# Fast MLE and MAPE-Based Device Activity Detection for Grant-Free Access via PSCA and PSCA-Net

arXiv: https://arxiv.org/abs/2503.15259 · HTML: https://mlsanity.com/paper/2503.15259/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)
- [Parallel Successive Convex Approximation for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1406.3665/) (2014)
- [Deep Neural Network Based Active User Detection for Grant-free NOMA Systems](https://mlsanity.com/paper/1912.11782/) (2019)
- [Jointly Sparse Signal Recovery and Support Recovery via Deep Learning with Applications in MIMO-based Grant-Free Random Access](https://mlsanity.com/paper/2008.01992/) (2020)
- [Algorithm Unrolling for Massive Access via Deep Neural Network with Theoretical Guarantee](https://mlsanity.com/paper/2106.10426/) (2021)
- [Joint Design of Measurement Matrix and Sparse Support Recovery Method via Deep Auto-encoder](https://mlsanity.com/paper/1910.04330/) (2019)
- [Faster Activity and Data Detection in Massive Random Access: A Multi-armed Bandit Approach](https://mlsanity.com/paper/2001.10237/) (2020)
- [Activity Detection for Massive Connectivity in Cell-free Networks with Unknown Large-scale Fading, Channel Statistics, Noise Variance, and Activity Probability: A Bayesian Approach](https://mlsanity.com/paper/2401.16775/) (2024)
- [Statistical Device Activity Detection for OFDM-based Massive Grant-Free Access](https://mlsanity.com/paper/2112.15354/) (2021)
- [Jointly Sparse Signal Recovery via Deep Auto-Encoder and Parallel Coordinate Descent Unrolling](https://mlsanity.com/paper/2002.02628/) (2020)
- [Jointly Sparse Support Recovery via Deep Auto-encoder with Applications in MIMO-based Grant-Free Random Access for mMTC](https://mlsanity.com/paper/2005.02389/) (2020)
- [An Efficient Active Set Algorithm for Covariance Based Joint Data and Activity Detection for Massive Random Access with Massive MIMO](https://mlsanity.com/paper/2102.03490/) (2021)
- [Accelerating Coordinate Descent via Active Set Selection for Device Activity Detection for Multi-Cell Massive Random Access](https://mlsanity.com/paper/2104.12984/) (2021)
- [ML and MAP Device Activity Detections for Grant-Free Massive Access in Multi-Cell Networks](https://mlsanity.com/paper/2106.10438/) (2021)
- [MLE-based Device Activity Detection under Rician Fading for Massive Grant-free Access with Perfect and Imperfect Synchronization](https://mlsanity.com/paper/2306.06734/) (2023)

## Abstract (arXiv)

Fast and accurate device activity detection is the critical challenge in grant-free access for supporting massive machine-type communications (mMTC) and ultra-reliable low-latency communications (URLLC) in 5G and beyond. The state-of-the-art methods have unsatisfactory error rates or computation times. To address these outstanding issues, we propose new maximum likelihood estimation (MLE) and maximum a posterior estimation (MAPE) based device activity detection methods for known and unknown pathloss that achieve superior error rate and computation time tradeoffs using optimization and deep learning techniques. Specifically, we investigate four non-convex optimization problems for MLE and MAPE in the two pathloss cases, with one MAPE problem being formulated for the first time. For each non-convex problem, we develop an innovative parallel iterative algorithm using the parallel successive convex approximation (PSCA) method. Each PSCA-based algorithm allows parallel computations, uses up to the objective function's second-order information, converges to the problem's stationary points, and has a low per-iteration computational complexity compared to the state-of-the-art algorithms. Then, for each PSCA-based iterative algorithm, we present a deep unrolling neural network implementation, called PSCA-Net, to further reduce the computation time. Each PSCA-Net elegantly marries the underlying PSCA-based algorithm's parallel computation mechanism with the parallelizable neural network architecture and effectively optimizes its step sizes based on vast data samples to speed up the convergence. Numerical results demonstrate that the proposed methods can significantly reduce the error rate and computation time compared to the state-of-the-art methods, revealing their significant values for grant-free access.