In this paper, we consider interactive nonlinear problem of multiple users in cognitive radio system. A new model that represents a cognitive radio system with N pairs of nonlinear transmitters and receivers is suggested. The model is represented with a baseband equivalent multi-input system based on complex Taylor series and weight functions. The power spectral density (PSD) of the received signal is analytically extracted using the autocorrelation function of the model output. The error vector magnitude (EVM) degradation due to interactive nonlinear problem is also analyzed. The spectral and EVM degradation analysis are verified by comparing the analytical results with the simulated ones.