Complex-Valued Frequency Estimation Network and Its Applications to Superresolution of Radar Range Profiles

Frequency estimation of multiple sinusoidals is fundamental in statistical signal processing. In this article, we focus on 1-D complex signals and propose a complex-valued network for frequency estimation, referred to as cResFreq, which overcomes the drawbacks of DeepFreq and 2-D ResFreq, that is, the performance loss associated with processing complex-valued signals by a real-valued network. First, weights of a hidden layer are optimized to approximate varieties of complex-valued complete basis vectors, and the locally uncorrelated noise suppression is realized by convolutional kernels. The feature maps/coarse frequency representations after a modulus operation are subsequently processed by real-valued residual blocks for obtaining a high-resolution frequency representation. Numerical experiments exhibit the superior performance of the proposed method in terms of resolution, estimation accuracy, and detection capability for weak components. Finally, the cResFreq is applied to realize the superresolution of range profiles in radar systems. The results based on the synthetic and real signals demonstrate that the HRRPs obtained by the cResFreq provide more target details, which shows promise in automatic target recognition (ATR). The codes can be found in https://github.com/panpp-git/cResFreq.