A 12-bit, 1-GS/s SAR-assisted pipeline ADC with background distortion and split-ADC-like gain calibrations is presented. The ADC includes an input buffer where its distortion is tackled by calibration. A low-cost auxiliary channel is introduced that serves as a reference for the calibration. It employs only a quarter of the input swing of the main channel, thus achieving adequate linearity. The auxiliary channel is further utilized for the gain calibration, where a split-ADC-like calibration is proposed to ease residue amplifier design constraint. The coefficients in the digital post-distortion filter are iterated through a multi-step multi-layer LMS algorithm, which converges faster and is more robust than its single-step counterpart. The buffered ADC works under a 1 V power supply thanks to the calibration, consuming 19.2 mW, where the input buffer contributes 18% of the total power. The calibration improves the SFDR by >14 dB within the 1st Nyquist zone, and >8dB up to 4th Nyquist input zone. The design achieves 59.3 dB SNDR and 67.1 dB SFDR at Nyquist input. The entire calibration converges within 1×10 iterations.