Explainable Wideband Spectrum Signal Reconstruction Based on Primal-Dual Hybrid Gradient Network

In wireless communication scenarios, compressed sensing emerges as an efficient technique for wideband spectrum sensing, which is a key building block for detecting spectrum holes with a sub-Nyquist sampling rate. However, traditional compressed spectrum reconstruction methods exhibit poor reconstruction performance and high complexity, due to the manual parameter optimization and hundreds or thousands of iterations. Spurred by the excellent learning capability of deep learning (DL), DL-based reconstruction methods have been proposed and achieved better reconstruction performance. But the black-box nature of DL models results in poor interpretability. To solve these problems, this letter proposes a wideband spectrum signal reconstruction (WSSR) algorithm by combining primal-dual hybrid gradient (PDHG) algorithm with DL technique through deep unfolding, and refers to it as PDHG deep reconstruction network (PDHG-Net). Parameters in PDHG-Net, such as regularization and step size, are learned in an end-to-end manner by DL rather than being adjusted manually. Results show that PDHG-Net can reduce reconstruction error by 16.25% on average compared with four state-of-the-art WSSR methods.