Accurate and Efficient Algorithms for Cognitive Radio Modeling Applications Under the i.n.i.d. Paradigm

Given that the statistical analysis of the frequency band of interest are available, it has been shown that adaptive searching for white spaces could improve by 70% when compared with random searching. In this paper, we characterize and provide a statistical estimation of the number of channels available for opportunistic usage by secondary users (SUs) in a spectrum band. However, following the independent but not identically distributed (i.n.i.d.) paradigm, predicting the exact distribution of the count of available channels is not only computationally intense due to the number of combinations but infeasible in practice, as well, even for frequency bands with a moderate number of channels. Existing research has resorted to approximations that lacked accuracy and efficiency. To resolve this problem, we propose three novel methods based on convolution, recursive, and hybrid convolution-recursive methods that can efficiently compute the exact distribution in frequency bands with a large number of channels. We assess their efficiency by analyzing each algorithm's time complexity and running time and then further comparing their performance against existing models in the literature. Moreover, knowing the availability of the channel's immediate neighbors can allow efficient power management and prioritize channel allocation to SUs. Therefore, we categorize available channels into three different types based on the occupancy of its two adjacent channels and then model their availability. Additionally, from a network performance analysis perspective, predicting the count of available channels has to be evaluated against the probability of detecting these channels within the same i.n.i.d. framework. Respectively, we propose a novel approach to calculate the probability of detecting multiple channels simultaneously. Finally, we validate the effectiveness of the proposed models using several real-time measurements and further present two associated applications where one features novel 2-D (time and frequency) availability prediction.