In this paper, we investigate the joint device activity and data detection in
massive machine-type communications (mMTC) with a one-phase non-coherent
scheme, where data bits are embedded in the pilot sequences and the base
station simultaneously detects active devices and their embedded data bits
without explicit channel estimation. Due to the correlated sparsity pattern
introduced by the non-coherent transmission scheme, the traditional approximate
message passing (AMP) algorithm cannot achieve satisfactory performance.
Therefore, we propose a deep learning (DL) modified AMP network (DL-mAMPnet)
that enhances the detection performance by effectively exploiting the pilot
activity correlation. The DL-mAMPnet is constructed by unfolding the AMP
algorithm into a feedforward neural network, which combines the principled
mathematical model of the AMP algorithm with the powerful learning capability,
thereby benefiting from the advantages of both techniques. Trainable parameters
are introduced in the DL-mAMPnet to approximate the correlated sparsity pattern
and the large-scale fading coefficient. Moreover, a refinement module is
designed to further advance the performance by utilizing the spatial feature
caused by the correlated sparsity pattern. Simulation results demonstrate that
the proposed DL-mAMPnet can significantly outperform traditional algorithms in
terms of the symbol error rate performance.

本文中，我们研究了使用单相不相干方案进行大规模机器型通信（mMTC）中的关节设备活动和数据检测，其中数据位嵌入到导联序列中，基站同时检测活动设备及其嵌入的数据位而无需显式通道估计；针对非相干传输方案引入的相关稀疏性模式，传统的幅度估计传输（AMP）算法无法达到令人满意的性能，因此，我们提出了一种深度学习修改的 AMP 网络（DL-mAMPnet）。DL-mAMPnet 通过有效利用导联活动相关性来增强检测性能。DL-mAMPnet 通过将 AMP 算法展开为前馈神经网络来构建，将 AMP 算法的原理数学模型与强大的学习能力相结合，从而使两种技术的优势得到了发挥。DL-mAMPnet 引入了可训练参数来近似相关稀疏性模式和大规模衰落系数。此外，设计了一种细化模块，通过利用相关稀疏性模式引起的空间特性进一步提高性能。仿真结果表明，所提出的 DL-mAMPnet 在符号误差率性能方面可以显著优于传统算法。

非相干大规模机器通信的模型驱动深度学习

Model-Driven Deep Learning for Non-Coherent Massive Machine-Type  Communications

Iterative thresholding algorithms are well-suited for high-dimensional
problems in sparse recovery and compressive sensing. The performance of this
class of algorithms depends heavily on the tuning of certain threshold
parameters. In particular, both the final reconstruction error and the
convergence rate of the algorithm crucially rely on how the threshold parameter
is set at each step of the algorithm. In this paper, we propose a
parameter-free approximate message passing (AMP) algorithm that sets the
threshold parameter at each iteration in a fully automatic way without either
having an information about the signal to be reconstructed or needing any
tuning from the user. We show that the proposed method attains both the minimum
reconstruction error and the highest convergence rate. Our method is based on
applying the Stein unbiased risk estimate (SURE) along with a modified gradient
descent to find the optimal threshold in each iteration. Motivated by the
connections between AMP and LASSO, it could be employed to find the solution of
the LASSO for the optimal regularization parameter. To the best of our
knowledge, this is the first work concerning parameter tuning that obtains the
fastest convergence rate with theoretical guarantees.

本文提出一种无需用户调整阈值参数的自动方式，采用修改过的梯度下降算法和 Stein 无偏风险估计，实现高稀疏恢复和压缩感知算法中的最小重构误差和最高收敛速率，为参数调整领域的最快收敛率理论保障提供了解决方案。

无参数最优近似信息传递

Parameterless Optimal Approximate Message Passing

Consider the noisy underdetermined system of linear equations: y=Ax0 + z0,
with n x N measurement matrix A, n < N, and Gaussian white noise z0 ~
N(0,\sigma^2 I). Both y and A are known, both x0 and z0 are unknown, and we
seek an approximation to x0. When x0 has few nonzeros, useful approximations
are obtained by l1-penalized l2 minimization, in which the reconstruction \hxl
solves min || y - Ax||^2/2 + \lambda ||x||_1.
Evaluate performance by mean-squared error (MSE = E ||\hxl - x0||_2^2/N).
Consider matrices A with iid Gaussian entries and a large-system limit in which
n,N\to\infty with n/N \to \delta and k/n \to \rho. Call the ratio MSE/\sigma^2
the noise sensitivity. We develop formal expressions for the MSE of \hxl, and
evaluate its worst-case formal noise sensitivity over all types of k-sparse
signals. The phase space 0 < \delta, \rho < 1 is partitioned by curve \rho =
\rhoMSE(\delta) into two regions. Formal noise sensitivity is bounded
throughout the region \rho < \rhoMSE(\delta) and is unbounded throughout the
region \rho > \rhoMSE(\delta). The phase boundary \rho = \rhoMSE(\delta) is
identical to the previously-known phase transition curve for equivalence of l1
- l0 minimization in the k-sparse noiseless case. Hence a single phase boundary
describes the fundamental phase transitions both for the noiseless and noisy
cases. Extensive computational experiments validate the predictions of this
formalism, including the existence of game theoretical structures underlying
it. Underlying our formalism is the AMP algorithm introduced earlier by the
authors. Other papers by the authors detail expressions for the formal MSE of
AMP and its close connection to l1-penalized reconstruction. Here we derive the
minimax formal MSE of AMP and then read out results for l1-penalized
reconstruction.

论文研究了稀疏信号的 l1 惩罚重构问题，在稳健性和性能之间取得了平衡，开发了新的算法并通过计算实验证明了其表现。