To study the performance of multi-reconfigurable intelligent surface （RIS） assisted communication network with the presence of the same frequency interference at the receiving end， this paper deploys multiple RIS of different geometric sizes as relays in the wireless channel to improve the performance of the communication network， and assumes that the wireless channels associated with different RISs are independent and non-uniformly distributed. Channels associated with different reflector surfaces in the same RIS are independently and identically distributed. The end-to-end channel coefficients are approximated to the Gamma distribution， and the exact expressions of outage probability（OP）、ergodic capacity（EC） and OP asymptotic expressions are derived based on the Gamma distribution. Monte Carlo simulation is used to verify the correctness of the analysis results. The research shows that the number of RIS， the number of interference items and the interference signal power play a crucial role in the cooperative transmission performance of multi-RIS auxiliary communication networks.