Symbol Error Analysis of Linear Receivers in Terahertz Channels under Channel-Noise Dependence

This paper develops a comprehensive framework for the performance analysis of linear detectors, namely zero-forcing (ZF) and minimum mean-square error (MMSE), under diverse terahertz (THz) channel conditions. Three fading models are considered: Rayleigh fading, the $α$--$μ$ distribution for indoor THz environments, and the mixture-gamma (MG) distribution for outdoor THz scenarios. Semi-analytical, approximate, and asymptotic expressions for the symbol error rate (SER) are derived, explicitly incorporating the correlation between the channel and the additive noise arising from hardware impairments. This correlation is characterized using both statistical approaches and copula-based methods to effectively capture complex dependency structures. The theoretical findings are validated through simulations, demonstrating strong agreement with the derived expressions and confirming the accuracy and robustness of the proposed framework. The results demonstrate the significant impact of channel--noise dependence on THz-band receiver performance and verify the expected performance degradation of biased MMSE receivers in point-to-point links employing higher-order quadrature amplitude modulation. Specifically, at a target SER of $10^{-3}$, a 70\% correlation results in approximately a 6.5~dB degradation in the effective signal-to-noise ratio, with mismatched MMSE detection incurring an additional 1~dB loss compared to ZF. Nonetheless, MMSE offers enhanced numerical stability under severe channel fading conditions, where channel inversion causes noise amplification.