Average error rate analysis of the fading channel model with second-order scattering and fluctuating line-of-sight

Abstract

This paper presents an in-depth analysis of the average bit error rate (ABER) for a novel fading channel model that incorporates second-order scattering and a fluctuating line-of-sight (LoS) component. The analysis includes both exact closed-form expressions and asymptotic approximations for various modulation schemes, including coherent and non-coherent, with both large and small constellation sizes (e.g., QPSK and 256-QAM) under different propagation scenarios (i.e., light fading and heavy fading). The derived analytical expressions are supported by computationally efficient approximations using the Gauss-Laguerre quadrature integration method, which requires 10-15 terms to achieve reasonable accuracy. The upper bound on the error induced by truncation of the derived exact expressions is also derived and studied. It is demonstrated that, in the case of heavy fading conditions, truncation to 5 terms is sufficient to achieve at least four-digit accuracy. All the derived exact results are appended with their high-SNR approximations. Through extensive numerical simulations, the accuracy of these expressions is validated, demonstrating close agreement with both the analytical and Monte Carlo simulation results, and it is demonstrated that most of high-SNR approximations are tight even for moderate SNR values (i.e., $10-20$ dB). To highlight the cogency of the derived results, a series of comparisons with the well-known simplified models (including Rayleigh, Rician, Rician shadowed, double-Rayleigh, and double-Rayleigh with fluctuating line-of-sight) were performed. The study also explores the channel's performance under hyper-Rayleigh conditions (both analytically and numerically), identifying the key parameters that influence communication quality in severe fading environments. The results reveal that the proposed channel model provides robust ABER performance across a range of modulations, particularly under conditions of heavy fading (i.e., shadowing parameter $m<1$). Additionally, the findings help identify the diversity order and coding gain, as well as offer new insights into the impact of weak and strong Rayleigh components on overall system performance.