  Kernel method is a very powerful tool in machine learning. The trick of
kernel has been effectively and extensively applied in many areas of machine
learning, such as support vector machine (SVM) and kernel principal component
analysis (kernel PCA). Kernel trick is to define a kernel function which relies
on the inner-product of data in the feature space without knowing these feature
space data. In this paper, the kernel trick will be employed to extend the
algorithm of spectrum sensing with leading eigenvector under the framework of
PCA to a higher dimensional feature space. Namely, the leading eigenvector of
the sample covariance matrix in the feature space is used for spectrum sensing
without knowing the leading eigenvector explicitly. Spectrum sensing with
leading eigenvector under the framework of kernel PCA is proposed with the
inner-product as a measure of similarity. A modified kernel GLRT algorithm
based on matched subspace model will be the first time applied to spectrum
sensing. The experimental results on simulated sinusoidal signal show that
spectrum sensing with kernel PCA is about 4 dB better than PCA, besides, kernel
GLRT is also better than GLRT. The proposed algorithms are also tested on the
measured DTV signal. The simulation results show that kernel methods are 4 dB
better than the corresponding linear methods. The leading eigenvector of the
sample covariance matrix learned by kernel PCA is more stable than that learned
by PCA for different segments of DTV signal.
