# Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters

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## Abstract

**:**

## 1. Introduction

## 2. Spectrum Sensing Overview

#### Sensed Signals

## 3. Analysis of the Collected Data

## 4. Proposed Rapid Estimation Method

- The
**ED**block calculates the optimal value for T and identifies the channels in which PU signals are detected, marking them as used channels; otherwise they are identified as TVWS channels. - The
**SA**block obtains the statistical parameters of the sensed signals (i.e., $\overline{\mathrm{W}}$, $\overline{\mathrm{X}}$, ${\sigma}_{W}$, and ${\sigma}_{X}$) used to identify ${P}_{fa}$ and ${P}_{d}$ for each case. With this information, it creates a plot of the PDF curves. - The
**RA**block plots the ROC curves for each point sensed and identifies tendencies or patterns for each case.

#### 4.1. ED Results

#### 4.2. SA and RA Results

#### 4.3. REM Block

- Parameter I is the first auxiliary parameter obtained, and it represents the projection line of the intersection point between $W\left(p\right)$ and $X\left(p\right)$, as shown in Figure 7b. Parameter I marks the limit that separates the noise of the signal components of the composite signal $X\left(p\right)$, and it can be calculated using$$I=W\left(p\right)\cap X\left(p\right)$$
- Parameter ${Z}_{1}X$ is represented by a line plotted in the upper limit of $X\left(p\right)$. To calculate its coordinates, we have to consider a Z-score that delimits 99% vs. 1% of the AUC in the right side of normal curve $X\left(p\right)$. This reference parameter will be very helpful to find the peak values of the composite signal $X\left(p\right)$, which usually are the PU signals. To determine the value of ${Z}_{1}X$ we can use$${Z}_{1}{X}_{i}=\overline{\mathrm{X}}\left({p}_{i}\right)+{\sigma}_{Xi}\ast 2.33$$
- Parameter ${\tau}_{\overline{\mathrm{W}}}$ refers to the distance measured from the $\overline{\mathrm{W}}$ and ${Z}_{1}X$. It provides an idea of how spread out the composite signal $X\left(p\right)$ in reference to noise signal $W\left(p\right)$ is. If ${\tau}_{\overline{\mathrm{W}}}$ is bigger, this means that more $PU$s were detected in the $X\left(p\right)$ signal.
- Parameter ${\tau}_{I}$ refers to the distance measured from the I intersection line and ${Z}_{1}X$. It can be interpreted as the separation of the noise and the PU components in the composite signal $X\left(p\right)$.
- Parameter ${\tau}_{T}$ refers to the distance measured from the defined value of T and ${Z}_{1}X$. It provides an idea of how spread out the ${P}_{d}$ AUC is.
- Parameter ${\tau}_{\overline{\mathrm{X}}}$ refers to the distance measured from the $\overline{\mathrm{X}}$ and ${Z}_{1}X$, and it provides an idea of how spread out the composite signal $X\left(p\right)$ is. By finding ${\tau}_{\overline{\mathrm{W}}}$-${\tau}_{\overline{\mathrm{X}}}$, we can identify how close the $W\left(p\right)$ and $X\left(p\right)$ signals are. The closer they are, the less $PU$s are found.
- Parameter $\mathrm{\Phi}$ refers to the numerical ratio obtained when dividing the standard deviation for the composite signal to the standard deviation of the sensed noise, as expressed by$$\mathrm{\Phi}=\frac{{\sigma}_{X}}{{\sigma}_{W}}$$This parameter allows us to find the relation between the ${\sigma}_{X}$ and ${\sigma}_{W}$ with the purpose to know how spread out $X\left(p\right)$ is to estimate the presence of $PU$. Based on this rate, we can affirm that, when the value of $\mathrm{\Phi}$ is lower, it means the less PUs in $X\left(p\right)$. On the other hand, when the value of $\mathrm{\Phi}$ is higher, it means there is less TVWS in the composite signal. The value for $\mathrm{\Phi}\simeq 1$ represents that the only signal present in the TV-UHF band is the noise $W\left(p\right)$. Here, we can use the Rose criterion explained in [22] and mentioning that a $\mathrm{\Phi}\simeq 4$ would be an adequate reference value to estimate the presence of $W\left(p\right)$ and $PU$ signals.

## 5. Results and Discussion

#### 5.1. Reference Channels

#### 5.2. Confusion Matrix

#### 5.3. PU Decision Matrix

- ${P}_{d}$ calculated from collected readings.
- ${P}_{dmax}$ calculated from Scenario 1.
- The value for ${\tau}_{\overline{\mathrm{X}}}$.
- The value of $\alpha $.
- Preferred order to find E-TVWS.

#### 5.4. Final Results

## 6. Conclusions and Future Work

#### 6.1. Conclusions

#### 6.2. Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of the proposed rapid estimation method: the first block collects information on $W\left(p\right)$, $Xo\left(p\right)$, geolocation, and time stamp. The second block detects Primary Users (PU) and unused channels, stochastic and mathematical information, and Receiver Operation Characteristics (ROC). The third block applies the rapid method to estimate Television White Spaces (TVWS).

**Figure 2.**TV-UHF spectrum samples were collected by using two Radio Frequency Explorer (RFE) devices in parallel, one to characterize the noise signal $W\left(p\right)$ and another to collect the composite signal ${X}_{o}\left(p\right)$, together with a GPS receptor antenna to geolocate the readings. Each reading consisted of 112 samples for the composite signal and 112 samples for noise. The separation between two samples was 1.76 MHz, and all 112 samples covered 198 MHz, which is the TV-UHF bandwidth.

**Figure 3.**Example measurements: (

**a**) noise of the system, $W\left(p\right)$; (

**b**) composite signal sensed, ${X}_{o}\left(p\right)$; and (

**c**) the presence of the PU clearly observed when ten sampled points overlapped in order to illustrate the behaviour of the UHF TV spectrum in the sensed area.

**Figure 5.**Different values for threshold are plotted to show that ${T}_{high}$ produces missed detection of real PU signals and that ${T}_{low}$ produces some noise signals which are be considered PUs. In both cases, there are errors in the obtained results. An adequate value for T is plotted, which maintains enough distance from the noise floor to avoid false alarms and missed detection. This equilibrium is obtained when T considers a ${P}_{fa}$ of $3\%$.

**Figure 6.**Channels detected as used are coloured in gray, whereas channels considered as TVWS are in white. Channel 37 is in yellow because it is assigned for other purposes. Panels (

**a**–

**c**) correspond to points 1–3, respectively.

**Figure 7.**Collected signal representation: (

**a**) the Probability Density Function (PDF) of $W\left(p\right)$ is represented in blue, the PDF of ${X}_{o}\left(P\right)$ is plotted with a magenta dotted line, and the PDF of $X\left(p\right)$ is plotted with red dotted line. Notice that ${X}_{o}\left(P\right)$ and $X\left(P\right)$ curves have the same means and standard deviations; (

**b**) the normal PDF curves of $W\left(p\right)$, $X\left(p\right)$, and lines labelled as I and T delimit four areas under the curve (AUC). It is possible to identify ${P}_{d}$ in green, ${P}_{fa}$ in blue, ${P}_{m}$ in orange, the ${P}_{n}$ in gray.

**Figure 8.**ROC curve where ${P}_{fa}$ is the input and ${P}_{d}$ is calculated: panel (

**a**) shows a single ROC, and panel (

**b**) shows the overlapped ROC curves from ten different points sensed.

**Figure 9.**Two-point readings are plotted, for which panels (

**a**,

**d**) represent the $X\left(p\right)$ signal sensed. In panels (

**b**,

**e**), the PDF representations for $W\left(p\right)$ and $X\left(p\right)$ are presented, and panels (

**c**,

**f**) illustrate their respective Receiver Operation Characteristics (ROC) curves, where we can observe different patterns.

**Figure 10.**Diagram of the rapid estimation method proposed that shows the data flow process: Data collected by the Mobil Spectrum Sensing Station (MSSS) are combined and fed into three sub-blocks, namely, the Energy Detection (ED), the Statistical Analysis (SA), and the ROC Analysis (RA). The output of these blocks is introduced in the Rapid Estimation Method (REM) block to obtain an estimation of the TVWS (E-TVWS).

**Figure 11.**Energy Detection (ED) results for points 1 and 6: (

**a**) point 1, with 10 used channels, which are 35, 38, 40, 41, 42, 43, 44, 45, 47, and 48, means 32.25% usage and (

**b**) point 6, with 15 used channels, which are 20, 21, 26, 31, 32, 38, 39, 40, 41, 42, 43, 44, 45, and 49, means 46.87% usage.

**Figure 12.**Statistical Analysis (SA) results for example points: (

**a**) PDFs of ten points that are overlapped. It is easy to observe that each point corresponds to different PDF curves. The shape variation is related to the number of energy peaks detected in the ED block. (

**b**) ROC curves overlapped for points 1 to 10, where the horizontal axis scale has been modified to observe the variation in ${P}_{d}$ for a ${P}_{fa}=3\%$, shown by the green arrows.

**Figure 13.**REM parameters were used to find the estimation of the TVWS (E-TVWS), where sensed parameters are obtained by the MSSS, whereas calculated and auxiliary parameters are obtained by the signal analysis block.

**Figure 14.**In the plot that represents the PDF of the sensed signals, we draw a reference line named ${Z}_{1}X$, which is defined by a Z-score that separates 99% vs. 1% of the AUC of $X\left(p\right)$. Additionally, we observe its distance from T, I, $\overline{\mathrm{X}}$, and $\overline{\mathrm{W}}$, denoted as ${\tau}_{T}$, ${\tau}_{I}$ ${\tau}_{\overline{\mathrm{X}}}$, and ${\tau}_{\overline{\mathrm{W}}}$, respectively.

**Figure 15.**PDFs of sensed parameters $W\left(p\right)$ and $X\left(p\right)$ showing calculated parameters $\overline{\mathrm{W}}$, $\overline{\mathrm{X}}$, and T as well as auxiliary parameters I and ${Z}_{1}X$ for points P1 (

**a**) to P9 (

**i**).

**Figure 16.**Extreme cases analyzed: (

**a**) ROC curves for Scenarios 1 and 2 in full scale; (

**b**) extreme ROC curves for Scenarios 1 and 2 vs. the ${P}_{TVWS}$ curves for points P1 to P10. Green arrows indicates the upper and lower limits for ${P}_{d}$ corresponding to 3% to find E-TVWS.

Ord | Characteristic | Values |
---|---|---|

1 | Frequency Range | 240 MHz to 960 MHz |

2 | Span | 0.112 MHz to 300 MHz |

3 | Frequency Resolution | 1 kHz |

4 | Average Noise Level | −115 dBm |

5 | Amplitude Resolution | 0.5 dBm |

6 | Automatic RBW | 2.6 kHz to 600 kHz |

$\mathit{Point}$ | $\mathit{PU}$ | ${\mathit{P}}_{\mathit{d}}$ | $\overline{\mathbf{W}}$ | ${\mathit{\sigma}}_{\mathit{W}}$ | $\overline{\mathbf{X}}$ | ${\mathit{\sigma}}_{\mathit{X}}$ | ${\mathit{Z}}_{\mathit{X}}$ | I | T | ${\mathit{Z}}_{1}\mathit{X}$ |
---|---|---|---|---|---|---|---|---|---|---|

P1 | 10 | 37.15 | −109.05 | 1.8764 | −106.36 | 4.8409 | −0.3280 | −106.46 | −105.53 | −95.827 |

P2 | 9 | 42.42 | −109.26 | 2.1576 | −106.35 | 5.9925 | −0.1913 | −106.18 | −105.20 | −92.401 |

P3 | 12 | 47.17 | −109.28 | 2.1431 | −105.74 | 6.8842 | −0.0710 | −106.00 | −105.25 | −89.702 |

P4 | 12 | 41.22 | −108.08 | 2.0791 | −105.79 | 7.2981 | −0.2218 | −104.77 | −104.17 | −88.784 |

P5 | 14 | 49.37 | −109.29 | 2.0040 | −105.63 | 6.8174 | −0.0158 | −106.15 | −105.52 | −89.743 |

P6 | 15 | 56.17 | −109.25 | 1.7163 | −104.78 | 8.0119 | 0.1552 | −106.22 | −106.02 | −86.112 |

P7 | 15 | 42.38 | −109.47 | 2.0123 | −106.57 | 4.5941 | −0.1922 | −106.88 | −105.68 | −95.869 |

P8 | 16 | 50.82 | −109.37 | 2.1551 | −105.16 | 7.7402 | 0.0205 | −105.92 | −105.32 | −87.124 |

P9 | 12 | 50.16 | −109.42 | 2.0332 | −105.57 | 7.0974 | 0.0039 | −106.20 | −105.60 | −89.030 |

P10 | 12 | 45.85 | −109.12 | 2.1267 | −105.83 | 6.8013 | −0.1041 | −105.88 | −105.12 | −89.987 |

Ord | From | To | Name |
---|---|---|---|

1 | $\overline{\mathrm{W}}$ | ${Z}_{1}X$ | ${\tau}_{\overline{\mathrm{W}}}$ |

2 | I | ${Z}_{1}X$ | ${\tau}_{I}$ |

3 | $\overline{\mathrm{X}}$ | ${Z}_{1}X$ | ${\tau}_{\overline{\mathrm{X}}}$ |

4 | T | ${Z}_{1}X$ | ${\tau}_{T}$ |

$\mathit{Point}$ | ${\mathit{\tau}}_{\overline{\mathbf{W}}}$ | ${\mathit{\tau}}_{\mathit{I}}$ | ${\mathit{\tau}}_{\mathit{T}}$ | ${\mathit{\tau}}_{\overline{\mathbf{X}}}$ |
---|---|---|---|---|

P1 | 13.226 | 10.631 | 9.698 | 11.279 |

P2 | 16.859 | 13.774 | 12.802 | 13.962 |

P3 | 19.577 | 16.302 | 15.548 | 16.040 |

P4 | 19.296 | 15.989 | 15.387 | 17.005 |

P5 | 19.546 | 16.407 | 15.779 | 15.884 |

P6 | 23.139 | 20.110 | 19.912 | 18.668 |

P7 | 13.598 | 11.009 | 9.814 | 10.704 |

P8 | 22.532 | 19.064 | 18.480 | 18.227 |

P9 | 20.394 | 17.173 | 16.571 | 16.537 |

P10 | 19.134 | 15.891 | 15.135 | 15.847 |

$\mathit{Point}$ | $\mathit{PU}$ | ${\mathit{P}}_{\mathit{d}}$ | $\overline{\mathbf{W}}$ | ${\mathit{\sigma}}_{\mathit{W}}$ | $\overline{\mathbf{X}}$ | ${\mathit{\sigma}}_{\mathit{X}}$ | ${\mathit{Z}}_{\mathit{X}}$ | I | T | ${\mathit{Z}}_{1}\mathit{X}$ |
---|---|---|---|---|---|---|---|---|---|---|

Scenario 1 | 32 | 83.89 | −109.22 | 2.1952 | −94.66 | 10.901 | −0.9966 | −104.79 | −105.09 | −69.261 |

Scenario 2 | 0 | 3.70 | −109.36 | 1.7327 | −108.80 | 1.5323 | 1.7879 | −105.97 | −106.06 | −105.23 |

Ord | ${\mathit{P}}_{\mathit{d}}$ | ${\mathit{P}}_{\mathit{m}}$ | $\mathit{PPV}$ |
---|---|---|---|

P1 | 37.15 | 13.67 | 92.52 |

P2 | 42.42 | 6.45 | 93.39 |

P3 | 47.17 | 4.34 | 94.02 |

P4 | 41.22 | 3.22 | 93.21 |

P5 | 49.37 | 3.67 | 94.27 |

P6 | 56.17 | 0.96 | 94.92 |

P7 | 42.38 | 10.31 | 93.38 |

P8 | 50.82 | 3.09 | 94.42 |

P9 | 50.16 | 3.38 | 94.35 |

P10 | 45.85 | 4.44 | 93.85 |

Average | 93.81 |

**Table 7.**TVWS decision matrix: PU presence, channel numbers to identify them, percentage in the band of interest, and preferred order to be assigned.

PU Presence (%) | Channels | TV-UHF Band | TVWS Preferred Order |
---|---|---|---|

$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}1\to \phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}0$ | 19, 22, 23, 24, 27, 30, 33, 34, 36, 51 | 31.25% | 1 |

$20\to \phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}1$ | 28, 29, 35, 46, 47, 48 | 18.75% | 2 |

$40\to 21$ | 20, 25 | 6.25% | 3 |

$60\to 41$ | 26 | 3.13% | 4 |

$80\to 61$ | 21, 31, 32, 38, 39, 49, 50 | 21.87% | 5 |

$100\to 81$ | 40, 41, 42, 43, 44, 45 | 18.75% | 6 |

Ord | ${\mathit{P}}_{\left(\mathit{TVWS}\right)}$ | ${\mathit{R}}_{\left(\mathit{TVWS}\right)}$ | Variation | ${\mathit{D}}_{\left(\mathit{TVWS}\right)}$ |
---|---|---|---|---|

1 | 52.72 | 68.75 | 16.03 | 16 |

2 | 48.30 | 71.88 | 23.57 | 15 |

3 | 44.32 | 62.50 | 18.18 | 14 |

4 | 49.31 | 62.50 | 13.19 | 15 |

5 | 42.47 | 56.25 | 13.78 | 13 |

6 | 36.37 | 53.13 | 16.36 | 11 |

7 | 48.34 | 54.12 | 4.79 | 15 |

8 | 41.26 | 53.13 | 8.74 | 13 |

9 | 41.81 | 62.50 | 20.69 | 13 |

10 | 45.83 | 62.50 | 17.07 | 14 |

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## Share and Cite

**MDPI and ACS Style**

Corral-De-Witt, D.; Ahmed, S.; Rojo-Álvarez, J.L.; Tepe, K.
Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters. *Telecom* **2020**, *1*, 161-180.
https://doi.org/10.3390/telecom1030012

**AMA Style**

Corral-De-Witt D, Ahmed S, Rojo-Álvarez JL, Tepe K.
Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters. *Telecom*. 2020; 1(3):161-180.
https://doi.org/10.3390/telecom1030012

**Chicago/Turabian Style**

Corral-De-Witt, Danilo, Sabbir Ahmed, José Luis Rojo-Álvarez, and Kemal Tepe.
2020. "Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters" *Telecom* 1, no. 3: 161-180.
https://doi.org/10.3390/telecom1030012