Dual Null Detection Points Removal and Time-Domain Sensitivity Analysis of a Self-Injection-Locked Radar for Small-Amplitude Motion Sensing

Abstract

Compared with a conventional Doppler radar in which target displacement results in phase modulation, target displacement in a self-injection-locked oscillator (SILO)-based radar results in frequency modulation. Since the instantaneous phase is the time integral of frequency, the SILO-based radar is considered to have higher sensitivity than the conventional Doppler radar. However, a direct comparison between the SILO-based radar and the conventional Doppler radar is still needed to quantitatively understand the sensitivity difference. This article provides a rigorous time-domain analysis of the sensitivity of the SILO-based radar with a delay-based frequency demodulator for small-amplitude periodic motions. The analysis follows an approach similar to the time-domain analysis for the conventional Doppler radar. It reveals that two null detection point mechanisms could arise in SILO-based radar systems. The target distance may introduce one null detection point, and the delay added in the frequency demodulator may introduce another. Furthermore, this article also proposes an SILO-based radar with dual null detection points’ removal. Unlike the Doppler radar, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I/Q$ </tex-math></inline-formula> demodulation eliminates the null detection point introduced by the target distance, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I/Q$ </tex-math></inline-formula> demodulation in the SILO-based radar only eliminates the null detection point introduced by the delay cable. To overcome the other null detection point mechanism, a phase shifter is introduced after the LNA. Experiments were carried out to validate the proposed time-domain analysis and demonstrate that both the techniques need to be used simultaneously to remove both null detection points in the system. The sensitivity comparison was performed using a conventional Doppler radar and an SILO-based radar built with identical microwave components.