Chromatic dispersion-enhanced signal-signal beating interference (SSBI) considerably affects the performance of intensity-modulation and direct-detection (IM/DD) fiber transmission systems. For recovering optical fields from received double sideband signals after propagating through IM/DD transmission systems, Gerchberg-Saxton (G-S) iterative algorithms are promising, which, however, suffers slow convergence speeds and local optimization problems. In this paper, we propose a multi-constraint iterative algorithm (MCIA) to extend the Gerchberg-Saxton-based linearized detection. The proposed technique can accelerate the convergence speed and realize nonlinear-equalization-free detection. Based on the data-aided iterative algorithm (DIA) and the decision-directed data-aided iterative algorithm (DD-DIA), the proposed technique reuses redundant bits from channel coding to not only correct decision errors but also enforce the constraints on the task function to further accelerate the whole optical field retrieval processing. Simulation results show that, compared with the DD-DIA, the MCIA reduces the received optical power (ROP) by about 1.5-dB for a 100-Gb/s over 50-km SSMF PAM-4 signal transmission at the SER of 2×10-2. For a 100-Gb/s over 400-km SSMF transmission system, just 30 MCIA iterations is needed, which is 30% reduction in iteration count compared with the DD-DIA. For further increased transmission capacities, the MCIA can improve the symbol error rate (SER) by two orders of magnitude compared with the conventional IA. To validate the effectiveness of the MCIA, we also conduct experiments to transmit 92-Gb/s PAM-4 signals over 50-km IM/DD fibre systems. We find that the MCIA has an 1-dB ROP improvement compared with the DD-DIA. Compared with Volterra nonlinear equalization, the BERs of the MCIA with a simple linear equalizer are reduced by more than one order of magnitude with only 52 MCIA iterations