Fading Evaluation in a Robust Spectrum Sensing System Based on Phase Difference Distribution

In this paper, we delve deeper into a blind and robust spectral sensing technique, namely cosine feature recognition detection (CRD), based on the phase difference distribution of the received signal. The CRD algorithm is evaluated over various comprehensive fading environments, especially Rayleigh, Rice, Nakagami-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {m}$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\alpha }$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\kappa }$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula>, Extended <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\eta }$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula>, and their special cases. We derive closed-form formulas for the probability of detection and asymptotic expressions for the probability of miss detection considering the mentioned fading models and evaluate the performance of the CRD spectrum sensing system under various propagation conditions. We quantify the achievable diversity order and coding gain as a function of the propagation parameters. We draw conclusions about how each physical propagation phenomenon affects this promising spectrum sensing technique and compare its performance against the energy detector (ED) technique under a realistic scenario with severe fading conditions, noise uncertainty, and frequency mismatch, highlighting the potential of the CRD algorithm for practical implementation. Additionally, a Hybrid ED-CRD technique is proposed, which improves the detection capability of the CRD without increasing the number of collected samples.