptation for some time before being outdated.
In practical systems, the available CSI often lies in between these two levels; instantaneous CSI with some estimation/quantization error is combined with statistical information.
Mathematical description
In a narrowband flat-fading channel with multiple transmit and receive antennas (MIMO), the system is modeled as
where
where the mean value is zero and the noise covariance matrix
Instantaneous CSI
Ideally, the channel matrix
where
Statistical CSI
In this case, the statistics of
for some known channel covariance matrix
Estimation of CSI
Since the channel conditions vary, instantaneous CSI needs to be estimated on a short-term basis. A popular approach is so-called training sequence (or pilot sequence), where a known signal is transmitted and the channel matrix
Let the training sequence be denoted
By combining the received training signals
with the training matrix
With this notation, channel estimation means that
Least-square estimation
If the channel and noise distributions are unknown, then the least-square estimator (also known as the minimum-variance unbiased estimator) is
where
where
MMSE estimation
If the channel and noise distributions are known, then this a priori information can be exploited to decrease the estimation error. This approach is known as Bayesian estimation and for Rayleigh fading channels it exploits that
The MMSE estimator is the Bayesian counterpart to the least-square estimator and becomes
where
and is minimized by a training matrix
Data-aided versus blind estimation
In a data-aided approach, the channel estimation is based on some known data, which is known both at the transmitter and at the receiver, such as training sequences or pilot data. In a blind approach, the estimation is based only on the received data, without any known transmitted sequence. The tradeoff is the accuracy versus the overhead. A data-aided approach requires more bandwidth or it has a higher overhead than a blind approach, but it can achieve a better channel estimation accuracy than a blind estimator.