Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse problem by unfolding iterative algorithms as neural networks. Typically, research concerning DL assume a fixed number of network layers. However, it ignores a key character in traditional iterative algorithms, where the number of iterations required for convergence changes with varying sparsity levels. By investigating on the projected gradient descent, we unveil the drawbacks of the existing DL methods with fixed depth. Then we propose an end-to-end trainable DL architecture, which involves an extra halting score at each layer. Therefore, the proposed method learns how many layers to execute to emit an output, and the network depth is dynamically adjusted for each task in the inference phase. We conduct experiments using both synthetic data and applications including random access in massive MTC and massive MIMO channel estimation, and the results demonstrate the improved efficiency for the proposed approach.

中文翻译：

---

解决通信系统中的稀疏线性逆问题：具有自适应深度的深度学习方法

噪声线性测量的稀疏信号恢复问题出现在无线通信的许多领域。近年来，基于深度学习 (DL) 的方法吸引了研究人员的兴趣，通过将迭代算法展开为神经网络来解决稀疏线性逆问题。通常，关于 DL 的研究假设网络层数是固定的。然而，它忽略了传统迭代算法中的一个关键特征，即收敛所需的迭代次数随着稀疏程度的变化而变化。通过研究投影梯度下降，我们揭示了现有固定深度深度学习方法的缺点。然后我们提出了一个端到端的可训练 DL 架构，它在每一层都包含一个额外的停止分数。因此，所提出的方法学习执行多少层以发出输出，并且在推理阶段为每个任务动态调整网络深度。我们使用合成数据和应用进行实验，包括大规模 MTC 中的随机访问和大规模 MIMO 信道估计，结果证明了所提出方法的效率提高。