Compressive Spectrum Sensing with Temporal-Correlated Prior Knowledge Mining

Table 2

The proposed spectrum sensing algorithm flow.

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Spectrum sensing algorithm with temporal-correlated prior knowledge mining

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(1) Initialize various parameters, including the number of Nyquist samples , the maximum sparsity , the energy decision threshold , the number of Monte Carlo cycles , the orthonormal basis , the observation matrix , and the sensing matrix

(2) For the spectrum at moment, use the -norm convex optimization model to obtain the spectrum measurement value at moment

(3) Consider small changes in the spectrum between moment and moment. We consider that the probability of a random spectrum change is 3% (in practice, PUs’ spectrum utilization is about 15% according to the report of FCC, and thus, the spectrum state changes with a small probability. The value of such probability depends on the type of service, and the service arriving rate is usually modeled as a Poisson distribution. Hence, the reasonable spectrum change probability is less than 5% according to our experience.). The initial frequency spectrum changes slightly and becomes , and we get a new observation value

(4) When we estimate the spectrum at moment, we merge the spectrum prior information at moment. Process the prior information with the follow steps
 (a) Set a threshold value . For each element in vector , if the element is smaller than , set it to 0. And for the other elements, keep the value unchanged
 (b) Use symbolic function to process the which we get in (a). And set

(5) According to the convex model: , we can obtain the spectrum at moment

(6) Repeat the process of step (3), step (4), and step (5) to get the spectrum information related to the time series

(7) According to the recovered spectrum information, we calculate the probability of false alarm, the probability of correct detection, and the standardized mean square error (MSE) of different CS algorithms and compare the performance of these CS algorithms

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