# Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems

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## Abstract

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## 1. Introduction

- The presentation of the mathematical model which defines the ED process based on the SLC method in MIMO-OFDM systems.
- The development of a novel algorithm for simulating the ED process impacted by the different operating parameters in CRNs based on the MIMO-OFDM transmission.
- The presentation of the simulation results indicating the impact of false alarm probability on detection probability for the different operating parameters, such as the SNRs, the number of samples, the Tx powers of the PU, the modulation types and the SISO, symmetric and asymmetric MIMO transmissions with different Tx and Rx antenna combinations.

## 2. Literature Review

## 3. System Model and Formulation of ED Process

#### 3.1. Model of the Analyzed System

_{.}Consequently, all signals transmitted over the M Tx antennas by one PU can be expressed as: $\mathit{s}={\displaystyle \sum}_{\mathit{m}=1}^{\mathit{M}}{\mathit{s}}_{\mathit{m}}$.

#### 3.2. Process of Energy Detection

#### 3.3. False Alarm and Detection Probabilities

## 4. Algorithm for Simulating Energy Detection Process

Algorithm 1. The pseudocode of the proposed ED process. |

1: INPUT: mimo_ofdm_received_signal_M× r, number of samples (N), SNR_loop, DT factor (${\rho}^{\prime}$), NU factor (ρ), noise variance (${\sigma}_{{n}_{i}}^{2})$, range of${P}_{f{a}_{i}}$and number of Monte Carlo simulations (kk)2: OUTPUT: Probability of detection (${P}_{d})$3: ON INITIALIZED Received MIMO-OFDM signal (mimo_ofdm_received_signal_M×r) do: Step 1: Simulation of interdependence between the detection probability (${P}_{d}$) and false alarm probability (${P}_{fa}$)4: set kk = number of Monte Carlo simulations 5: set${P}_{fa}$= probability of false alarm in interval [0,1] 6: FOR p = 1:length (${P}_{fa}$)7: i1= 0; 8: FOR i = 1:10,000; Step 2: Modeling the impact of NU on the received signal9: Noise uncertiaity ($\rho $> 1.00) = sqrt(${\mathsf{\sigma}}_{w}^{2}{}_{r}\left(n\right)>1.00$). * randn (1, framelen); 10: received_signal_M× r = mimo_ofdm_received_signal_M×r + Noise uncertaiity; Step 3: Calculation of energy of received signal based on SLC method11: REPEATE FOR r = 1:R12: energy_calc_r = abs(received_signal_M×r).^2; 13: END Step 4:Test statistic calculation (based on (7))14: FOR r = 1:R15: test_stat = sum(energy_calc_r); 16: END Step 5: Threshold evaluation17: thresh (p) = ((qfuncinv(${P}_{fa}$(p)). * ρ./sqrt(N))+ ρ)./${\rho}^{\prime}$; Step 6: Decision making process (based on (8), (9))18: IF (test_stat >= thresh (p));19: i1 = i1 + 1; 20: END21: END Step 7: Monte Carlo simulation-determining${P}_{d}$(based on (15))22: ${P}_{{d}_{i}}$(p) = i1/kk; 23: END24: UNTIL ${P}_{{d}_{i}}$= [0,1] |

#### 4.1. Algorithm for Simulating the ED Process in MIMO-OFDM Systems

#### 4.2. Relevance of the Simulation Algorithm

## 5. Simulation Results

#### 5.1. Simulation Software and Parameters

#### 5.2. Impact of the SNR on the ED Probability

#### 5.3. Impact of Tx Power on ED Probability

#### 5.4. Impact of Number of Samples on ED Probability

#### 5.5. Impact of Modulation Type on the ED Probability

_{Tx}= 100 mW) and SNR level (SNR = −15 dB). The obtained results presented in Figure 6 indicate that the modulation type has no direct impact on the PU signal detection for any Tx–Rx branch (antenna) combination of an OFDM communication system. It is assumed that in margin adaptive systems that are based on the transmission of OFDM signals with a constant PU Tx power the modulation type is dynamically adjusted, and that these adjustments do not have a direct impact on the ED performance of the PU signal.

#### 5.6. Impact of Symmetric and Asymmetric MIMO Transmission on ED Probability

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AWGN | Additive white Gaussian noise |

CR | Cognitive radio |

CRN | Cognitive radio networks |

CSI | Channel state information |

CSS | Cooperative spectrum sensing |

DSA | Dynamic spectrum access |

DT | Dynamic threshold |

ED | Energy detection |

EGC | Equal gain combining |

IoT | Internet of Things |

ISI | Inter-symbol interference |

MIMO | Multiple-input multiple-output |

MISO | Multiple-input single-output |

NU | Noise uncertainty |

OFDM | Orthogonal frequency division multiplexing |

Probability density function | |

PU | Primary user |

RF | Radio frequency |

ROC | Receiver operating characteristic |

SISO | Single-input single-output |

SL | Square law |

SLC | Square-law combining |

SNR | Signal-to-noise ratio |

SS | Spectrum sensing |

STBC | Space–time block codes |

SU | Secondary users |

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**Figure 1.**Block diagram of the ED process based on SLC in a MIMO-OFDM system with M Tx and R Rx branches.

**Figure 2.**The ROC curves presenting the ED performance for different SNR values equal to: (

**a**) −20 dB, (

**b**) −15 dB and (

**c**) −10 dB.

**Figure 3.**The ROC curves presenting the ED performance for the different PU Tx powers and an SNR of −15 dB in (

**a**) SISO and (

**b**) 2 × 2 MIMO communication systems.

**Figure 4.**The ROC curves presenting the ED performance for the different PU Tx powers and the SNR of −20 dB in (

**a**) SISO, (

**b**) 2 × 2, (

**c**) 2 × 4 and (

**d**) 2 × 6 MIMO communication systems.

**Figure 5.**The ROC curves presenting the ED performance for the different number of samples in (

**a**) the SISO system with a PU Tx power of 100 mW, (

**b**) the SISO system with a PU Tx power of 1 W, (

**c**) the MIMO 2 × 2 system with a PU Tx power of 100 mW and (

**d**) the MIMO 2 × 2 system with a PU Tx power of 1 W.

**Figure 6.**The ROC curves presenting the ED performance for signal transmission with different modulation schemas in (

**a**) SISO, (

**b**) symmetric MIMO (2 × 2) and (

**c**) asymmetric MIMO (2 × 3) systems.

**Figure 7.**The ROC curves presenting ED performance for MIMO system impacted with different PU Tx powers and modulation schemes.

**Figure 8.**The ROC curves presenting the ED performance for the asymmetric 2 × 3, 2 × 4, 4 × 2 and 3 × 2 MIMO-OFDM communication systems.

**Figure 9.**The ROC curves presenting the ED performance for the symmetric 2 × 2, 3 × 3, 4 × 4 and 5 × 5 MIMO-OFDM communication systems.

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

${H}_{1}$ | The hypothesis that determines the presence of the PU signal |

${H}_{0}$ | The hypothesis that determines the absence of the PU signal |

m | Number of PU Tx branches (antennas) |

r | Number of SU Rx branches (antennas) |

M | Total number of transmit antennas at the PU |

R | Total number of receiving antennas at the SU |

N | Total number of samples used in the detection process |

${P}_{m}$ | Transmit (Tx) power allocated through the m-th antenna element of the PU |

P | Total instantaneous Tx power of the PU transmitted over the M Tx branches |

${\mathit{s}}_{m}$ | The complex signal transmitted over the m-th Tx antenna of the PU |

$\mathit{s}$ | The overall complex signal transmitted by the PU from the M Tx branches |

${\mathit{y}}_{r}\left(n\right)$ | The received signal at the r-th Rx branch (antenna) of the SU during the n-th SS period |

$\mathit{Y}\left(n\right)$ | The overall signal received at the R Rx branches (antennas) of the SU during the n-th SS period |

${\mathit{h}}_{r}\left(n\right)$ | Channel gain between the M Tx antennas and the r-th Rx branch (complex vector of size ${\u2102}^{1\mathrm{XM}}$) during the n-th SS period |

${\mathit{s}}_{r}\left(n\right)$ | Signal vector ${\u2102}^{\mathrm{MX}1}$ received during the n-th sample at the r-th Tx branch (antenna) |

${\mathit{w}}_{r}\left(n\right)$ | Complex noise vector at the r-th Rx branch (antenna) of the SU in the n-th SS period |

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

${\gamma}_{SLC}\left(n\right)$ | Total SNR associated with the M Rx antenna branches in the moment of the n-th SS period |

$\overline{{\gamma}_{SLC}}\left(n\right)$ | Average SNR detected at the location of the SU device for all R Rx antenna branches in the n-th SS period |

${\Lambda}_{r}$ | Test statistics of the signals received over the r-th Rx branch (antennas) at the SU |

${\Lambda}_{SLC}$ | Total test statistics of the signals received over the R Rx branches (antennas) at the SU |

$\mathbb{V}ar\left[\xb7\right]$ | Variance operation |

$\mathbb{E}\left[\xb7\right]$ | Expectation operation |

${P}_{fa}$ | False alarm probability |

${P}_{d}$ | Detection probability |

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

$\lambda $ | Detection threshold |

ρ | NU factor |

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

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

Transmission type of the PU signal | OFDM |

Number of transmitted antennas | 1–5 |

Number of received antennas | 1–6 |

Type of OFDM (constellation) | QPSK, 16 QAM, 64 QAM |

Analyzed channel noise model | AWGN |

Number of samples (FFT size) | 128, 256, 512, 1024 |

The SNRs value at the location of the SU (dB) | −20, −15 and −10 dB |

The detection and false alarm probability ranges | 0–1 |

Number of Monte Carlo iterations/simulations | 10,000 |

NU factor $\rho $ DT factor ${\rho}^{\prime}$ | 1.02 1.01 |

Server Number | CPU Type | RAM (GB) | CPU Frequency (GHz) |
---|---|---|---|

Server 1 | Intel(R) Core(TM)—i7 4771 | 8.00 | 3.5 |

Server 2 | Intel(R) Core(TM)—i5 6200 | 4.00 | 2.4 |

Server 3 | Intel(R) Core(TM)—i5 6200 | 8.00 | 2.4 |

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**MDPI and ACS Style**

Lorincz, J.; Ramljak, I.; Begusic, D. Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems. *Sensors* **2021**, *21*, 6881.
https://doi.org/10.3390/s21206881

**AMA Style**

Lorincz J, Ramljak I, Begusic D. Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems. *Sensors*. 2021; 21(20):6881.
https://doi.org/10.3390/s21206881

**Chicago/Turabian Style**

Lorincz, Josip, Ivana Ramljak, and Dinko Begusic. 2021. "Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems" *Sensors* 21, no. 20: 6881.
https://doi.org/10.3390/s21206881