The matched filter output of pulse compression radar is associated with range sidelobes along with the mainlobe. To reduce these sidelobes, different types of windows are used as weighing function at the receiver. When the target is in motion, the reflected signal is Doppler-shifted version of the original transmitted signal. If this Doppler-shifted signal is passed through the receiver matched filter, it produces very low Peak to Sidelobe Ratio (PSR). In this paper, we have proposed the use of convolutional windows at the receiver along with amplitude tapered or phase distorted transmitted Linearly Frequency Modulated (LFM) signal to get high PSR value in Doppler shift condition. Exhaustive simulation studies are carried out for Time-Bandwidth ( TB ) product of 50 and 100 and it is found that convolutional windows provide superior PSR performance over conventional windows.