Recently proposed universal filtered multicarrier (UFMC) system is not an orthogonal system in multipath channel environments and might cause significant performance loss. In this paper, the authors propose a cyclic prefix (CP) based UFMC system and first analyze the conditions for interference-free one-tap equalization in the absence of transceiver imperfections. Then the corresponding signal model and output signal-to-noise ratio expression are derived. In the presence of carrier frequency offset, timing offset, and insufficient CP length, the authors establish an analytical system model as a summation of desired signal, intersymbol interference, intercarrier interference, and noise. New channel equalization algorithms are proposed based on the derived analytical signal model. Numerical results show that the derived model matches the simulation results precisely, and the proposed equalization algorithms improve the UFMC system performance in terms of bit error rate.