To solve the problem of imprecise upper bound expression of three-branch signal detection（TBSD） scheme, a TBSD scheme of spectrum-amplitude coded optical code division multiple access（SAC-OCDMA） system is proposed, a rigorous mathematical model is established, and the scheme is numerically evaluated and simulated. The simulation results show that the scheme can completely eliminate multi-user interference（MUI） at the transmission rate of 500 Mb/s and 1 Gb/s, and most MUI can be eliminated at the transmission rate of 5 Gb/s, which proves the accuracy of the mathematical model.