# A Robust Method Based on Deep Learning for Compressive Spectrum Sensing
## 1 Introduction  
With the advent of fifth-generation (5G) commercialization, global mobile data consumption and the number of connected devices have surged exponentially, intensifying the scarcity of spectrum resources [1]. The traditional static spectrum allocation strategy leads to inefficient utilization and further exacerbates the conflict between spectrum supply and demand. Cognitive radio technology presents a promising solution by dynamically analyzing the spectrum environment and enabling secondary users (SUs) to opportunistically access an underutilized spectrum, known as spectrum holes [2]. As the cornerstone of cognitive radio, spectrum sensing is crucial for ensuring its operational effectiveness. To identify more available channels, wideband spectrum sensing (WSS) has been proposed. Traditional WSS techniques rely on the Nyquist sampling theorem, which mandates a sampling rate of at least twice the maximum signal frequency. Recently, WSS based on compressed sensing theory has emerged as a promising alternative, significantly reducing the sampling rate requirements for analog-to-digital converters (ADCs). Compressive spectrum sensing (CSS) algorithms can be broadly categorized into two types. The first type avoids signal reconstruction and directly assesses spectrum occupancy from compressivemeasurements [3]. The second type decomposes CSS into two steps: initially performing sparse signal reconstruction, followed by utilizing the reconstructed signals for WSS [4]. In cognitive radio, compressed sensing (CS) leverages the sparsity of wideband spectrum signals in domains such as frequency and spatial, thereby substantially reducing the sampling rate requirements for devices and enabling cost-effective wideband spectrum sampling [5]. The original signal can be reconstructed from low-rank subsamples using specialized algorithms. Traditional CS reconstruction algorithms can be broadly categorized into two types: greedy algorithms and convex optimization-based algorithms, both of which have achieved significant advancements. Greedy algorithms include methods such as the matching pursuit (MP) algorithm [6], orthogonal matching pursuit (OMP) algorithm [7], regularized orthogonal matching pursuit (ROMP) algorithm [8], and compressive sampling matching pursuit (CoSaMP) algorithm [9]. However, these methods require prior knowledge for optimal operation. On the other hand, convex optimization-based algorithms, including ISTA [10], fast iterative shrinkage-thresholding algorithm (FISTA) [11], and alternating direction method of multipliers (ADMM) [12], exhibit robust reconstruction capabilities. Nonetheless, tuning parameters such as regularization weights and penalty factors within the ADMM algorithm remains challenging and often relies on empirical approaches [13]. Deep learning-based approaches, leveraging the robust learning capabilities of neural networks, have demonstrated remarkable success in signal reconstruction [14; 15]. [PERSON] et al. proposed a compressed sensing (CS)-based image reconstruction algorithm that enhances noisy image reconstruction performance using stacked denoising auto-encoders (SDA) [16]. However, the SDA model relies on fully connected neural networks with extensive interlayer weights, resulting in high computational complexity. To mitigate this issue, a neural network architecture inspired by ISTA was developed for image reconstruction, offering both interpretability and competitive performance [17]. More recently, the ISTA deep reconstruction network (ISTADR-Net) was introduced for reconstructing wideband spectrum signals [18]. Additionally, robust ADMM (R-ADMM), which integrates deep learning into the ADMM framework, has demonstrated promising reconstruction results [13]. Despite these advancements, most existing methods have yet to fully incorporate the block sparsity features (BSFs) inherent in wideband spectrum signals during the reconstruction process [19]. After obtaining the reconstructed wideband signal through the reconstruction algorithm, WSS can be performed.