ADMM–Net: A Deep Learning Approach for Parameter Estimation of Chirp Signals Under Sub-Nyquist Sampling

Parameter estimation of chirp signals plays an important role in the field of radar countermeasures. Compressed sensing (CS) based sub-Nyquist sampling and parameter estimation methods alleviates the pressure on hardware systems to acquire and process chirp signals with large time-bandwidths. In this paper, a framework based on the fractional Fourier transform (FrFT) and alternating direction method of multipliers network (ADMM-Net) is proposed to realize chirp signal parameter estimation under sub-Nyquist sampling. The whole framework is composed of multiple parallel ADMM-Nets, where each ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures of the ADMM algorithm for optimizing a CS-based $p$ -order FrFT spectral estimation model. The chirp rate and central frequency of chirp signals are obtained through a two-dimensional search on the spectrum image output by the network group. Experiments demonstrate that the proposed ADMM-Net-based method can achieve higher estimation accuracy and computational efficiency at lower signal-to-noise ratios and sampling ratios than traditional CS methods. We also demonstrate that the proposed ADMM-Net-based framework has strong generalization ability for multi-component chirp signals. Furthermore, we further generalize ADMM-Net to GADMM-Net, in which the activation function is data-driven instead of model-driven. Experiments demonstrate that GADMM-Net significantly improves on the basic ADMM-Net and achieves higher spectral resolution with faster computation speed.