In this paper, we investigate the impact of two pulse shapes on the performance of a real-time free-space optical communication link. The two candidate pulse shapes are the square-root raised cosine and Xia pulse, respectively which are tested as the basis function for multi-band carrier-less amplitude and phase modulation. We first develop a real-time system based on a Xilinx Zynq ZCU102 system-on-chip platform utilising a high-resolution analogue-to-digital-converter. We then generate multi-band carrier-less amplitude and phase modulation formats using it and test the error vector magnitude whilst varying parameters. We emulate the fog environment utilising neutral density filters and evaluate the error performance of the link under increasingly poor visibility conditions. We show that contrary to previous reports, the SRRC pulse shape offers superior performance over the first-order Xia pulse in the FSO environment operating at data rates exceeding 1 Gb/s.