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This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design algorithms for joint user activity detection, delay detection, and channel estimation. By exploiting the sparsity on both user activity and delays, we formulate a hierarchical sparse signal recovery problem in both the single-antenna and the multiple-antenna scenarios. While traditional compressed sensing algorithms can be applied to these problems, they suffer high computational complexity and often require the perfect statistical information of channel and devices. This paper solves these problems by designing the Learned Approximate Message Passing (LAMP) network, which belongs to model-driven deep learning approaches and ensures efficient performance without tremendous training data. Particularly, in the multiple-antenna scenario, we design three different LAMP structures, namely, distributed, centralized and hybrid ones, to balance the performance and complexity. Simulation results demonstrate that the proposed LAMP networks can significantly outperform the conventional AMP method thanks to their ability of parameter learning. It is also shown that LAMP has robust performance to the maximal delay spread of the asynchronous users.
In sketched clustering, a dataset of $T$ samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity independe
In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-fa
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative pr
Given a high-dimensional data matrix ${boldsymbol A}in{mathbb R}^{mtimes n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${boldsymbol u}^tin{mathbb R}^n$, ${boldsymbol v}^tin{mathbb R}^m$, indexed by $tin{0,1,2dots}$
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform mat