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MLE-based Device Activity Detection under Rician Fading for Massive Grant-free Access with Perfect and Imperfect Synchronization

Wang Liu, Ying Cui, Feng Yang, Lianghui Ding, Jun Sun

TL;DR

The paper addresses device activity detection in massive grant-free IoT access under Rician fading, incorporating LoS components and imperfect synchronization. It develops MLE-based formulations for both synchronous and three asynchronous scenarios, and proposes three algorithmic families: Prop-MLE-Syn (coordinate-descent for the synchronous case) and Prop-MLE-Small/Large (BCD-based asynchronous solvers with and without FFT/IFFT acceleration). The key contributions include analytical coordinate updates that generalize Rayleigh-based results, a systematic FFT/IFFT acceleration for large offset ranges, and comprehensive complexity analyses with strong empirical gains (up to ~50-65% error reductions and substantial speedups) over state-of-the-art methods. This work significantly enhances activity detection performance in IoT mMTC settings where LoS components and synchronization imperfections are prevalent, and provides practical, scalable algorithms for real-world deployment.

Abstract

Most existing studies on massive grant-free access, proposed to support massive machine-type communications (mMTC) for the Internet of things (IoT), assume Rayleigh fading and perfect synchronization for simplicity. However, in practice, line-of-sight (LoS) components generally exist, and time and frequency synchronization are usually imperfect. This paper systematically investigates maximum likelihood estimation (MLE)-based device activity detection under Rician fading for massive grant-free access with perfect and imperfect synchronization. We assume that the large-scale fading powers, Rician factors, and normalized LoS components can be estimated offline. We formulate device activity detection in the synchronous case and joint device activity and offset detection in three asynchronous cases (i.e., time, frequency, and time and frequency asynchronous cases) as MLE problems. In the synchronous case, we propose an iterative algorithm to obtain a stationary point of the MLE problem. In each asynchronous case, we propose two iterative algorithms with identical detection performance but different computational complexities. In particular, one is computationally efficient for small ranges of offsets, whereas the other one, relying on fast Fourier transform (FFT) and inverse FFT, is computationally efficient for large ranges of offsets. The proposed algorithms generalize the existing MLE-based methods for Rayleigh fading and perfect synchronization. Numerical results show that the proposed algorithm for the synchronous case can reduce the detection error probability by up to 50.4% at a 78.6% computation time increase, compared to the MLEbased state-of-the-art, and the proposed algorithms for the three asynchronous cases can reduce the detection error probabilities and computation times by up to 65.8% and 92.0%, respectively, compared to the MLE-based state-of-the-arts.

MLE-based Device Activity Detection under Rician Fading for Massive Grant-free Access with Perfect and Imperfect Synchronization

TL;DR

The paper addresses device activity detection in massive grant-free IoT access under Rician fading, incorporating LoS components and imperfect synchronization. It develops MLE-based formulations for both synchronous and three asynchronous scenarios, and proposes three algorithmic families: Prop-MLE-Syn (coordinate-descent for the synchronous case) and Prop-MLE-Small/Large (BCD-based asynchronous solvers with and without FFT/IFFT acceleration). The key contributions include analytical coordinate updates that generalize Rayleigh-based results, a systematic FFT/IFFT acceleration for large offset ranges, and comprehensive complexity analyses with strong empirical gains (up to ~50-65% error reductions and substantial speedups) over state-of-the-art methods. This work significantly enhances activity detection performance in IoT mMTC settings where LoS components and synchronization imperfections are prevalent, and provides practical, scalable algorithms for real-world deployment.

Abstract

Most existing studies on massive grant-free access, proposed to support massive machine-type communications (mMTC) for the Internet of things (IoT), assume Rayleigh fading and perfect synchronization for simplicity. However, in practice, line-of-sight (LoS) components generally exist, and time and frequency synchronization are usually imperfect. This paper systematically investigates maximum likelihood estimation (MLE)-based device activity detection under Rician fading for massive grant-free access with perfect and imperfect synchronization. We assume that the large-scale fading powers, Rician factors, and normalized LoS components can be estimated offline. We formulate device activity detection in the synchronous case and joint device activity and offset detection in three asynchronous cases (i.e., time, frequency, and time and frequency asynchronous cases) as MLE problems. In the synchronous case, we propose an iterative algorithm to obtain a stationary point of the MLE problem. In each asynchronous case, we propose two iterative algorithms with identical detection performance but different computational complexities. In particular, one is computationally efficient for small ranges of offsets, whereas the other one, relying on fast Fourier transform (FFT) and inverse FFT, is computationally efficient for large ranges of offsets. The proposed algorithms generalize the existing MLE-based methods for Rayleigh fading and perfect synchronization. Numerical results show that the proposed algorithm for the synchronous case can reduce the detection error probability by up to 50.4% at a 78.6% computation time increase, compared to the MLEbased state-of-the-art, and the proposed algorithms for the three asynchronous cases can reduce the detection error probabilities and computation times by up to 65.8% and 92.0%, respectively, compared to the MLE-based state-of-the-arts.
Paper Structure (17 sections, 8 theorems, 59 equations, 5 figures, 4 tables, 3 algorithms)

This paper contains 17 sections, 8 theorems, 59 equations, 5 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Contributions
  4. System Model
  5. Synchronous Case
  6. Asynchronous Cases
  7. MLE-based Device Activity Detection in Synchronous Case
  8. MLE Problem Formulation
  9. CD Algorithm
  10. MLE-based Device Activity Detection in Asynchronous Cases
  11. MLE Problem Formulation
  12. BCD Algorithms
  13. BCD Algorithm for Small Offset Ranges
  14. BCD Algorithm for Large Offset Ranges
  15. Comparisons of Algorithm \ref{['Alg:Ri_asyn_ts']} and Algorithm \ref{['Alg:Ri_asyn_IM']}
  16. ...and 2 more sections

Key Result

Theorem 1

For all $n \in \mathcal{N}$, the optimal solution of the problem in (Prob:cd_Ri_syn) is given by: where with $\alpha_{n }$, $\beta_{n }$, and, $\eta_{n }$ given by (alpha_syn), (beta_syn), and (eta_syn), respectively.

Figures (5)

  • Figure 1: Error probability versus $\kappa$, $L$, $M$, and $p$ in the synchronous case.
  • Figure 2: Error probability versus $\kappa$, $L$, $M$, and $p$ in the asynchronous cases.
  • Figure 3: Error probability versus $D$ and $\Omega$.
  • Figure 4: Computation time versus $D$ and $\Omega$.
  • Figure 5: Error probability and computation time versus $Q$.

Theorems & Definitions (10)

  • Theorem 1: Optimal Solution of Problem in (\ref{['Prob:cd_Ri_syn']})
  • Remark 1: Connection to Rayleigh Fading
  • Theorem 2: Convergence of Algorithm \ref{['Alg:Ri_syn']}
  • Theorem 3: Optimal Solution of Problem in (\ref{['Prob:bcd_ray']}) for Asynchronous Case-$i$
  • Remark 2: Connection to Rayleigh Fading
  • Lemma 1: Equivalent Forms of $\boldsymbol\alpha_{\textup{t},n}$, $\boldsymbol\beta_{\textup{t},n}$, and $\boldsymbol\eta_{\textup{t},n}$
  • Lemma 2: Equivalent Forms of $\boldsymbol\alpha_{\textup{f},n}$, $\boldsymbol\beta_{\textup{f},n}$, and $\boldsymbol\eta_{\textup{f},n}$
  • Lemma 3: Equivalent Forms of $\boldsymbol\alpha_{\textup{(t,f)},n}$, $\boldsymbol\beta_{\textup{(t,f)},n}$, and $\boldsymbol\eta_{\textup{(t,f)},n}$
  • Lemma 4: Computational Complexity Comparisons of Algorithm \ref{['Alg:Ri_asyn_ts']} and Algorithm \ref{['Alg:Ri_asyn_IM']} for Arbitrary Parameters
  • Lemma 5: Computational Complexity Comparisons of Algorithm \ref{['Alg:Ri_asyn_ts']} and Algorithm \ref{['Alg:Ri_asyn_IM']} for Large Parameters