This article explores a multicarrier modulation system known as filter bank multicarrier offset quadrature amplitude modulation (FBMC-OQAM). The performance of polar-coded multicarrier systems, especially FBMC-OQAM, has not been extensively studied. This research involves analyzing the system error rate of polar-coded FBMC-OQAM in two realistic channel environments: frequency-selective Rician and frequency-selective Rayleigh, using MATLAB software. A comprehensive bit error rate (BER) analysis in the context of frequency-selective fading has been conducted. Simulation results demonstrate that BER significantly improves when polar codes are applied to FBMC-OQAM. Furthermore, the error-correcting capability of polar codes can be enhanced by using random code interleavers, which provide additional coding gain in fading channels. The findings of this study highlight the promising potential of polar-coded multicarrier modulation systems for next-generation wireless communication networks.