# Operational Characteristics of Square-Law Combining Energy Detector in MIMO-OFDM Cognitive Radio Systems

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## Abstract

**:**

## 1. Introduction

- A mathematical modelling of the parameters for the assessment of the effectiveness of the ED process employing the SLC technique in MIMO-OFDM transmission systems affected by NU changes and DDT adaptation.
- The verifying of an algorithm that enables the simulation of the ED process assessment in SISO- and MIMO-OFDM transmission systems.
- An elaboration on how the different levels of DDT adjustment and NU variations affect the ROC curves when the ED process is performed with a different number of transmitting and receiving antennas, as well as varied sensing sample totals, PU transmitting powers, modulation techniques, and SNR values.

## 2. Literature Review

## 3. Fundamentals of the ED Process

#### Properties of the Receiver Operating Characteristic Curves

_{0}and H

_{1}is comparable to that of a random guess. As shown in Figure 2, spaces above or below the curve presenting random guess processes represent the good or poor signal detection accuracy, respectively. If the line is near the random guess curve, the ED process is less precise and vice versa (Figure 2). Additionally, the area under the curve (AUC) is a dimension used to define precise signal detection. The greater the area under the curve, the more precise the signal detection is, and vice versa (Figure 2). The ROC-AUC model is being further used in this work as it represents the most commonly used model for analysing PU signal detection efficiency.

## 4. Mathematical Description of the Principles of ED Using SLC in MIMO-OFDM Systems

#### 4.1. Mathematical Representation of the Detection and False Alarm Probability in MIMO Systems

#### 4.2. Mathematical Formulation of the Role of Detection Threshold on ED Process

#### 4.3. Mathematical Formulation of the Role of Noise Uncertainty in the ED Process

#### 4.4. Mathematical Formulation of the Combined Role of Noise Uncertainty and Detection Threshold on the ED Process

## 5. Implementation of the Simulation Algorithm

Algorithm 1. Simulation phases of the ED SS employing SLC with one PU and one SU in a wireless communication system. |

1. Input: Number of Rx antenna: r = R, Number of Tx antenna m = M,Modulation type: m-PSK/m-QAM, Number of detection samples: N, Tx power of PU: P _{Tx}, Number of Mote-Carlo simulations: mk,OFDM symbol length: length_mimo_ofdm_data, transmitted signal by the PU: M⨯r.2. FOR ${P}_{fa}$ range [0,1] andFOR a number of mk iterations3. Modelling the impact of AWGN noise with variance ${\sigma}_{w}^{2}\left(n\right)$ AWGN_DDT ($\rho $= 1.00$,{\rho}^{\prime}$1.00)= sqrt(${\sigma}_{w}^{2}\left(n\right)$ = 1.00).*randn (1, leght_ data_ ofdm _ mimo); AWGN_NUDDT (ρ > 1.00, p’> 1.00)= sqrt(${\sigma}_{w}^{2}\left(n\right)$ > 1.00).*randn (1, leght_ data_ ofdm _ mimo); 4. Computation of received signal impacted with AWGN M⨯r_OFDM_ DDT = M⨯r + AWGN_DDT;M⨯r_OFDM_ NUDDT = M⨯r + AWGN_NUDDT;5. REPEATE FOR r= 1:R energy calculationcalculation _energy_ DDT = abs( M⨯r_OFDM_ DDT).^2;calculation _energy_ NUDDT= abs( M⨯r_OFDM_ NUDDT).^2;END6. FOR r = 1:R ${\mathsf{\Lambda}}_{SLC}$ calculation based on (3)statistic_ test_DDT = sum(calculation _energy_ DDT); statistic_ test_NUDDT = sum(calculation _energy_ DDT); END7. Evaluation of ${\lambda}_{fa}^{NUDDT}$ according to (21) threshold_DDT = ((qfuncinv(${P}_{fa}$)./sqrt(N))+ 1)./$\rho \prime $; threshold_NUDDT = ((qfuncinv(${P}_{fa}$).* ρ./sqrt(N))+ ρ)./$\rho \prime $; 8. Process of making a decision based on (4) IF (statistic_test_ DDT >= threshold_DDT);ENDIF (statistic_test_ NUDDT >= threshold_NUDDT);ENDEND9. Evaluation ${P}_{d}^{NU}$ ${P}_{d}^{DDT}$ and ${P}_{d}^{NUDDT}$ using Monte Carlo simulation (based on (2)) END10. Until ${P}_{d}^{NU},{P}_{d}^{DDT},{P}_{d}^{NUDDT}$= [0, 1] |

**Mxr**signal detected at each of the R Rx branches of the SU, serves as the input signal of the ED process. To get reliable simulation results, several Monte-Carlo simulations (mk) were executed, and the efficiency of the ED method was assessed through the generation of ROC curves for the probability of false alarms in the range [0, 1] (Table 2). The impact of the AWGN with zero mean and variance ${\sigma}_{w}^{2}\left(n\right)$ on ED process was modelled in line 3 of Algorithm 1.

**Y(n)**(Figure 1) was divided into two different types. The first type of received signal (

**M**

**⨯**

**r**_OFDM_ DDT) was detected using the DDT adaptation for the MIMO-OFDM communication system which is not impacted by the NU variations ($\rho $ = 1.00, ${\rho}^{\prime}$> 1.00). The second type of the MIMO-OFDM signal (

**M**

**⨯**

**r**_OFDM_ NUDDT) was detected by the DDT adjustments in a simulated environment which takes into consideration the impact of the NU variations ($\rho $> 1.00, ${\rho}^{\prime}$ > 1.00). By employing the SLC approach, the energy calculation of the signal detected over all R Rx antennas (calculation _energy_ DDT, calculation _energy_ NUDDT) was performed in line 5 of Algorithm 1 (Figure 3).

## 6. Simulation Results and Analysis

#### 6.1. Review of the Simulation Software and Parameters

#### 6.2. The Role of the Number of Tx-Rx Chains in the ED Sensing Efficiency

#### 6.3. The Role of Various DDT Adaption Levels and NU Fluctuations on the ED Sensing Efficiency

#### 6.4. The Role of Various PU Transmit Power Levels on the ED Sensing Performance

#### 6.5. The Role of Different Numbers of Asymmetric and Symmetric MIMO Transmission Branches in the ED Sensing Efficiency

#### 6.6. The Role of Various SNR Levels on the ED Sensing Efficiency

#### 6.7. The Role of Various Number of Detection Samples on the ED Sensing Efficiency

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Mangold, S.; Zhong, Z.; Challapali, K.; Chou, C.-T. Spectrum agile radio: Radio resource measurements for opportunistic spectrum usage. In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM ’04.), Dallas, TX, USA, 29 November–3 December 2004; pp. 3467–3471. [Google Scholar] [CrossRef]
- Otermat, D.T.; Otero, C.E.; Kostanic, I. Analysis of the FM radio spectrum for Internet of Things opportunistic access via Cognitive Radio. In Proceedings of the 2015 IEEE 2nd World Forum on Internet of Things (WF-IoT), Milan, Italy, 14–16 December 2015; pp. 166–171. [Google Scholar] [CrossRef]
- Rwodzi, J. Energy-Detection Based Spectrum Sensing for Cognitive Radio on a Real-Time SDR Platform. Master’s Thesis, Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa, 2016. [Google Scholar]
- Mahmoud, H.A.; Yucek, T.; Arslan, H. OFDM for cognitive radio: Merits and challenges. IEEE Wirel. Commun.
**2009**, 16, 6–15. [Google Scholar] [CrossRef] - Pan, G.; Li, J.; Lin, F. A cognitive radio spectrum sensing method for an OFDM signal based on deep learning and cycle spectrum. Int. J. Dig. Multimed. Broad.
**2020**, 2020, 5069021. [Google Scholar] [CrossRef] - Xiao, Y.; Hu, F. Cognitive Radio Networks, 1st ed.; Auerbach Publications: Boca Raton, FL, USA, 2008; pp. 3–37. [Google Scholar]
- Patil, P.; Patil, M.R.; Itraj, S.; Bomble, U.L. A Review on MIMO OFDM Technology Basics and More. In Proceedings of the International Conference on Current Trends in Computer, Electrical, Electronics and Communication (CTCEEC), Mysore, India, 8–9 September 2017; pp. 119–124. [Google Scholar] [CrossRef]
- Eduardo, A.F.; Caballero, R.G.G. Experimental evaluation of performance for spectrum sensing: Matched filter vs energy detector. In Proceedings of the IEEE Colombian Conference on Communication and Computing (IEEE COLCOM 2015), Popayan, Colombia, 13–15 May 2015; pp. 1–6. [Google Scholar] [CrossRef]
- Arar, A.M.; Masri, A.M.; Ghannam, H.O.; Tumar, I.K. A proposed scheme for dynamic threshold versus noise uncertainty in cognitive radio networks (DTNU). Wirel. Pers. Commun.
**2017**, 96, 4543–4555. [Google Scholar] [CrossRef] - Thuo, N. An Adaptive Threshold Energy Detection Technique with Noise Variance Estimation for Cognitive Radio Sensor Networks. Master’s Thesis, Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa, 2015. [Google Scholar]
- Rodes, L.; Kaushik, A.; Sharma, S.K.; Chatzinotas, S.; Jondral, F. Square-Law Selector and Square-Law Combiner for Cognitive Radio Systems: An Experimental Study. In Proceedings of the 2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), Montreal, QC, Canada, 18–21 September 2016; pp. 1–5. [Google Scholar] [CrossRef][Green Version]
- Kuppusamy, V.; Mahapatra, R. Primary user detection in OFDM based MIMO Cognitive Radio. In Proceedings of the 2008 3rd International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CrownCom 2008), Singapore, 15–17 May 2008; pp. 1–5. [Google Scholar] [CrossRef]
- Ustok, R.F. Spectrum Sensing Techniques for Cognitive Radio Systems with Multiple Antennas. Master’s Thesis, Electrical and Electronic Engineering Department, Izmir Institute of Technology, Izmir, Turkey, 2009. [Google Scholar]
- Ranjeeth, M. Cooperative spectrum sensing with square law combining diversity reception. In Proceedings of the 2015 3rd International Conference on Signal Processing, Communication and Networking (ICSCN), Chennai, India, 26–28 March 2015; pp. 1–6. [Google Scholar] [CrossRef]
- Digham, F.F.; Alouini, M.S.; Simon, M.K. On the energy detection of unknown signals over fading channels. IEEE Trans. Commun.
**2007**, 55, 3575–3579. [Google Scholar] [CrossRef] - Tellambura, C. Spectrum sensing methods and their performance. In Handbook of Cognitive Radio, 1st ed.; Springer Nature: Singapore, 2018; pp. 163–185. [Google Scholar]
- Zhang, J.; Liu, L.; Liu, M.; Yi, Y.; Yang, Q.; Gong, F. MIMO spectrum sensing for cognitive radio-based Internet of things. IEEE Internet Things J.
**2020**, 7, 8874–8885. [Google Scholar] [CrossRef] - Lorincz, J.; Ramljak, I.; Begušić, D. A review of the noise uncertainty impact on energy detection with different OFDM system designs. Comp. Commun.
**2019**, 148, 185–207. [Google Scholar] [CrossRef] - Lorincz, J.; Ramljak, I.; Begušić, D. A survey on the energy detection of OFDM signals with dynamic threshold adaptation: Open Issues and Future Challenges. Sensors
**2021**, 21, 3080. [Google Scholar] [CrossRef] [PubMed] - Lorincz, J.; Ramljak, I.; Begušić, D. Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems. Sensors
**2021**, 21, 6881. [Google Scholar] [CrossRef] [PubMed] - Lorincz, J.; Ramljak, I.; Begušić, D. Performance Analyses of Energy Detection Based on Square-Law Combining in MIMO-OFDM Cognitive Radio Networks. Sensors
**2021**, 21, 7678. [Google Scholar] [CrossRef] [PubMed] - Lorincz, J.; Ramljak, I.; Begušić, D. Analysis of the Impact of Detection Threshold Adjustments and Noise Uncertainty on Energy Detection Performance in MIMO-OFDM Cognitive Radio Systems. Sensors
**2022**, 22, 631. [Google Scholar] [CrossRef] [PubMed] - Atapattu, S.; Tellambura, C.; Jiang, H. Energy Detection for Spectrum Sensing in Cognitive Radio; Springer International Publishing AG: New York, NY, USA, 2014; pp. 11–38. [Google Scholar]
- Gkonis, P.K.; Trakadas, P.T.; Kaklamani, D.I. A Comprehensive Study on Simulation Techniques for 5G Networks: State of the Art Results, Analysis, and Future Challenges. Electronics
**2020**, 9, 468. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Operational blocks of the MIMO-OFDM communication system employing ED spectrum sensing realized by the SLC technique.

**Figure 2.**The ROC curve indicating the interdependence among the detection and false alarm probability.

**Figure 4.**The ROC curves for various NU and DDT factor combinations in (

**a**) SISO and (

**b**) 2 × 2 MIMO-OFDM systems characterized by transmission with m-PSK/m-QAM modulation, N = 128, SNR = −15 dB and P

_{Tx}= 100 mW.

**Figure 5.**The ROC curves for various NU and DDT factor combinations in asymmetric 2 × 3 MIMO systems characterized by transmission with m-PSK/m-QAM modulation, N = 128, SNR = −15 dB and P

_{Tx}= 100 mW.

**Figure 6.**The ROC curves for various levels of NU and DDT factors in (

**a**) SISO systems with the PU transmitting at 100 mW, (

**b**) SISO systems with the PU transmitting at 10 W, (

**c**) 2 × 2 MIMO systems with the PU transmitting at 100 mW, and (

**d**) 2 × 2 MIMO system with the PU transmitting at 10 W and for transmission characterized with QPSK modulation, N = 128 and SNR = −15 dB.

**Figure 7.**The ROC curves for various NU and DDT factor combinations in asymmetric MIMO (2 × 3 and 3 × 2) systems for transmission characterized with QPSK modulation, N = 128, SNR = −15 dB and P

_{Tx}= 100 mW.

**Figure 8.**The ROC curves for various NU and DDT factor combinations in SISO and symmetric MIMO systems for transmission characterized with QPSK modulation, N = 128, SNR = −15 dB and P

_{Tx}= 100 mW.

**Figure 9.**The ROC curves for various NU and DDT factor combinations and for different values of the SNRs (−20, −15, and −10 dB) in (

**a**) SISO and (

**b**) 2 × 2 MIMO systems for transmission characterized with QPSK modulation, N = 128 and P

_{Tx}= 100 mW.

**Figure 10.**The ROC curves for the various NU and DDT factor combinations and distinct number of detection samples (128, 256, 512) in (

**a**) SISO and (

**b**) MIMO systems for transmission characterized with QPSK modulation, SNR = −15 dB and P

_{Tx}= 100 mW.

Symbol | Meaning |
---|---|

M | The PU’s total number of transmitting (Tx) antennas installed at the PU |

R | The SU’s total number of receiving (Rx) antennas installed at the SU |

m | The number of transmitting (Tx) antennas installed at the PU |

r | The number of receive (Rx) antennas installed at the SU |

N | Total number of samples utilized in the ED procedure without DDT and the NU variations |

${N}^{NU}$ | Total number of samples utilized in the ED procedure with NU |

${N}^{DDT}$ | Total number of samples utilized in the DDT-ED procedure |

${N}^{NUDDT}$ | Total number of samples utilized in the DDT-ED procedure affected by NU |

$\mathit{s}$ | A complex signal sent from the PU side using M Tx antennas |

${\mathit{s}}_{\mathit{m}}$ | A complex signal sent from the PU side using m-th antenna |

P | Total PU power emitted via M Tx antennas |

${P}_{m}$ | The power emitted via the m-th antenna at the PU side |

$\mathit{Y}\left(n\right)$ | The overall received signal by all SUs R Rx antennas in the n-th SS period |

${\mathit{h}}_{\mathit{r}}\left(n\right)$ | Gain of the channel between the M Tx antenna and the r-th Rx branch in the n-th sensing interval |

${\mathit{y}}_{\mathit{r}}\left(n\right)$ | The received signal at the SUs r-th Rx antennas in the n-th SS interval |

${\mathit{w}}_{\mathit{r}}\left(n\right)$ | The noise of the signal received by SU via the r-th Rx antennas in the n-th SS interval |

${s}_{r}\left(n\right)$ | Signal vector received at the r-th Tx branch within the n-th sensing interval |

${\sigma}_{{s}_{r}}^{2}\left(n\right)$ | Received signal variance at the r-th Rx branch of the SUs in the n-th SS interval |

${\sigma}_{w}^{2}{}_{r}\left(n\right)$ | Noise variance of the signal detected at the SUs r-th Rx antenna observed in the n-th SS interval |

${\sigma}_{wNU}^{2}\left(n\right)$ | The variance of AWGN noise used in the ED contaminated by NU |

${\sigma}_{wNUDDT}^{2}\left(n\right)$ | The variance of AWGN noise in the DDT-ED process contaminated by NU variation |

${\Lambda}_{SLC}$ | The cumulative test statistics for signals collected at the SU through the R Rx antennas |

${\Lambda}_{r}$ | The signal test statistics for the SU’s r-th Rx antenna branches |

${\gamma}_{SLC}\left(n\right)$ | The SNR ratio for the R SU receive antennas in the n-th SS interval |

${\gamma}_{r}\left(n\right)$ | SNR at the SU’s r-th receive antenna branches during the n-th SS period |

$\overline{{\gamma}_{SLC}}\left(n\right)$ | The average SNR ratio observed by the SU device for all R Rx antenna branches during the n-th SS interval |

${P}_{d}$ | Probability of detection for ED processes executed without the use of DDT and fluctuation in NU |

${P}_{fa}$ | Probability of false alarm for ED processes executed without the use of DDT and fluctuation in NU |

${P}_{d}^{NU}$ | Probability of detection for ED process affected by NU variation |

${P}_{fa}^{NU}$ | Probability of false alarm in ED process affected by NU variation |

${P}_{d}^{DDT}$ | Probability of detection for DDT ED process |

${P}_{fa}^{DDT}$ | Probability of false alarm for DDT ED process |

${P}_{d}^{NUDDT}$ | Probability of detection for DDT ED process affected by NU variation |

${P}_{fa}^{NUDDT}$ | Probability of false alarm for DDT ED process affected by NU variation |

λ | DT without adaptation to DDT and the effect of NU variation |

${\lambda}_{d}$ | DT following CDR principles |

${\lambda}_{fa}$ | DT following CFAR principles |

${\lambda}_{d}^{DDT}$ | Detection threshold for DDT ED process |

${\lambda}_{fa}^{DDT}$ | False alarm threshold for DDT ED process |

${\lambda}_{d}^{NU}$ | Detection threshold affected by NU variation |

${\lambda}_{fa}^{NU}$ | False alarm threshold affected by NU variation |

${\lambda}_{d}^{NUDDT}$ | Detection threshold for DDT ED process affected by NU variation |

${\lambda}_{fa}^{NUDDT}$ | False alarm threshold for DDT ED process affected by NU variation |

${\lambda}^{\prime DDT}$ | DT interval for DDT ED process without NU variation |

${\lambda}^{\prime NUDDT}$ | DT interval for DDT ED process affected by NU variation |

ρ | Parameter of noise uncertainty (NU), NU factor |

${\rho}^{\prime}$ | Parameter of dynamic detected threshold (DDT), DDT factor |

${H}_{1}$ | The hypothesis explains why the licensed (PU) signal exists. |

${H}_{0}$ | The hypothesis explains why the licensed (PU) signal isn’t present. |

Parameters | Type/Quantity |
---|---|

DDT factor/parameter $\rho \prime $ | 1.00, 1.03, 1.05 |

NU factor/parameter $\rho $ | 1.00, 1.03, 1.05 |

Type of PU signal | OFDM |

Tx power of PU (W) | 0.1, 10 |

OFDM modulation type | QPSK, 64 QAM, 16 QAM, |

Number of detection samples | 128, 256, 512 |

SNR at the SU point (dB) | −20, −15, −10 |

The quantity of the PU Tx branches | 1–4 |

The quantity of the SU Rx branches | 1–4 |

Number of Monte Carlo iterations | 10,000 |

False alarm and detection probability range | [0–1] |

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**MDPI and ACS Style**

Ramljak, I.; Begušić, D.; Lorincz, J. Operational Characteristics of Square-Law Combining Energy Detector in MIMO-OFDM Cognitive Radio Systems. *Appl. Sci.* **2022**, *12*, 4684.
https://doi.org/10.3390/app12094684

**AMA Style**

Ramljak I, Begušić D, Lorincz J. Operational Characteristics of Square-Law Combining Energy Detector in MIMO-OFDM Cognitive Radio Systems. *Applied Sciences*. 2022; 12(9):4684.
https://doi.org/10.3390/app12094684

**Chicago/Turabian Style**

Ramljak, Ivana, Dinko Begušić, and Josip Lorincz. 2022. "Operational Characteristics of Square-Law Combining Energy Detector in MIMO-OFDM Cognitive Radio Systems" *Applied Sciences* 12, no. 9: 4684.
https://doi.org/10.3390/app12094684