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Summary This paper addresses the performance of wireless fading channels, namely, Rayleigh, Rician, and Nakagami‐m fading channels, taking both noiseless and additive noisy cases into account. The performance metrics investigated are channel capacity, channel model variance estimation, required average description length based on Shannon entropy, and relative entropy and symbol error probability assessment. Taylor expansion is considered as an approximation for the aforementioned metrics together with the compressed sensing (CS) compressibility rule. Technical comments are provided for supporting simulation results. Mathematical interpretations are provided to support the simulation results along with feasible applications in 5G wireless systems. Conclusions and future research directions finalize the paper.

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