Minimizing Misclassification for Cooperative Spectrum Sensing Using $M$-Ary Hypothesis Testing.

In traditional spectrum sensing, binary hypothesis testing has been used to detect whether a frequency band is being occupied by the primary user or not. In this correspondence paper, we investigate $M$ -ary hypothesis testing for spectrum sensing to further identify the signal type of the primary user. Linear cooperation among spatially distributed cognitive radios is applied to combine the observation statistics and make a final decision. The problem of data fusion is formulated as minimizing the total probability of misclassification subject to the constraint on the probability of successful classification. To deal with the non-convex problem formulated, we develop two solutions in this paper. In the first solution, we transform the problem into an unconstrained one, and adopt a zooming-based search algorithm to iteratively update multiple continuous variables until convergence. This solution requires searching all possible combinations of variables. To reduce the computation complexity and achieve closed-form analytical expressions, in the second solution, we decompose the original problem into multiple subproblems, each with the objective of minimizing an individual probability of misclassification. These subproblems can lead to closed-form expressions, and the weights are chosen as the best ones that correspond to the minimum total probability of misclassification. The proposed solutions are examined numerically, and the results show that the decomposition-based solution can achieve performance comparable to the zooming-based one but with much less complexity. [ABSTRACT FROM AUTHOR]