# Kronecker-Based Fusion Rule for Cooperative Spectrum Sensingwith Multi-Antenna Receivers

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

## 3. GLRT Based Detection Scheme

## 4. GLRT Based on Kronecker Product

#### 4.1. SPKP-GLRT

Algorithm 1 ML based Non-Iterative Flip-Flop |

#### 4.2. MPKP-GLRT

## 5. Numerical Results

**Figure 2.**Receiver operating characteristic (ROC) curves: L = 4, K = 10, N = 70, κ = −15 dB. Solid Lines and Dashed Lines α

_{nu}= 2.

**Figure 3.**Area under the ROC curve to asses the effects of the sample size N, using, κ = −15 dB. Solid Lines α

_{nu}= 1, Dashed lines α

_{nu}= 2.

**Figure 4.**Area under the ROC curve to asses the effects of Noise uncertainty α

_{nu}= 2, N = 70, κ = −15 dB.

**Figure 5.**Area under the ROC curve to asses the effect of Shadowing, σ

_{dB–Spread}: N = 60, κ = −15 dB and Solid Lines α

_{nu}= 1, Dashed lines α

_{nu}= 2.

**Figure 6.**Area under the ROC curve to asses the effect of number of antennas: N = 60, κ = −15 dB and α

_{nu}= 1.

**Figure 7.**Area under the ROC curve to asses the effect of number of antennas: N = 60, κ = −15 dB and α

_{nu}= 2.

**Figure 8.**P

_{D}vs average signal-to-noise ratio (SNR): Number of sensors K = 10, number of antennas L = 4, N = 100 and α

_{nu}= 1.

## 6. Conclusions

## Author Contributions

## Conficts of Interest

## References

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**MDPI and ACS Style**

Ali, S.; Jansson, M.; Seco-Granados, G.; López-Salcedo, J.A.
Kronecker-Based Fusion Rule for Cooperative Spectrum Sensingwith Multi-Antenna Receivers. *Electronics* **2014**, *3*, 675-688.
https://doi.org/10.3390/electronics3040675

**AMA Style**

Ali S, Jansson M, Seco-Granados G, López-Salcedo JA.
Kronecker-Based Fusion Rule for Cooperative Spectrum Sensingwith Multi-Antenna Receivers. *Electronics*. 2014; 3(4):675-688.
https://doi.org/10.3390/electronics3040675

**Chicago/Turabian Style**

Ali, Sadiq, Magnus Jansson, Gonzalo Seco-Granados, and José A. López-Salcedo.
2014. "Kronecker-Based Fusion Rule for Cooperative Spectrum Sensingwith Multi-Antenna Receivers" *Electronics* 3, no. 4: 675-688.
https://doi.org/10.3390/electronics3040675