Kernel Feature Template Matching for Spectrum Sensing

Feature template matching (FTM) was proposed by Zhang and Qiu in 2011 for spectrum sensing in cognitive radio. Theoretical analysis for FTM is, however, missing in the literature. This paper will address this issue. Another new direction suggested by this paper is a nonlinear version of FTM, which is called kernel FTM (KFTM). The proposed nonlinear algorithm is performed on data mapped to a kernel space usually with higher dimension by a general nonlinear mapping. The high-dimensional data are cheaply operated with the so-called kernel trick. Furthermore, higher order statistics is considered in the proposed algorithm. Simulations using the real-world measurements of digital television (DTV) signal show that a gain of more than 4 dB can be achieved for KFTM over its linear counterpart FTM. Theoretical analysis is conducted for KFTM (that can be directly applied to FTM). For the first time, a theoretical justification is also performed for FTM. The concentration inequalities of KFTM, which are valid for arbitrary dimensions, are established as a result of concentration of measure phenomenon. The closed-form expressions of the probability distributions (under null hypothesis) are derived for both FTM and KFTM under different kernel functions. The obtained closed-form results agree with simulations. The closed-form expressions of the decision thresholds for a target false-alarm probability are obtained as well. The thresholds are noise power independent; thus, the proposed algorithm overcomes the difficulty of noise uncertainty.