We experimentally demonstrate Kramers-Kronig detection of four 20 Gbaud 16-quadrature-amplitude-modulated (QAM) channels after 50 km fiber transmission using two soliton Kerr combs as signal sources and local oscillators. The estimated carrier phase at the receiver for each of the channels is relatively similar due to the coherence between the frequency comb lines. The standard deviation of the estimated carrier phase difference of the channels is less than 0.08 rad after 50 km single-mode fiber (SMF) transmission. This enables the carrier phase recovery derived from one channel to be shared among multiple channels. In the back-to-back scenario, the bit error rate (BER) performance for shared carrier phase recovery shows an optical signal-to-noise ratio penalty of ${\sim}{0.5}\;{\rm dB}$∼0.5dB compared to the BER performance for carrier phase recovery when derived for each channel independently. BERs below the forward error correction threshold are achieved after 50 km SMF transmission with both independent and shared carrier phase recovery for four 20-Gbaud 16-QAM signals.