Jacobi Elliptic Chirps for Sub-Nyquist Multi-Target Ranging

Sub-Nyquist sampling is an attractive way to reduce the hardware cost of wideband pulse-compression radar, but it introduces coherent alias-induced replicas in the matched-filter range profile, producing spurious peaks known as ghost targets. Existing frequency-modulated waveforms face a practical trade-off in this regime: linear frequency-modulated (LFM) pulses provide compact range responses but are highly susceptible to ghost-target detections, whereas hyperbolic frequency-modulated (HFM) pulses suppress ghosts at the cost of degraded target separability. To overcome this trade-off, we propose a sine-over-cosine Jacobi elliptic frequency-modulated waveform, referred to as SC-EFM, in which the elliptic modulus tunes the instantaneous-frequency (IF) curvature while preserving the pulse duration and bandwidth of conventional benchmarks. We characterize the sub-Nyquist folding structure of SC-EFM and derive closed-form expressions for the multi-target and ghost-target detection probabilities. Numerical results show that SC-EFM significantly suppresses ghost detections relative to LFM while matching its target separability, and substantially outperforms HFM in resolving close targets, providing a unified waveform solution for ghost-resilient sub-Nyquist multi-target ranging.