Channel state information on arvau

Wikipedia / Channel state information

In wireless communications, channel state information (CSI) is the 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.

CSI needs to be estimated at the receiver and usually quantized and fed back to the transmitter (although reverse-link estimation is possible in time-division duplex (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CSI can be estimated with reasonable accuracy and used for transmission adaptation for some time before being outdated.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

are the channel matrix and the noise vector, respectively. The noise is often modeled as circular symmetric complex normal with

is known.

Instantaneous CSI

is known perfectly. Due to channel estimation errors, the channel information can be represented as

is the estimation error covariance matrix. The vectorization, as multivariate random variables are usually defined as vectors.

Statistical CSI

are known. In a Rayleigh fading channel, this corresponds to knowing that

Estimation of CSI

Since the channel conditions vary, instantaneous CSI needs to be estimated is estimated using the combined knowledge of the transmitted and received signal.

is transmitted over the channel as

, the total training signalling becomes

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

denotes the conjugate transpose. The estimation mean squared error (MSE) is proportional to

denotes the trace is a scaled identity matrix as a (scaled) identity matrix of the same size that the number of transmit antennas.

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

denotes the Kronecker product has the dimension of the number of receive antennas. The estimation MSE is

that in general can only be derived through numerical optimization. But there exist heuristic solutions with good performance based on waterfilling is smaller than the number of transmit antennas.. In absence of an accurate knowledge of these correlation matrices, robust choices need to be made to avoid MSE degradation.

Neural network estimation

With the advances of deep learning there has been work that shows that the channel state information can be estimated using Neural network such as 2D/3D CNN and obtain better performance with fewer pilot signals. The main idea is that the neural network can do a good interpolation in time and frequency.

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.