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Abstract In this letter, a novel digital pre‐distortion (DPD) scheme for an end‐to‐end forward link (FL) channel in a satellite internet network (SIN) is first proposed. It aims at the unprecedented challenge of the model of non‐stationary (NS) cascade response consisting of channel fading and non‐linear behaviour of onboard payload. Unlike most existing schemes, the proposed DPD scheme explores a new model to describe the distortion with improved band‐limited memory polynomial (BLMP) by the equivalent response. To decrease the complexity of utilization, the authors design a new strategy to divide the unified non‐stationary situation into several different stationary situations. Meanwhile, a space‐time‐frequency stationary window function (STF‐WF) is proposed to compensate for the signal distortion. The experimental results demonstrate that the proposed schemes realize maximum total degradation (TD) gain by 15%.