Doppler spectrum width, which relates to wind turbulence, is one of the essential parameters of coherent LIDAR. Using the Fourier transform theorem and the definition of correlation function, the power spectrum function in the stationary condition is deduced. The effects of pulse shape, pulse duration and the windowing are included. The spectrum width resulted from the turbulence is given under Kolmogorov turbulence model. Based on the power spectrum theory, the spectrum broadening by different pulse shapes and pulse durations are calculated. To validate the accuracy of the theory and usage in the retrieval of turbulence parameters, the numerical simulations of the echo signal are carried out in turbulence conditions. The statistics characteristics of the spectrum broadening from laser pulse shapes and durations are inverted and compared. The results show that the spectrum broadening varies greatly due to the selection of pulse shapes and pulse durations, and the numerical simulation is in accordance with the theory results.