# Table 3 CSI descriptors

Descriptor Formula Description
Mean $$\mu = \frac {1}{N}\sum \limits _{n=0}^{N-1} h_{n}$$ The arithmetic mean of the CSI.
Standard deviation $$\sigma = \sqrt {\frac {1}{N-1}\sum \limits _{n=0}^{N-1} (h_{n} - \mu)^{2}}$$ The standard deviation of the CSI.
Fano factor $$\text {FF} = \frac {\sigma ^{2}}{\mu }$$ The ratio between the variance of the CSI and its arithmetic mean.
Spectral centroid $$f_{n} = (3n-6\text {RB}) 15~\text {kHz} \text {SC} = \frac {\sum \limits _{n=0}^{N-1} h_{n} f_{n}}{\sum \limits _{i=0}^{N-1} h_{i}}$$ The “center of mass” calculated as the weighted mean of the frequency values with CSI normalized magnitudes as weights.
Spectral lambda $$\lambda = -\frac {1}{N-1} \sum \limits _{n=1}^{N-1} \frac {h_{n}-h_{n-1}}{f_{n}-f_{n-1}} \frac {2}{h_{n}+h_{n-1}}$$ The mean of the derivative function for the CSI.
Spectral entropy $$\text {SE} = -\sum \limits _{n=0}^{N-1} \frac {h_{n}}{\sum \limits _{j=0}^{N-1} h_{j}} \log _{2} \frac {h_{n}}{\sum \limits _{i=0}^{N-1} h_{i}}$$ The amount of information contained in the CSI.
Spectral flatness $$\text {SF} = \frac {\sqrt [N]{\prod \limits _{n=0}^{N-1}} h_{n}}{\frac {1}{N} \sum \limits _{n=0}^{N-1} h_{n}}$$ A measure used in digital signal processing to quantify how noise-like the CSI is.
Spectral slope $$\text {SSL} = \frac {\sum \limits _{n=0}^{N-1} (f_{n}-\overline {f}_{n})(h_{n}-\mu)}{\sum \limits _{n=0}^{N-1} (f_{n}-\overline {f})^{2}}$$ A measure of the slope of the spectral shape of CSI.
Spectral spread $$\text {SSP} = \sqrt {\frac {\sum \limits _{n=0}^{N-1} {h_{n}} (f_{n}-\text {SC})^{2}}{\sum \limits _{i=0}^{N-1} {h_{i}}}}$$ A measure of how the spectrum is distributed around its centroid.
Spectral moment $$\eta _{j} = \frac {\sum \limits _{n=0}^{N-1} {h_{n}} f_{n}^{j}}{\sum \limits _{i=0}^{N-1} {h_{i}}}$$ The jth order spectral moment of the CSI.
Spectral central moment $$\xi _{j} = \frac {\sum \limits _{n=0}^{N-1} {h_{n}} (f_{n}-\text {SC})^{j}} {\sum \limits _{i=0}^{N-1} {h_{i}}}$$ The jth order spectral central moment of the CSI.
Spectral kurtosis $$\text {SKU} = \frac {\sum \limits _{n=0}^{N-1} {h_{n}} T_{n}^{4}} {\sum \limits _{i=0}^{N-1} {h_{i}}}, \quad T_{n} = \frac {f_{n} - \text {SC}}{\sqrt {\xi _{2}}}$$ A measure of the “tailedness” of the CSI.
Spectral skewness $$\text {SSK} = \frac {\sum \limits _{n=0}^{N-1} {h_{n}} T_{n}^{3}} {\sum \limits _{i=0}^{N-1} {h_{i}}}$$ A measure of the asymmetry of the CSI about its spectral centroid.
1. The list of CSI statistical and shape descriptors