###### Abstract  
To ensure effective spectrum usage, cognitive radio networks (CRNs) are being investigated extensively. The important function of CRNs is spectrum sensing (SS). This is the process of sensing the unused frequency spectrum and deciding whether the signal transmission of a primary user (PU) exists. In this work, the results of a performance analysis related to detecting PU signals using the energy detection (ED) SS method realized by employing the square-law combining (SLC) technique are presented. The assessment of the effectiveness of the ED method is performed in relation to prominent communication technology based on Orthogonal Frequency Division Multiplexing (OFDM) and Multiple-Input Multiple-Output (MIMO) transmissions. Due to the impact of changes in the noise power of the PU signal, referred to as noise uncertainty (NU), the MIMO-OFDM transmission in a real communication environment cannot guarantee accurate sensing performed by employing ED based on the SLC method at the secondary user (SU). More precise SS can be achieved if dynamic detection threshold (DDT) changes are employed according to the channel conditions impacted by NU. Thus, this work investigated the effect of NU variations and DDT adjustments on the detection probability for various levels of false alarm probability. This interdependence is presented as receiver operating characteristic (ROC) curves. A mathematical model including different operational parameters was developed to define the fundamental parameters of the ED method based on the SLC approach. Using the developed mathematical model, an algorithm was created which simulates SLC ED processes using DDT in single-input single-output (SISO)- and MIMO-OFDM communication systems affected by NU. Based on the simulation results, comprehensive analyses of the impact of versatile DDT adaptations and NU variations on the shape of the ROC curves for the ED process performed with different numbers of transmitting and receiving antenna, modulation techniques, detection sample numbers, PU transmitting powers, and SNR values are presented. ROC curves; energy detection; noise uncertainty; dynamic detection threshold; spectrum sensing; false alarm; probability; MIMO; OFDM; SLC; cognitive; networks +
Footnote †: journal: Medical Imaging  
are spectrum users, due to the status of PUs as licensed users, they get precedence when using the spectrum. The SUs, as unlicensed users (also known as \"cognitive users\"), have less precedence when it comes to spectrum exploitation, and they use the spectrum when licensed users (PUs) do not transmit. Thus, when the PU is not active, the activity of the SU can lead to the utilization of the currently unused spectrum. This contributes to the reduction of the spectrum scarcity problem [4; 5]. Various local spectrum sensing (SS) techniques have been introduced in published works. Energy detection (ED) is the core SS technique and the most prevalent in practice. This is because the ED method does not require prior information about the licensed user's (PU) signal and the goal of the ED SS process is to detect the received signal energy in a specific part of the frequency spectrum. Additionally, the ED SS approach is less complex when compared with other known local SS approaches and this is an important implementation advantage that results in the broad practical implementation of the ED method [6]. Nevertheless, the ED method has different drawbacks such as the inability to distinguish between signals and noise in low signal-to-noise ratio (SNR) environments, and has degradation of sensing precision in the presence of uncertainty in noise power (referred to as \"noise uncertainty\" (NU)). This is the consequence of the nature of the ED process which is based on a comparison of the energy level of the received signal with the predefined detection threshold (DT) level. The DT level is determined by the amount of energy contained in the noise.