We have proposed a laser-phase-fluctuation-insensitive optical coherent detection scheme assisted by a digital signal processing (DSP) technique for radio-over-fiber (RoF) systems. In this system, a "two-tone" local light is used for an individual optical coherent detection of both the carrier and the modulated components of RoF signal, where a frequency separation of two-tone local light is the same as that of RoF signal. To distinguish the carrier and the modulated components in the process of optical coherent detection, they have to be separated in the optical domain. In this paper, we proposed a new optical coherent detection scheme with an "offset-frequency-spaced two-tone" local light, which is also in principle insensitive to the laser phase fluctuation and is assisted by the DSP technique. In the proposed scheme, it is not required to separate the carrier and the modulated components in the optical domain because they can be easily separated in the electrical domain after the photodetection. Therefore, the system configuration is expected to be simpler than that in the previous scheme. First, we explain the principle of our new proposal and experimentally demonstrate the data recovery. Then, the influence of the frequency detuning between photo-detected modulated and unmodulated signals is discussed. Moreover, the transmission performance with an error vector magnitude (EVM) is also evaluated for the optical coherent detection of a 10-Gbaud quadrature-phase-shift-keying RoF signal after a 20-km-long standard single-mode fiber transmission. As a result, it is shown that the EVM of less than 12.4 %rms is achieved.