Finite-Rate-of-Innovation-Sampling-Based Super-Resolution Radar Imaging

We address the problem of estimating target locations that are sparse in a pulse-Doppler radar's unambiguous region by sampling the received signal at sub-Nyquist rates. The received signal is modeled as a finite-rate-of-innovation (FRI) signal, and the problem of estimating the delays in a single transceiver radar is formulated as one of recovery of sparse common-support (SCS) FRI signals, which arises in the context of channel estimation in multiple input, multiple output communication systems. The delays are estimated by the SCS-FRI reconstruction method. We present a new method termed delay focusing to estimate the Doppler shifts. To obtain overall performance gains, we also present an extended method called dual focusing, which combines both delay and Doppler focusing schemes, and has the capability to superresolve targets in the delay-Doppler plane. The performance of the recovery methods in the presence of noise is also analyzed. We demonstrate that the proposed estimation methods are robust to noise. Monte Carlo performance analysis in the presence of noise shows that the dual focusing method accurately resolves closely spaced targets and yields a significant decrease in normalized mean-square error of up to 10-20 dB for the estimated Doppler shifts. We also simulate the scenario where multiple targets are in a formation, that is, when they are closely spaced along both delay and Doppler axes, and show that the dual focusing method achieves a hit rate of nearly 100% at a much lower signal-to-noise ratios than that required for Doppler focusing.