Mathematical analysis for detection probability in cognitive radio networks over wireless communication channels

Abstract

In this study, the authors consider the problem of spectrum sensing based on energy detection method in cognitive radio over wireless communication channels when users experience fading and non-fading effects. The closed-form analytical expressions for the detection probability are derived over non-fading additive white Gaussian noise channel and Rayleigh and log-normal shadowing fading channels. The detection probability involves Marcum-Q function, summations and integrations in the early research papers, which are replaced by closed-form expressions in this study. The probability distribution function of fading channels is used to obtain the expressions for detection probability. The new derived numerical results are simulated under various parameters. The performance of the derived theoretical expressions closely matches with the simulated results.

Keywords

• mathematical analysis
• cognitive radio
• wireless channels
• radio spectrum management
• signal detection
• fading channels
• Gaussian noise
• Rayleigh channels
• mathematical analysis
• detection probability
• cognitive radio networks
• wireless communication channels
• spectrum sensing
• energy detection method
• nonfading effects
• analytical expressions
• nonfading additive white Gaussian noise channel
• lognormal shadowing fading channels
• Rayleigh shadowing fading channels
• Marcum-Q function
• closed-form expressions
• probability distribution function