Accurate Near-Range Displacement Sensing in Single-Channel FMCW Radar via CZT-MLE Compensation for SL-IQI

Frequency-modulated continuous-wave (FMCW) radar is increasingly deployed for near-range micromotion sensing in vital-sign and industrial monitoring, where accurate extraction of the detailed displacement waveform is critical. Many practical platforms adopt a single-channel (real-valued) receiver front end, which reduces RF/ADC hardware, power consumption, and long-term analog calibration burden compared with quadrature I/Q chains. However, applying a real-input range discrete Fourier transform (DFT) introduces spectral leakage that creates a distinct digital nonideality, referred to as spectral-leakage-induced I/Q imbalance (SL-IQI). Although SL-IQI occurs for any off-grid beat frequency, it is most pronounced in the first few range bins commonly used for near-range sensing. This article derives a rigorous theoretical model for SL-IQI in single-channel FMCW front ends and presents a deterministic compensation for accurate displacement sensing. Building on this model, the proposed method applies a local chirp-Z transform (CZT) to refine the range spectrum, and a maximum-likelihood estimator (MLE) yields a high-resolution estimate of the fractional range bin index. The resulting coefficients then drive a widely linear inversion that cancels the conjugate component. The procedure is insensitive to DC offset and does not rely on long-arc coverage. It operates on a chirp-by-chirp basis and remains robust even for small-amplitude motions and spiral I/Q trajectories. Simulations and experiments with a 60-GHz single-channel FMCW sensor demonstrate that the proposed approach effectively suppresses SL-IQI. Crucially, it outperforms existing curve-fitting methods primarily for near-range targets, providing substantial improvements in displacement waveform quality and amplitude accuracy over existing methods.