Abstract
In this article, we will derive closed-form expressions of false alarm probabilities for a given threshold for the dimension estimation-based detector (DED) using Akaike information criterion (AIC) and the minimum description length (MDL) criterion. Specifically, the DED algorithm will be formulated as a binary hypothesis test using AIC and MDL curves. Based on the proposed statistic test, we will express the probability of false alarm of the DED algorithm for a fixed threshold using the cumulative density function for the distribution of Tracy-Widom of order two. The derived analytical decision thresholds are verified with Monte-Carlo simulations and a comparison between simulation and analytical results to confirm the theoretical results are presented. These results confirm the very good match between simulation and theoretic results.
Highlights
The discrepancy between current-day spectrum allocation and spectrum use suggests that radio spectrum shortage could be overcome by allowing a more flexible usage of the spectrum
In order to give an idea of the complexity of the dimension estimation-based detector (DED) algorithm, we provide in Figure 4 simulation results assessing the performance in terms of execution time of this algorithm in comparison with cyclostationarity based detector (CD) and energy detector (ED) algorithms
We find that the CD is the most complex among all, with over two time complexity compared to DED
Summary
The discrepancy between current-day spectrum allocation and spectrum use suggests that radio spectrum shortage could be overcome by allowing a more flexible usage of the spectrum. The study presented in [11] suggested to use model selection tools like Akaike information criterion (AIC) and the minimum description length (MDL) criterion to conclude on the nature of the sensed band. These tools were used as detection rules for the dimension estimation detector (DED) [12]. We will derive closed-form expressions of false alarm probabilities for a given threshold using both AIC and MDL criterion. The false alarm probability can be rewritten as PFA,AIC
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