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

Bowen Tan, Ying Cui

TL;DR

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.

Abstract

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.

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

TL;DR

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.

Abstract

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.

Paper Structure

This paper contains 29 sections, 11 theorems, 71 equations, 12 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model
  5. MLE and MAPE-Based Device Activity Detection for Known Pathloss
  6. MLE-Based Device Activity Detection for Known Pathloss
  7. MLE Problem for Known Pathloss
  8. PSCA-ML-K
  9. PSCA-ML-K-Net
  10. MAPE-Based Device Activity Detection for Known Pathloss
  11. MAPE Problem for Known Pathloss
  12. PSCA-MAP-K
  13. PSCA-MAP-K-Net
  14. MLE and MAPE-Based Device Activity Detection for Unknown Pathloss
  15. MLE-Based Device Activity Detection for Unknown Pathloss
  16. ...and 14 more sections

Key Result

Theorem 1

(i) $p^{\epsilon }_{\Upsilon_n}\left(\gamma_n\right) = p_{\Upsilon_n}\left(\gamma_n\right)$, for all $\gamma_n \in \{0\} \cup \left[g_{l,n},g_{u,n}\right]$. (ii) $p^{\epsilon }_{\Upsilon_n}\left(\gamma_n\right)$ is differentiable in $\left[0, g_{u,n}\right]$. (iii) $p^{\epsilon }_{\Upsilon_n}\left(

Figures (12)

  • Figure 1: Illustration of the system model.
  • Figure 2: Architectures of PSCA-ML-K-Net and PSCA-MAP-K-Net.
  • Figure 3: Architectures of PSCA-ML-UD-Net and PSCA-MAP-UR-Net.
  • Figure 4: Convergence at $N=1000, L=40, M=256$, and $P=23$dBm under the i.i.d. activity model.
  • Figure 5: Generalization ability w.r.t. $N$, $L$, and $P$ at $M=256$ for known $\mathbf{g}$ under the i.i.d. activity model.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Theorem 1: Properties of $p^{\epsilon }_{\Upsilon_n}\left(\gamma_n\right)$
  • Lemma 1: Optimal Solution of Problem \ref{['Prob_Surrogate_ML']}
  • Theorem 2: Convergence of PSCA-ML-K
  • Lemma 2: Optimal Solution of Problem \ref{['Prob_Surrogate_MAP']}
  • Theorem 3: Convergence of PSCA-MAP-K
  • Lemma 3: Optimal Solution of Problem \ref{['Prob_Surrogate_ML_U']}
  • Theorem 4: Convergence of PSCA-ML-UD
  • Lemma 4: Optimal Solution of Problem \ref{['Prob_Surrogate_MAP_U']}
  • Theorem 5: Convergence of PSCA-MAP-UR
  • Lemma 5
  • ...and 1 more