## 2 Related Works on the SS of OFDM Signals
The results of simulations indicated that the proposed detector based on the mean ambiguity function can yield good performance of energy detection in environments with low SNR and can be persistent to NU. Recent research attempts have been dedicated to finding the optimal detection threshold for SS based on ED (Table 1) [37; 38; 39; 40]. In Ref. [38], an approach based on a double threshold for an unequal scale sampling was proposed to reduce the impact of NU and asynchronous primary user occurrence. The results of the simulation confirmed the effectiveness of the proposed approach in terms of improving the detection probability, while keeping the false alarm probability within the demanded range. The performance of an ED under NU, while employing an optimal threshold and DT correction with Chi-square and Gaussian distributions of the received signal power, was studied in Ref. [39]. The results obtained showed that the selection of an optimal threshold in the ED process impacted by NU reduces the probability of error. A novel approach to DT selection based on an online learning algorithm was proposed to improve the performance of ED and the matched filter method through minimization of the overall error probability [40]. Presented simulation results confirmed that optimal threshold selection improves the performance of SS. A three-event ED algorithm based on optimal DT adjustment was proposed in Ref. [37]. The proposed algorithm minimizes in one iteration the probability of ED error based on [PERSON]'s method with forced convergence [37]. The developed method was analysed through simulations and results showed that the proposed method outperformed the conventional ED method. Although results presented in recently published literature showed that selection of optimal threshold improves ED performance (Table 1), they also showed \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Approach Analysed in the Literature** & **Description of the Analysed Approach** & **The Merit of the Analysed Approach** \\ \hline Only the ED approach with fixed detection threshold [7; 18; 24; 27; 34] & No influence related to the impact of NU and DT adaptation & The strong impact of NU and lack of DT adaptation significantly degrade the reliability of ED performance \\ \hline The ED approach impacted by NU and without DT adaptation [12; 25; 26; 28; 30; 31; 32; 36] & Analyses of ED performance taking into account the impact of the NU variations & Reduced detection probability of ED method due to impact of NU variation caused by thermal noise and interference from neighbor communication systems \\ \hline The ED approach with DT adaptation and without the impact of NU variations [8; 10; 11; 13; 37] &
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline Somewhat improved detection probability of ED method due to exploitation of DT adaptation but less realistic due to neglecting the impact of NU variations \\ \end{tabular} \\ \hline The ED approach impacted by NU variations and performed using DT adaptation [9; 16; 17; 38; 39; 40] & Analyses of ED performance based on the selection of the appropriate value of the DT impacted by the NU variations \\ \hline \end{tabular}
\end{table} 
Table 1: Overview of ED methods analysed in the literature and their corresponding merits. that no universal approach to a dynamic selection of optimal threshold currently exists and that finding the optimal threshold represents a challenging task. In Ref. [32], we showed the results related to the influence of NU on the energy misdetection probability of OFDM based systems in an MA system design. In addition, in Ref. [36] (Table 1), the analyses of the impact of NU on ED performed without DT adaptations for diverse OFDM based systems were shown. The results obtained indicated that the ED performance in different OFDM systems was significantly impaired by the NU. The results presented in this work are used as bases for analyses on how dynamic threshold adaptation impacts ED performance in OFDM systems which operate under versatile NU levels.