In this paper, a novel relaying technique is proposed to improve the bit-error rate (BER) performance and distance coverage of high-speed all-optical free-space optical (FSO) communication systems. Particularly, an optical amplifyand-forward (OAF) relaying technique using erbium-doped fiber amplifier (EDFA) combined with optical hard-limiter (OHL) is introduced. The use of OHL enables EDFA-based OAF relaying FSO systems to prevent the accumulation of amplified background noise, which significantly degrades the system performance when deploying multiple relays. For performance evaluation, we theoretically analyze the proposed system over atmospheric turbulence channels modeled by Gamma-Gamma distribution. A closed-form expression for the end-to-end BER bounds is therefore analytically formulated, taking into account other impacts of atmospheric channels including atmospheric attenuation and geometric spreading of the optical beam, as well as noises caused by background light and receiver. The numerical results, which are validated by Monte-Carlo (M-C) simulations, confirm the superiority of the proposed system in comparison with conventional ones.Index Terms-Optical amplify-and-forward relaying, optical hard-limiter, EDFA, background noise, atmospheric turbulence, channel loss, FSO communication systems.