<p>Recently, a novel composite fading model referred to as the Shadowed Beaulieu-Xie (SBX) fading model has been proposed. This model is particularly applicable to wireless communication systems operating in the millimeter-wave and terahertz frequency bands. It effectively captures the presence of an arbitrary number of line-of-sight (LOS) and non-line-of-sight (NLOS) signal components within the propagation environment. In this work, average symbol error probability (ASEP) analysis of wireless networks having a single-input single-output connection with Imperfect Phase Error (IPE) over the SBX fading channel is studied. The IPE results are due to the phase synchronization error introduced by a mismatch within a communication system. Subsequently, the ASEP for non-coherent M-ary frequency shift keying (NCMFSK) modulation schemes, M-ary phase shift keying (MPSK) modulation schemes and the M-ary differential phase shift keying (MDPSK) modulation scheme over the SBX fading channels are also examined. Here, the analysis employs a probability density function (PDF)-based approach to derive comprehensive analytical (closed-form) expressions for the ASEP analysis. Additionally, to provide a deeper understanding, simplified asymptotic expressions are developed. Finally, the effects of shadowing and fading on system performance are examined and validated through extensive simulation results.</p>