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We experimentally investigate the all-optical regeneration of constant envelope alternative modulation format signals at 40 Gb/s. The regeneration scheme is based on hard-limiting amplification in a saturated semiconductor optical amplifier (SOA) that can remove the signal intensity noise. Indeed a significant improvement of the signal quality is reported for either polarization shift keying (PolSK) and frequency shift keying (FSK) signal formats, both detected using simple schemes based on direct detection. The regeneration solution, however, is found to be quite limited for non-return-to-zero (NRZ) differential phase shift keying (DPSK) (demodulated using a 1-bit delay interferometer). Indeed, SOA saturation generates a detrimental nonlinear phase noise that can override the reduction of intensity noise.