Co-frequency and co-time full duplex(CCFD) is a promising technique for improving spectral efficiency in next generation wireless communication systems. However, for the applications of CCFD in a cellular network, severe co-channel interference is an essential problem. Specifically, there are two significant interferences, i.e., inter-terminal interference(ITI) and inter-cell interference(ICI), which lead to an obvious performance degradation. In this paper, two techniques are proposed for suppressing the ITI and ICI in a CCFD cellular system, respectively. The first technique is obtained by modeling the three-node CCFD system as the Z-channel. After deriving the sum-capacity of the Z-channel, a sum-capacity-achieving scheme based on successive interference cancellation(SIC) is proposed. The second technique is designed by combining the fractional frequency reuse scheme with CCFD. The performance gains of the proposed two techniques in terms of signalto-interference plus noise ratio(SINR) and sumcapacity are analyzed. Simulation results show that the proposed scheme can achieve significant interference suppression performance and higher system capacity, especially for cell edge users.