In this paper, microwave photonic signal generation based on the period-one dynamic of optically injected discrete mode (DM) semiconductor lasers has been experimentally demonstrated and numerically simulated. The results show that the frequency of the generated microwave increases linearly with the frequency detuning or optical injection ratio. In addition, a single optical feedback loop is sufficient to reduce the microwave linewidth without significantly deteriorating side mode suppression. The simulation results using a model considering the nonlinear dependencies of the carrier recombination agree well with the experimental results, which indicates that the nonlinear carrier recombination effect is important in determining the nonlinear dynamics of optically injected DM lasers