Table 3 CSI descriptors
From: CSI-based fingerprinting for indoor localization using LTE Signals
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. |