Forward-looking synthetic aperture radar is an essential tool in modern remote sensing applications, but its imaging is a challenging task. Few existing methods consider the curve trajectory. Aiming at the difficulty of resolution and the Doppler ambiguity in forward-looking SAR under the curve trajectory, this paper establishes a forward-looking multi-channel SAR system model and proposes a novel approach for the forward-looking SAR imaging under the curve trajectory. The approach is implemented by a two-step process: 1) The Doppler ambiguity under forward-looking mode is solved by adaptive beam-forming processing; and 2) A sparsity-driven optimization imaging algorithm is developed to enhance the azimuth angle resolution in the forward-looking direction, where the resolution gain aroused by the curve trajectory is exploited. The extensive simulation confirms the validity of the proposed approach.

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