This paper studies the joint estimation of channel fading and user activity for the uplink of a grant-free massive machine-type communication system. Comparing with previous studies, we consider more practical aspects of the system, including non-i.i.d. signature matrices, low-resolution quantization, and random users activated by an unknown sparse rate. A new estimation algorithm, termed hybrid decentralized generalized expectation consistent (HyDeGEC), is then derived based on a hybrid network that applies scalar message passing for the prior inference and vector message passing for the likelihood inference. This new algorithm outperforms many state-of-the-art techniques in terms of robustness (to non-i.i.d. signatures), complexity (in computation per iteration), and/or estimation accuracy (of the channel and the activity rate). The state evolution of the algorithm is also analyzed, which, as validated by simulations, can capture precisely the algorithm’s per-iteration behavior in MSE. Summing up, the algorithm we propose here is practically effective, computationally efficient, and theoretically analyzable.

The reconstruction of sparse signal is an active area of research. Different from a typical i.i.d. assumption, this paper considers a non-independent prior of group structure. For this more practical setup, we propose EM-aided HyGEC, a new algorithm to address the stability issue and the hyper-parameter issue facing the other algorithms. The instability problem results from the ill condition of the transform matrix, while the unavailability of the hyper-parameters is a ground truth that their values are not known beforehand. The proposed algorithm is built on the paradigm of HyGAMP (proposed by Rangan et al.) but we replace its inner engine, the GAMP, by a matrix-insensitive alternative, the GEC, so that the first issue is solved. For the second issue, we take expectation-maximization as an outer loop, and together with the inner engine HyGEC, we learn the value of the hyper-parameters. Effectiveness of the proposed algorithm is also verified by means of numerical simulations.

This letter considers the problem of a joint estimation for channel fading and user activity in an uplink grant-free massive MIMO system equipped with low-precision analog-to-digital converters (ADCs). Different from existing works, the joint estimation is formalized as a non-overlapping group problem, where the components of compound channel involving user activity indicator and channel fading are independent with condition distribution rather than independent Bernoulli-Gaussian. Based on this new formulation, a new algorithm leveraging hybrid generalized approximate passing (HyGAMP) is then developed including GAMP part (channel estimation) and loopy belief propagation (LBP) part (user activity detection), where the strong correlation among elements in each row of the channel matrix can be decoupled in LBP part. By exchanging the information between the GAMP part and the LBP part, the proposed algorithm improves the performance of channel estimation and user activity detection as compared to earlier results. In addition, the simulation results verify that the proposed algorithm develops the performance of conventional methods dramatically.

This letter considers a joint user activity, channel and data estimation problem in an uplink grant-free massive MIMO systems with low-precision analog-to-digital converters (ADCs). This joint estimation is firstly formalized as a non-overlapping group sparse problem, in which the components of compound channel follow independent conditional distribution. To address this problem, a new algorithm consists of the celebrated bilinear generalized approximate message passing (BiG-AMP) and loop belief propagation (LBP) is then proposed, where the strong connection of compound channel can be decoupled in LBP part. By exchanging the information between BiG-AMP part and LBP part, the proposed algorithm improves the performance of channel estimation compared with HyGAMP based method, in which the estimated payload data of proposed algorithm are utilized to aid channel estimation and it leads to relatively few pilot symbols to achieve equivalent channel and data estimation performances. The simulation results confirm that our proposed joint estimation algorithm improves the performance of the existing works in terms of user activity, channel and data estimation.

Generalized approximate message passing (GAMP) is an efficient algorithm for the estimation of independent identically distributed random signals under generalized linear model. The sum-product GAMP has long been recognized as an approximate implementation of the sum-product loopy belief propagation. In this letter, we propose to view the message passing in a new perspective of expectation propagation (EP). Comparing with the previous methods that were based on Taylor expansions, the proposed EP method could unify the derivations for the real and the complex GAMP, with a difference only in the setup of Gaussian densities.