To address the problem of too many model parameters in predistorters, this paper proposes a predistorter model simplification method for broadband power amplifier (PA) based on the theory of compressed sensing (CS). On the basis of the sparsity adaptive matching pursuit (SAMP) algorithm, the relevant support selection SAMP algorithm based on frequency domain notch (RSS-FNSAMP) is proposed. The PA behavior model can be simplified and used in the proposed segmented dual-feedback DPD system, and the out-ofband distortion masked by the in-band residual can be compensated, which not only enhanced the stability of the system, but also reduced its complexity and improved the linearization effect of DPD. To verify the method, a 35 dBm class F power amplifier is driven by 20 MHz LTE signal. The experimental results show that the normalized mean squared error (NMSE) is improved by 3~ 5 dB compared with ILA-SAMP, ILA-DOMP and segmented dual feedback-DOMP, and the adjacent channel power ratio ( ACPR) is improved by 25 dBc, which shows that the proposed method can improve the linearity of power amplifier while reducing the number of model parameters.