This paper presents an auxiliary-channel-assisted background calibration for ADC's input front-end (buffer + T/H) distortion and inter-stage gain error. The auxiliary channel is custom-designed which runs at a fractional speed of the main ADC with only moderate noise performance but high linearity. It also has a pseudo inter-stage gain characteristic as the main ADC, which incorporates with the multi-layer LMS procedure, facilitating a fast convergence speed. Verified in a 12-bit 1GS/s pipelined SAR ADC in 28nm CMOS, the SNDR and SFDR at Nyquist input are 59.28 dB and 67.09 dB SFDR, respectively. Just the distortion calibrations alone contribute >11.13dB SFDR improvement in the entire Nyquist band. Both the ADCs and input buffers work under a 1V supply, consuming 19.2mW with 17% from the buffer.