Deep-Unfolded Massive Grant-Free Transmission in Cell-Free Wireless Communication Systems

TL;DR

The paper tackles joint active user detection, channel estimation, and data detection (JACD) for massive grant-free transmission in cell-free wireless networks by formulating a sparsity-exploiting optimization problem solvable via forward-backward splitting. It introduces two solution paths: box-constrained FBS with a regularizer and PME-based JACD, together with soft-output AUD, complexity-reducing approximations, and a deep unfolding framework that learns hyper-parameters, yielding DU-ABC and DU-POEM. The authors demonstrate that the box-constrained FBS approach achieves top performance at high iteration counts, while the deep-unfolded variants deliver excellent AUD and DD with far fewer iterations, offering favorable trade-offs between accuracy and complexity. The work shows significant improvements in AUD, DD, and (to a lesser extent) CE, highlighting its potential for scalable JACD in dense cell-free mMTC systems and its applicability to real-time network processing. Overall, the framework provides a principled, trainable, low-complexity path to reliable grant-free operation in large-scale distributed antenna systems.

Abstract

Grant-free transmission and cell-free communication are vital in improving coverage and quality-of-service for massive machine-type communication. This paper proposes a novel framework of joint active user detection, channel estimation, and data detection (JACD) for massive grant-free transmission in cell-free wireless communication systems. We formulate JACD as an optimization problem and solve it approximately using forward-backward splitting. To deal with the discrete symbol constraint, we relax the discrete constellation to its convex hull and propose two approaches that promote solutions from the constellation set. To reduce complexity, we replace costly computations with approximate shrinkage operations and approximate posterior mean estimator computations. To improve active user detection (AUD) performance, we introduce a soft-output AUD module that considers both the data estimates and channel conditions. To jointly optimize all algorithm hyper-parameters and to improve JACD performance, we further deploy deep unfolding together with a momentum strategy, resulting in two algorithms called DU-ABC and DU-POEM. Finally, we demonstrate the efficacy of the proposed JACD algorithms via extensive system simulations.

Figures (7)

• Figure 1: Illustration of mMTC in a cell-free wireless communication system.
• Figure 2: Illustration of the signal matrix $\mathbf{X}$, where only 10 out of 50 UEs are active. Active UEs transmit unique pilots of length $R_{\text{P}} = 20$ and data symbols of length $R_{\text{D}} = 40$, represented by dark-colored squares. Inactive UEs transmit no signals; however, their unique pilots, which are known to the BS and represented by light-colored squares, can be used to improve JACD performance.
• Figure 3: Illustration of a channel matrix $\mathbf{H}$ for $10$ APs with $4$ antennas each and $50$ UEs, where $10$ UEs are active. Darker colors indicate larger absolute values; the boxed columns correspond to the active UEs (cf. Fig. \ref{['X']}).
• Figure 4: Architecture details of the DU-ABC and DU-POEM algorithms for JACD, differing only in the backward step.
• Figure 5: Diagrams of the coefficient $C_{\text{PME}}(\hat{x},\mathcal{S},\alpha,N_{\text{e}})$ with $\mathcal{S}=\{\pm \sqrt{0.5} \pm j\sqrt{0.5}\}$, $\alpha=0.02$, and $N_e=0.12$ (on the left) and its approximation $C_{\text{APME}}(\hat{x},\rho,\nu)$ with $\rho=3.49$ and $\nu=2.46$ (on the right).