With the increasing demand for access to the radio frequency spectrum, there has been an emergence of spectrum sharing radar systems. Along with this comes the need for rapid pulse-agility to avoid other time varying signals in the spectrum effectively. A software-defined radar (SDRadar) system that has been previously explored is further developed in this work to improve its spectrum sharing performance. To take advantage of the rapid reaction time of the improved system, pulse adaption occurs within a radar coherent processing interval, which causes significant distortion in the Doppler dimension. A simulation was formulated to show how the distortion becomes more significant as the magnitude of the adaptation increases. The distortion is also shown to significantly impact the number of false alarms detected, reducing the ability to verify true targets.