Sensors may employ a constant false alarm rate (CFAR) screening process in combination with edge-based echo detection. In one illustrative embodiment, a sensor controller includes: a transmitter, a receiver, and a processing circuit coupled to the transmitter and to the receiver. The transmitter drives a piezoelectric element to generate acoustic bursts. The receiver senses a response of the piezoelectric element to echoes of each acoustic burst. The processing circuit is operable to apply echo-detection processing to the response by: determining a derivative signal from the response; and detecting an echo based at least in part on a peak in the derivative signal indicating a rising and/or falling edge in the response. Signaling to the electronic control unit may specify a time of flight associated with each edge.