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The carrier frequency offset (CFO) is one of the critical parameters for degrading the overall performance of radio systems modulated with a scheme of multiple carriers. The evaluation of system performance for a multi-carrier coded-division multiple-access (MC-CDMA) radio system with CFO effect mentioned previously is investigated in this study. Apart from the aforementioned parameter, the other important parameter referred to as fading branch correlation (FBC) occurring in the propagating channel is rarely applied in the study of MC-CDMA systems' performance. For the sake of simplicity, subcarriers are typically considered independently. However, the randomisation incurred in generating CFO and FBC should be simultaneously considered to calculate the overall performance. The focus of this work is an aggregate investigation to determine which parameter, that is, CFO or FBC, primarily dominates the performance of an MC-CDMA system. Assume that applying the same quantity of CFO (ε) and FBC (λ) in serving the simulation, that is, both values of CFO and FBC are assumed and assigned in the interval of (0.4, 1.0). Moreover, several novel formulas include both CFO and FBC parameters and many three-dimensional curves are presented and illustrated in this article.