# Analysis of the Impact of Detection Threshold Adjustments and Noise Uncertainty on Energy Detection Performance in MIMO-OFDM Cognitive Radio Systems

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## Abstract

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## 1. Introduction

- The development of the explicit analytic mathematical expressions for the performance assessment of ED process employing SLC method impacted by NU and DT adjustments in MIMO-OFDM CR systems.
- The introduction of the simulation algorithm for executing the ED process by exploiting the SLC method in MIMO-OFDM CR networks affected by different levels of DT adjustments and NUs.
- The comprehensive analyses of simulation results through investigation of the influence of various parameters including the OFDM modulations, the SNRs, the MIMO Tx-Rx chains number, the false alarm probabilities, the Tx powers of PU, the number of sampling points used in ED, and the different levels of NU and DT adjustments on the probability of detection of the PU transmission.

## 2. Literature Overview

## 3. System Design and Explanation of the Energy Detection Operation

_{m}. The $P={{\displaystyle \sum}}_{m=1}^{M}{P}_{m}$ defines the overall instant Tx power of the PU transmitted via M Tx chains (Figure 1). Table 2 lists the descriptions of all parameters used in the analysis. The complex signal defined as ${\mathit{s}}_{m}={\mathit{s}}_{m,r}+\mathit{j}{\mathit{s}}_{m,i}$ is assumed as the signal transmitted via m-th Tx chain of PU (Figure 1). Hence, the signals carried via the M Tx chains of PU are expressed as $\mathit{s}={{\displaystyle \sum}}_{m=1}^{M}{\mathit{s}}_{m}$. The signal received by the SU at every R Rx chain (antenna) and sampled by n samples where n = 1,…, N can be formulated as:

**Y**(n) satisfies hypotheses ${H}_{0}$ or ${H}_{1}$. Therefore, in the process of deciding whether the PU is present or not, the threshold is compared with the sensed energy of the signal detected at the antennas of SU. The decision hypotheses ${H}_{1}$ is satisfied when the sensed energy of the signal detected at the antennas of SU is greater than the threshold. This results in the conclusion that the PU transmits in the dedicated band. The decision hypotheses ${H}_{0}$ is satisfied if the energy of the detected signal is lower than the DT. This results in the cognition that the signal of PU is absent. Thus, the result of this binary hypothesis test determines the SU activity in the terms of possible transmission in the PU frequency band.

#### 3.1. Process of Energy Detection

_{1}and H

_{0}, the false alarm and detection probability for ED SS employing SLC diversity technique in MIMO-OFDM CR systems was developed.

#### 3.2. Probabilities of False Alarm and Detection for MIMO-OFDM CR Systems

_{0}as ${P}_{fa}[\mathrm{Pr}({\mathsf{\Lambda}}_{SLC}>\lambda )|{H}_{0}]$. The false alarm probability (${P}_{fa}$) as a performance metric of ED employing the SLC method in MIMO communication systems can be defined as:

#### 3.3. Detection Threshold Estimation

#### 3.4. Estimation of Noise Uncertainty

#### 3.5. Energy Detection Process with NU and DT

## 4. Simulation Algorithm for the ED Employing SLC

Algorithm 1 Simulation of the ED in distinct working environments of MIMO-OFDM CR systems. |

1: INPUT: MIMO_OFDM_M×r, noise variance (${\sigma}_{w}^{2})$, number of sampling points (N), probability of false alarm (${P}_{fa}$), number of Monte Carlo simulations(pp), SNR simulation range (SNR), length of the MIMO-OFDM data (mimo_ofdm_len), DDT factor ($\rho \prime $), and NU factor (ρ),2: OUTPUT: Detection probability impacted by DT adjustment (${P}_{d}^{DT}$) and Detection probability impacted by NU and DT adjustment (${P}_{d}^{NUDT})$3: ON INITIALIZED: MIMO-OFDM signal (MIMO_OFDM_M×r) do:Step 1: Execution of simulation indicating detection probability impacted by DT adjustments (${P}_{d}^{DT}$) and Detection probability impacted by DT adjustments and NU (${P}_{d}^{NUDT}$) vs. SNR using (14) (22), (28), and (34)4: set pp = number of Monte Carlo simulations 5: set SNR = signal to noise ratio in interval [−25 dB, 25 dB] 6: FOR b = 1:length (SNR)7: j1 = 0; j2 = 0; 8: FOR pp = 1:10,000;Step 2: Modeling AWGN noise with varince ${\sigma}_{w}^{2}\left(n\right)$9: Noise_DT (ρ = 1.00, ${\rho}^{\prime}$> 1.00) = sqrt(${\sigma}_{w}^{2}(n)=1.00$).*randn (1, mimo_ofdm_len); 10: Noise_NUDT (ρ > 1.00, ${\rho}^{\prime}$> 1.00) = sqrt(${\sigma}_{w}^{2}(n)>1.00$).*randn (1, mimo_ofdm_len); Step 3: Estimation of received signal $y$(t)11: finall_OFDM_M×r_DT = MIMO_OFDM_M×r + Noise_DT; 12: finall_OFDM_M×r_NUDT = MIMO_OFDM_M×r + Noise_NUDT; Step 4: Energy estimation of received signal using SLC concept13: REPEATE FOR r= 1:R14: energy_calculation_DT = abs(finall_OFDM_M×r_DT).^2; 15: energy_calculation _NUDT= abs(finall_OFDM_M×r_NUDT).^2; 16: ENDStep 5: Estimation of test statistics based on mixing energies of R signals using (4) 17: FOR r= 1:R18: test_statistc_DT = sum(energy_calculation_DT); 19: test_statistic_NUDT = sum(energy_calculation_NUDT); 20: ENDStep 6: Threshold estimation using (18), (20), and (30), (32))21: threshold_DT (b) = ((qfuncinv(${P}_{fa}$(b))./sqrt(N))+ 1)./${\rho}^{\prime}$; 22: threshold_NUDT (b) = ((qfuncinv(${P}_{fa}$ (b)).* ρ./sqrt(N))+ ρ)./$\rho \prime $; Step 7: Making a final decision by using using (5) and (6)23: IF (test_statistc_DT >= threshold_DT (b));24: j1 = j1 + 1; 25: END26: IF (test_statistic_NUDT >= threshold_NUDT (b));27: j2 = j2 + 1; 28: END 29: ENDStep 8: Evaluation ${P}_{d}^{DT}$ and ${P}_{d}^{NUDT}$ using Monte Carlo simulation (based on (3))30: ${P}_{d}$_DT (b) = i1/pp; 31: ${P}_{d}$_NUDT (b) = i2/pp; 32: END33: UNTIL ${P}_{d}^{DT}$,${P}_{d}^{NUDT}$ = [0, 1] |

#### Execution Steps of the Simulation Algorithm

## 5. Results of Simulations

#### 5.1. Description of the Simulation Parameters and Software

#### 5.2. Effect of the Number of Transmit Chains on ED Efficiency

#### 5.3. Effect of NU and DT Adjustments on ED Efficiency

#### 5.4. Effect of the Transmit Power of PU on ED Sensing Efficiency

#### 5.5. Effect of Differences in the Number of MIMO Tx and Rx Chains on the ED Performance

#### 5.6. Effect of the Number of Sampling Points on ed Efficiency

#### 5.7. Effect of Probabilities of a False Alarm on the Efficiency of the ED Operation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

AWGN | Additive white Gaussian noise |

BS | Base station |

CFAR | Constant false alarm rate |

CR | Cognitive radio |

CRN | Cognitive radio networks |

CSI | Channel state information |

DSA | Dynamic spectrum access |

DT | Detection threshold |

DDT | Dynamic detection threshold |

ED | Energy detection |

EGC | Equal Gain Combining |

IoT | Internet of Things |

ISI | Inter-symbol interference |

LSA | Licensed shared access |

MIMO | Multiple-input multiple-output |

MISO | Multiple-input single-output |

NU | Noise uncertainty |

OFDM | Orthogonal frequency-division multiplexing |

PU | Primary user |

RF | Radiofrequency |

SISO | Single-input-single-output |

SIMO | Single-input multiple-output |

SL | Square-law |

SLC | Square-law combining |

SLS | Square-Law Selection |

SNR | Signal-to-noise ratio |

SS | Spectrum sensing |

STBC | Space-time block codes |

SU | Secondary users |

5G | Fifth-generation mobile network |

6G | Sixth-generation mobile network |

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**Figure 1.**Main blocks of the MIMO-OFDM wireless communication system for SS based on ED employing SLC technique.

**Figure 2.**The dependency of detection probability on SNR for ED performed with different combinations of DDT and NU factors in (

**a**) SISO, (

**b**) symmetric 2 × 2 MIMO and (

**c**) symmetric 4 × 4 MIMO communication systems.

**Figure 3.**The dependency of detection probability on SNR for ED performed with different combinations of DDT and NU factors in asymmetric 2 × 3 MIMO communication system.

**Figure 4.**The dependency of detection probability on SNR of ED performed with different combinations of DDT and NU factors in communication: (

**a**) SISO systems with 100 mW PU Tx power, (

**b**) SISO systems with 10 W PU Tx power, (

**c**) 2 × 2 MIMO systems with PU Tx power, (

**d**) 2 × 2 MIMO systems with 10 W PU Tx power, (

**e**) 4 × 4 MIMO systems with 100 mW PU Tx power and (

**f**) 4 × 4 MIMO systems with 10 W PU Tx power.

**Figure 5.**The dependency of detection probability on SNR for ED performed with versatile combinations of DDT and NU factors in SISO and asymmetric communication MIMO 2 × 6 and 6 × 2 systems.

**Figure 6.**The dependency of detection probability on SNR for ED performed with different combinations of DDT and NU factors in asymmetric communication MIMO 4 × 6 and 6 × 4 systems.

**Figure 7.**The dependency of the probability of detection on SNR for ED performed with the versatile number of sampling points and combinations of DDT and NU factors in (

**a**) SISO, (

**b**) 2 × 2 symmetric MIMO and (

**c**) 4 × 4 symmetric MIMO communication systems.

**Figure 8.**The dependency of detection probability on SNR for ED performed with different false alarm probabilities and combinations of DDT and NU factors in (

**a**) SISO, (

**b**) 2 × 2 symmetric MIMO and (

**c**) 4 × 4 symmetric MIMO communication systems.

Reference | Major Contribution |
---|---|

[18] | Improved SS at the SU side in a realistic environment by employing SLC and square-law selection (SLS) techniques. |

[19] | Software radio implementation of MIMO-OFDM. |

[20] | A comprehensive survey of OFDM transmission for wireless communications. |

[21] | A detailed survey on the performance requirements of 5G wireless cellular communication systems in terms of capacity, data rate, spectral efficiency, latency, energy efficiency, and quality of service. |

[22] | In comparison with single antenna CRs systems, significant improvement is observed in PU detection probability when ED based on the SLC technique is performed in MIMO CRs systems. |

[23] | Multiple antenna techniques and cyclostationary feature detection-based systems are proposed for ED. |

[24] | Analysis of cooperative spectrum sensing with ED over various fading channels using the SLC diversity scheme. |

[25] | Analyses of the problem of ED of an unknown signal over a multipath channel by employing SLC and SLS techniques. |

[26] | The tutorial presents a comprehensive overview of the ED-based SS and provides tools necessary for performing analyses of several SS algorithms. |

[27] | A survey of the NU impact on ED in communication systems with different OFDM system designs has been presented. |

[28] | A review of ED performance exploiting dynamic DT adaptations in the SISO-OFDM systems. |

[29] | Presentation of a novel approach based on subchannel and transmission power allocation that adaptively assigns the radio resources considering the interference caused to the PUs in multi-cell wireless networks. |

[30] | Analyses of the new communication approach based on the licensed shared access (LSA) spectrum sharing framework with in-band full-duplex multi-cell multi-user MIMO communication network as the licensee, which operates in the service region of a multi-user MIMO incumbent network. |

[31] | Presentation of the simulation algorithm that enables the performance analysis of the ED method employing the SLC technique in MIMO-OFDM CR systems and analyses of simulation results. |

[32] | Analyses of efficiency of ED SS - based on SLC technique in MIMO-OFDM Cognitive Radio Networks without the impact of NU and dynamic DT adjustments. |

[33] | Presentation of novel transmission solution based on adaptive beamforming with the coding scheme based on STBCs in IEEE 802.11 n WLAN systems. |

[34] | Presentation of the current state-of-the-art related to the research on SS by using ED with an extensive overview of basic theories in recent research, architectures for performing ED SS, the possible applications of ED and performance measurements of ED. |

[35] | The analysis of optimal DT selection for SS in a CRN using the ED approach is performed for fixed detection and false alarm probabilities. |

[36] | A survey of the fundamental concepts of CRN characteristics, functions, network architecture and applications is presented. |

[37] | The introduction of the ED SS which reduces the SNR-wall problem caused by the NU effects through the cooperation of multiple receivers for adapting the DT at each sensing point to the noise power present at the moment of SS. |

[38] | A new ED algorithm based on dynamic DT selection is presented and the relationship of detection sensitivity and ED performance with the impact of fluctuation of average noise power is investigated. |

[39] | Analyses of the influence of DDT and NU factor in the case of ED SSs on the detection and false alarm probability with the significance of their ratio on the sensing technique is analyzed and the expression of the empirical relationship between the sampling number and SNR is also proposed. |

[40] | Development of the analytical model for estimation of the statistical performance of the ED which can be used for setting the appropriate DT such that more spectrum sharing can be exploited, especially when combined with cooperative SS. |

Index | Description |
---|---|

${H}_{1}$ | The hypothesis which defines the existence of the PU signal |

${H}_{0}$ | The hypothesis which defines the non-existence of the PU signal |

m | The number of Tx chains on the PU side |

r | The number of Rx chains on the SU side |

M | The total number of PU Tx chains |

R | The total number of SU Rx chains |

N | The overall number of sampling points utilized for ED without DT adjustment and influence of NU |

${N}^{DT}$ | The overall number of sampling points utilized for ED with DT adjustment |

${N}^{NU}$ | The overall number of sampling points utilized for ED influenced by NU |

${N}^{NUDT}$ | The overall number of sampling points utilized for ED with DT adjustment and influence of NU |

${\mathit{s}}_{m}$ | The complex signal carried via the m-th Tx chain of the PU |

$\mathit{s}$ | The complex signal of the PU transmitted over the M Tx chains |

P | The total via M Tx chains transmitted instantaneous Tx power |

${P}_{m}$ | Instantaneous Tx power transmitted on the PU m-th antenna chain |

${y}_{r}\left(n\right)$ | Vector of the signal detected at r-th Rx chain of the SU in the n-th SS period |

$\mathit{Y}\left(n\right)$ | Vector of the signal received by all R Rx chains of the SU in the n-th SS period |

${\mathit{h}}_{r}\left(n\right)$ | Vector of channel gain among the M Tx chains and the r-th Rx chain in the n-th SS period |

${\mathit{s}}_{r}\left(n\right)$ | Vector of the signal detected within the n-th SS sample point at the SU r-th Tx chain |

${\mathit{w}}_{r}\left(n\right)$ | Vector of the noise impacting ED during the n-th SS period at the r-th Rx chain of the SU |

${\sigma}_{w}^{2}{}_{r}\left(n\right)$ | The variance of noise for the signal detected in n-th SS period at the SU r-th Rx chain |

${\sigma}_{{s}_{r}}^{2}\left(n\right)$ | The variance of the received signal in the n-th SS period at the r-th Rx chain of the SU |

${\sigma}_{wNU}^{2}\left(n\right)$ | AWGN variance used in the ED impacted with NU |

${\sigma}_{wNUDT}^{2}\left(n\right)$ | AWGN variance used in the ED impacted with NU and DT adjustments |

${\mathsf{\Lambda}}_{r}$ | Test statistics for signals detected at the r-th Rx chain (antenna) of the SU |

${\mathsf{\Lambda}}_{SLC}$ | The overall test statistics of all signals detected via the R receive (Rx) chains of the SU |

${\gamma}_{r}\left(n\right)$ | Signal-to-noise ratio at the r-th receive chain of the SU during the n-th SS period |

${\gamma}_{SLC}\left(n\right)$ | The total signal-to-noise ratio associated with the R SU receive antennas (chains) in the n-th SS period |

$\overline{{\gamma}_{SLC}}\left(n\right)$ | The mean signal-to-noise ratio detected by the SU during the n-th SS period for all R receive chains |

${P}_{f}$ | False alarm probability for ED performed without DT adjustments and impact of NU |

${P}_{d}$ | Detection probability for ED performed without DT adjustments and impact of NU |

${P}_{fa}^{NU}$ | False alarm probability for ED impacted with NU |

${P}_{d}^{NU}$ | Detection probability for ED impacted with NU |

${P}_{fa}^{DT}$ | False alarm probability for ED performed with DT adjustments |

${P}_{d}^{DT}$ | Detection probability for performed with DT adjustments |

${P}_{fa}^{NUDT}$ | False alarm probability for ED performed with DT adjustments and impact of NU |

${P}_{d}^{NUDT}$ | Detection probability for ED performed with DT adjustments and impact of NU |

$Q\left(x\right)$ | Standard Gaussian Q function |

λ | DT for ED performed without DT adjustments and impact of NU |

${\lambda}_{fa}$ | False alarm threshold in the case of ED performed based on CFAR principles |

${\lambda}_{d}$ | DT level for ED performed based on CDR principles |

${\lambda}_{d}^{DT}$ | DT for SLC ED performed with DT adjustments |

${\lambda}_{fa}^{DT}$ | False alarm threshold for ED performed with DT adjustments |

${\lambda}_{d}^{NU}$ | DT for ED impacted with NU |

${\lambda}_{fa}^{NU}$ | False alarm threshold for ED impacted with NU |

${\lambda}_{d}^{NUDT}$ | DT for SLC ED performed with DT adjustments and impacted with NU |

${\lambda}_{fa}^{NUDT}$ | False alarm threshold for ED performed with DT adjustments and impacted with NU |

${\lambda}^{\prime DT}$ | DT for ED performed without NU |

${\lambda}^{\prime NUDT}$ | DT for ED performed with DT adjustments and NU |

ρ | NU factor |

${\rho}^{\prime}$ | DDT factor |

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

PU signal modulation scheme | OFDM |

Number of Tx chains (antennas) of the PU | 1–4 |

Number of Rx chains (antennas) of the SU | 1–6 |

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

Model of the noise [28,34] | AWGN |

$\mathrm{Noise}\text{}\mathrm{variance}\text{}{\sigma}_{w}^{2}\text{}\mathrm{for}\text{}\mathrm{DT}\text{}(\rho =1.00,\text{}{\rho}^{\prime}1.00)$ [37,38,39,40] | 1.00 |

$\mathrm{Noise}\text{}\mathrm{variance}\text{}{\sigma}_{w}^{2}\text{}\mathrm{for}\text{}\mathrm{NU}\text{}\mathrm{and}\text{}\mathrm{DT}\text{}(\rho \text{}1.00,{\rho}^{\prime}1.00)$ [37,38,39,40] | 1.01 |

Number of sampling points for ED (FFT size) [28,34] | 128, 512, 1024 |

SNRs range at SU position (dB) [28,34] | −25–25 |

$\mathrm{DT}\text{}\mathrm{factor}\text{}\rho \prime $ [37,38,39,40] | 1.00, 1.03, 1.05 |

$\mathrm{NU}\text{}\mathrm{factor}\text{}\rho $ [37,38,39,40] | 1.00, 1.03, 1.05 |

Target false alarm probability [37,38,39,40] | 0.01, 0.2 |

Overall number of Monte Carlo simulations | 10,000 |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/s22020631

**AMA Style**

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(2):631.
https://doi.org/10.3390/s22020631

**Chicago/Turabian Style**

Lorincz, Josip, Ivana Ramljak, and Dinko Begušić.
2022. "Analysis of the Impact of Detection Threshold Adjustments and Noise Uncertainty on Energy Detection Performance in MIMO-OFDM Cognitive Radio Systems" *Sensors* 22, no. 2: 631.
https://doi.org/10.3390/s22020631