Mixerless Dual-Envelope CW Radar for Displacement Sensing Using Geometric Phase Diversity

Continuous-wave (CW) radar recovers displacement from return phase, but a single envelope measurement does not provide a unique phase coordinate. This paper presents a mixerless dual-envelope (2-ENV) approach in which two spatially separated envelope detectors measure the coherent sum of the target reflection and air-coupled transmitter leakage. The leakage serves as an over-air reference, while receive geometry provides the inter-channel phase diversity needed for I/Q-like reconstruction. The reconstruction has a 1/|sin(ΔΦ)| endpoint conditioning factor, and finite-record performance also depends on operating phase and motion arc. Simulations map these effects, modulation SNR, and fully blind five-parameter fitting. A 915 MHz prototype is evaluated in sequential matched-channel and simultaneous dual-channel experiments. The matched-channel sweep verifies the predicted endpoint-conditioning trend. Simultaneous measurements show that calibration-free five-parameter fitting is record-dependent as the available motion arc changes. The calibration-aided demodulation method (CADM) estimates the channel gains and phase difference from a 20 mm amplitude record and reuses them with per-record offset refitting. Across four non-calibration records, this fixed-setup transfer yields 1.8–5.0% normalized root-mean-square error. The results demonstrate calibrated displacement recovery using an over-air reference without a mixer, wired RF reference path, or self-injection-locked oscillator.