In
wireless communication
Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided med ...
s, 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
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...
,
fading
In wireless communications, fading is the variation of signal attenuation over variables like time, geographical position, and radio frequency. Fading is often modeled as a random process. In wireless systems, fading may either be due to mul ...
, 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
feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handle ...
to the transmitter (although reverse-link estimation is possible in
time-division duplex
A duplex communication system is a point-to-point system composed of two or more connected parties or devices that can communicate with one another in both directions. Duplex systems are employed in many communications networks, either to allow ...
(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
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reac ...
of a
digital filter
In signal processing, a digital filter is a system that performs mathematical operations on a Sampling (signal processing), sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other ma ...
. 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
Narrowband signals are signals that occupy a narrow range of frequencies or that have a small fractional bandwidth. In the audio spectrum, ''narrowband sounds'' are sounds that occupy a narrow range of frequencies. In telephony, narrowband is ...
flat-fading channel with multiple transmit and receive antennas (
MIMO
In radio, multiple-input and multiple-output (MIMO) () is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wirel ...
), the system is modeled as
[
:
where and are the receive and transmit vectors, respectively, and and are the channel matrix and the noise vector, respectively. The noise is often modeled as circular symmetric complex normal with
:
where the mean value is zero and the noise covariance matrix is known.
]
Instantaneous CSI
Ideally, the channel matrix is known perfectly. Due to channel estimation errors, the channel information can be represented as[
:
where is the channel estimate and is the estimation error covariance matrix. The vectorization was used to achieve the column stacking of , as ]multivariate random variable
In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge ...
s are usually defined as vectors.
Statistical CSI
In this case, the statistics of are known. In a Rayleigh fading
Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.
Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission ...
channel, this corresponds to knowing that[
:
for some known channel covariance matrix .
]
Estimation of CSI
Since the channel conditions vary, instantaneous CSI needs to be estimated
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...
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 is estimated using the combined knowledge of the transmitted and received signal.
Let the training sequence be denoted , where the vector is transmitted over the channel as
:
By combining the received training signals for , the total training signalling becomes
:
with the training matrix