Directly modulated lasers (DMLs) and electro-absorption modulated lasers (EMLs) are key transmitter options in future short-haul networks. However, both of them suffer from frequency chirp, which incurs nonlinear distortions, especially to high order modulation signals. In this paper, we investigate their application in PAM4-based digital mobile fronthaul and propose a scheme to remarkably improve the fidelity of radio signal. We first give a detailed study of the BER distribution of DML/EML based PAM4 signals and find that the BER of the second bit is much higher than that of the first bit in both systems. Accordingly, we propose to adopt sample bit interleaving to reduce the radio signal distortions caused by sample bit errors. Experimental results of 56Gbps I/Q data transmission reveal that, in a DML-based transmission system, the proposed scheme respectively leads to up to 8dB and 13dB EVM reduction to accommodate 33 × 100MHz 1024QAM OFDM signals and 64QAM OFDM signals in 10km and 20km cases. As well as in an EML-based transmission system, 14dB EVM reduction is achieved in 10km to finally accommodate 33 × 100MHz 256QAM OFDM signal.