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As the limited communication spectrum can not meet the demand of the exponential growth of intelligent connected devices in the internet of things(IoT) and typical smart city applications, in this paper, we propose a tractable spectrum sensing method based on Rao detection over non-Gaussian noise, such as generalized Gaussian noise(GGN), Gaussian mixture noise(GMN) and symmetric alpha-stable distribution (<inline-formula> <tex-math notation="LaTeX">$\text{S}\alpha \text{S}$ </tex-math></inline-formula>) noise, multi-path fading channels environment to alleviate the issue of spectrum scarcity. In this method, there are unknown parameters in the multi-path fading channels. When the probability density function (P.D.F.) of non-Gaussian noise has a closed-form expression, the spectrum sensing method based on Rao detection is used. Otherwise the P.D.F. for <inline-formula> <tex-math notation="LaTeX">$\text{S}\alpha \text{S}$ </tex-math></inline-formula> noise is estimated firstly by using non-parametric kernel estimation method, which addresses the issue that <inline-formula> <tex-math notation="LaTeX">$\text{S}\alpha \text{S}$ </tex-math></inline-formula> noise has no closed-form P.D.F. expression, and then the performance of spectrum sensing is derived based on the theory of Rao detection in multi-path fading channels over typical smart city applications. Simulation results show that the accuracy of estimated P.D.F. for <inline-formula> <tex-math notation="LaTeX">$\text{S}\alpha \text{S}$ </tex-math></inline-formula> noise and the performance of spectrum sensing under different <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> values over indoor, outdoor, and vehicle fading channels environment.