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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 :\mathbf = \mathbf\mathbf + \mathbf where \mathbf and \mathbf are the receive and transmit vectors, respectively, and \mathbf and \mathbf are the channel matrix and the noise vector, respectively. The noise is often modeled as circular symmetric complex normal with :\mathbf \sim \mathcal(\mathbf,\,\mathbf) where the mean value is zero and the noise covariance matrix \mathbf is known.


Instantaneous CSI

Ideally, the channel matrix \mathbf is known perfectly. Due to channel estimation errors, the channel information can be represented as :\mbox (\mathbf_) \sim \mathcal(\mbox(\mathbf),\,\mathbf_) where \mathbf_ is the channel estimate and \mathbf_ is the estimation error covariance matrix. The vectorization \mbox() was used to achieve the column stacking of \mathbf, 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 \mathbf 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 :\mbox (\mathbf) \sim \mathcal(\mathbf,\,\mathbf) for some known channel covariance matrix \mathbf.


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 \mathbf is estimated using the combined knowledge of the transmitted and received signal. Let the training sequence be denoted \mathbf_1,\ldots,\mathbf_N, where the vector \mathbf_i is transmitted over the channel as :\mathbf_i = \mathbf\mathbf_i + \mathbf_i. By combining the received training signals \mathbf_i for i=1,\ldots,N, the total training signalling becomes :\mathbf= mathbf_1, \ldots,\mathbf_N= \mathbf\mathbf + \mathbf with the training matrix \mathbf= mathbf_1, \ldots,\mathbf_N/math> and the noise matrix \mathbf= mathbf_1, \ldots,\mathbf_N/math>. With this notation, channel estimation means that \mathbf should be recovered from the knowledge of \mathbf and \mathbf.


Least-square estimation

If the channel and noise distributions are unknown, then the least-square estimator (also known as the
minimum-variance unbiased estimator In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. For pra ...
) is :\mathbf_ = \mathbf \mathbf^H(\mathbf \mathbf^H)^ where ()^H denotes the
conjugate transpose In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m \times n complex matrix \mathbf is an n \times m matrix obtained by transposing \mathbf and applying complex conjugation to each entry (the complex conjugate ...
. The estimation
mean squared error In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference betwee ...
(MSE) is proportional to :\mathrm (\mathbf \mathbf^H)^ where \mathrm denotes the trace. The error is minimized when \mathbf \mathbf^H is a scaled
identity matrix In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the obje ...
. This can only be achieved when N is equal to (or larger than) the number of transmit antennas. The simplest example of an optimal training matrix is to select \mathbf 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 ('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, Justification (epistemology), justification, or argument by their reliance on experience. knowledge is independent from any ...
'' information can be exploited to decrease the estimation error. This approach is known as
Bayesian estimation In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior probability, posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently ...
and for Rayleigh fading channels it exploits that :\mbox (\mathbf) \sim \mathcal(0,\,\mathbf), \quad \mbox(\mathbf) \sim \mathcal(0,\,\mathbf). The MMSE estimator is the Bayesian counterpart to the least-square estimator and becomes :\mbox(\mathbf_) = \left(\mathbf^ + (\mathbf^T \, \otimes\, \mathbf)^H \mathbf^ (\mathbf^T \, \otimes\, \mathbf) \right)^ (\mathbf^T \, \otimes\, \mathbf)^H \mathbf^ \mbox(\mathbf) where \otimes denotes the
Kronecker product In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vector ...
and the identity matrix \scriptstyle \mathbf has the dimension of the number of receive antennas. The estimation MSE is : \mathrm \left(\mathbf^ + (\mathbf^T \, \otimes\, \mathbf)^H \mathbf^ (\mathbf^T \, \otimes\, \mathbf) \right)^ and is minimized by a training matrix \mathbf that in general can only be derived through numerical optimization. But there exist heuristic solutions with good performance based on waterfilling. As opposed to least-square estimation, the estimation error for spatially correlated channels can be minimized even if N is smaller than the number of transmit antennas. Thus, MMSE estimation can both decrease the estimation error and shorten the required training sequence. It needs however additionally the knowledge of the channel correlation matrix \mathbf and noise correlation matrix \mathbf. 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 Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience a ...
there has been work that shows that the channel state information can be estimated using
Neural network A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...
such as 2D/3D CNN and obtain better performance with less pilot signals. The main idea is that the
neural network A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or signal pathways. While individual neurons are simple, many of them together in a network can perfor ...
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 In electronics and telecommunications, a radio transmitter or just transmitter (often abbreviated as XMTR or TX in technical documents) is an electronic device which produces radio waves with an antenna (radio), antenna with the purpose of sig ...
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 A trade-off (or tradeoff) is a situational decision that involves diminishing or losing on quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and anoth ...
is the accuracy versus the overhead. A data-aided approach requires more
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
or it has a higher overhead than a blind approach, but it can achieve a better channel estimation
accuracy Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value''. ''Precision'' is how close the measurements are to each other. The ...
than a blind estimator.


See also

* Channel sounding


References

{{reflist, refs= A. Tulino, A. Lozano, S. Verdú
Impact of antenna correlation on the capacity of multiantenna channels
IEEE Transactions on Information Theory, vol 51, pp. 2491-2509, 2005.
E. Björnson, B. Ottersten
A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels with Rician Disturbance
IEEE Transactions on Signal Processing, vol 58, pp. 1807-1820, 2010.
J. Kermoal, L. Schumacher, K.I. Pedersen, P. Mogensen, F. Frederiksen
A Stochastic MIMO Radio Channel Model With Experimental Validation
{{Webarchive, url=https://web.archive.org/web/20091229154616/http://www.its.caltech.edu/~taocui/page/tutorial/mimo_channel.pdf , date=2009-12-29 , IEEE Journal on Selected Areas Communications, vol 20, pp. 1211-1226, 2002.
M. Biguesh and A. Gershman
Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals
{{webarchive , url=https://web.archive.org/web/20090306172253/http://www.comm.ccu.edu.tw/~comtsliu/CourseInformation/DetectionEstimation07Fall/DetectionEstimation07FallFinalPaper.pdf , date=March 6, 2009 , IEEE Transactions on Signal Processing, vol 54, pp. 884-893, 2006.
Y. Li, L.J. Cimini, and N.R. Sollenberger
Robust channel estimation for OFDM systems with rapid dispersive fading channels
IEEE Transactions on Communications, vol 46, pp. 902-915, July 1998.
M. D. Nisar, W. Utschick and T. Hindelang
Maximally Robust 2-D Channel Estimation for OFDM Systems
IEEE Transactions on Signal Processing, vol 58, pp. 3163-3172, June 2010.
A. Zhuang, E.S. Lohan, and M. Renfors, "Comparison of decision-directed and pilot-aided algorithms for complex channel tap estimation in downlink WCDMA systems", in Proc. of 11th IEEE Personal and Indoor Mobile Radio Communications (PIMRC), vol. 2, Sept. 2000, p. 1121-1125.


External links


Atheros CSI Tool

Linux 802.11n CSI Tool
Wireless Information theory Radio resource management Telecommunication theory