After extracting the degraded samples, classic strategies employ interpolation to retrieve misplaced data. A Teager–Kaiser energy operator has been demonstrated to help locate transient interference. A covariance matrix incorporating noncontaminated samples is developed based on the heightened correlation between clutter and target echoes. As a result, a matrix-pencil strategy-based interference alleviation method is suggested, which characterizes the interference by its characteristic spectrum dissimilarity. However, when clutter and interference overlap, the performance of these methods may degrade. Following clutter filtering, one noticeable strategy is threshold detection based on the high interference-to-noise ratio (INR) technique. The foundations of the first type of technique are comparable: they determine interferences and utilize sequential interpolation to rebuild lost signals. The first method is currently widely utilized, which detects and locates interference in the time domain the typical algorithms corresponding to the first technique can be referred to in. Three types of techniques are known for eliminating transient interferences that survive the beamforming stage: (1) conventional removal approaches with interference location and subsequent interpolation-based reconstruction (2) subspace decomposition interpolation-free methods (3) simultaneous location and removal. As a result, heightened grating lobes in the Doppler spectrum make determining targets challenging. These sparse OTHR signals will generate an exceedingly severe broadening of the clutter during coherent accumulation. In this sense, the time domain signal can be seen as a partly sampled signal.

Furthermore, modern radar systems must be multi-mode and multi-functional to track and detect several targets simultaneously. Generally speaking, the transient interference can raise the noise level by up to 20 dB, observably lowering the target detection ability. Transient interference will submerge potential targets because of its high energy and temporal transience. The OTHR signal is typically contaminated by environmental noise and transient interferences such as air noise, meteor trail echoes, and other electromagnetic devices. Even though modern OTHR systems have many benefits, they can have limitations. When compared to typical radar systems, it has advantages such as a great observing range, broad coverage, and anti-concealed capacity. The over-the-horizon radar (OTHR) transmits high-frequency (HF) band (3–30 MHz) signals, and radio signals propagated to the ionosphere are reflected to the ground to detect targets. Both simulation and real-measured OTHR data proved the proposed approach’s performance. Compared with traditional sparse solution methods, the presented approach can balance the efficiency and accuracy of OTHR signal spectrum reconstruction. By solving the Doppler sparsity-constrained optimization with the trained network, the complete Doppler spectrum is reconstructed effectively for target detection. Therefore, the processed signal can be seen as a sparse OTHR signal. Firstly, transient interferences are identified based on the sparse basis representation and then excised. This article proposes a modified Alternating Direction Method of Multipliers (ADMM)-Net to reconstruct the target and clutter spectrum of sparse OTHR signals so that target detection can be performed normally. The sparse OTHR signal will raise serious grating lobes using conventional methods and thus degrade target detection performance. In addition, modern OTHR needs to carry out multi-target detection from sea to air, resulting in the sparse sampling of echo data. Transient interference often submerges the actual targets when employing over-the-horizon radar (OTHR) to detect targets.

Doppler effect equation for radar