We propose and experimentally demonstrate a novel scheme which can simultaneously realize wavelength-preserving and phase-preserving amplitude noise compression of a 40 Gb/s distorted non-return-to-zero differential-phase-shift keying (NRZ-DPSK) signal. In the scheme, two semiconductor optical amplifiers (SOAs) are exploited. The first one (SOA1) is used to generate the inverted signal based on SOA's transient cross-phase modulation (T-XPM) effect and the second one (SOA2) to regenerate the distorted NRZ-DPSK signal using SOA's cross-gain compression (XGC) effect. In the experiment, the bit error ratio (BER) measurements show that power penalties of constructive and destructive demodulation at BER of 10-9 are -1.75 and -1.01 dB, respectively. As the nonlinear effects and the requirements of the two SOAs are completely different, quantum-well (QW) structures has been separately optimized. A complicated theoretical model by combining QW band structure calculation with SOA's dynamic model is exploited to optimize the SOAs, in which both interband effect (carrier density variation) and intraband effect (carrier temperature variation) are taken into account. Regarding SOA1, we choose the tensile strained QW structure and large optical confinement factor to enhance the T-XPM effect. Regarding SOA2, the compressively strained QW structure is selected to reduce the impact of excess phase noise induced by amplitude fluctuations. Exploiting the optimized QW SOAs, better amplitude regeneration performance is demonstrated successfully through numerical simulation. The proposed scheme is intrinsically stable comparing with the interferometer structure and can be integrated on a chip, making it a practical candidate for all-optical amplitude regeneration of high-speed NRZ-DPSK signal.