Performance Analysis of Polar Codes Over Fox’s H-Fading Channels With RHI and IQI Impairments

Abstract

This study examined the error probability performance of polar codes across Fox’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -fading (FHF) channels while taking into account in-phase and quadrature-phase imbalance (IQI), as well as residual hardware impairments (RHI). This fading model generalizes most of the commonly used fading and turbulence models where Málaga- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {M}$ </tex-math></inline-formula> turbulence is taken into account as a specific case of FHF in this paper. Specifically, an upper bound on block error probability (BLER) for the successive cancellation (SC) decoding method of polar codes is derived in terms of the Fox’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -function. According to numerical results, by lengthening polar codes and changing the properties of fading channels, it is possible to decrease the impact of system impairments on the error probability performance.