A radar sensing system includes at least one transmitter, at least one receiver and a processor. The at least one transmitter transmits a power shaped RF signal. The transmitted RF signal decreases in power over time. The at least one receiver receives a reflected RF signal. The reflected RF signal is the transmitted RF signal reflected from targets in the environment. The reflected RF signal is down-converted and the result provided to the processor. The processor samples the down-converted reflected RF signal during a plurality of time intervals to produce a sampled stream. The different time intervals of the plurality of time intervals will contain different signal levels of RF signals reflected from the targets. The processor also selects samples in the sampled stream over a selected time interval of the plurality of time intervals that is free of RF signals reflected off of near targets.