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Exploiting Device Heterogeneity in Grant-Free Random Access: A Data-Driven Approach

Alix Jeannerot, Malcolm Egan, Jean-Marie Gorce

TL;DR

This work tackles grant-free random access in large-scale wireless networks where device activity is heterogeneous and imperfectly estimated. It develops an importance-weighted stochastic gradient approach to optimize slot allocation under activity estimation errors, proving almost-sure convergence to a stationary point. The method demonstrates robustness across symmetric, asymmetric, and GAMP-based error models with substantial throughput gains over error-unaware baselines. The results support practical deployment by enabling reliable, high-throughput GFRA in IoT networks despite realistic activity estimation imperfections.

Abstract

Grant-free random access (GFRA) is now a popular protocol for large-scale wireless multiple access systems in order to reduce control signaling. Resource allocation in GFRA can be viewed as a form of frame slotted ALOHA, where a ubiquitous design assumption is device homogeneity. In particular, the probability that a device seeks to transmit data is common to all devices. Recently, there has been an interest in designing frame slotted ALOHA algorithms for networks with heterogeneous activity probabilities. These works have established that the throughput can be significantly improved over the standard uniform allocation. However, the algorithms for optimizing the probability a device accesses each slot require perfect knowledge of the active devices within each frame. In practice, this assumption is limiting as device identification algorithms in GFRA rarely provide activity estimates with zero errors. In this paper, we develop a new algorithm based on stochastic gradient descent for optimizing slot allocation probabilities in the presence of activity estimation errors. Our algorithm exploits importance weighted bias mitigation for stochastic gradient estimates, which is shown to provably converge to a stationary point of the throughput optimization problem. In moderate size systems, our simulations show that the performance of our algorithm depends on the type of error distribution. We study symmetric bit flipping, asymmetric bit flipping and errors resulting from a generalized approximate message passing (GAMP) algorithm. In these scenarios, we observe gains up to 40\%, 66\%, and 19\%, respectively.

Exploiting Device Heterogeneity in Grant-Free Random Access: A Data-Driven Approach

TL;DR

This work tackles grant-free random access in large-scale wireless networks where device activity is heterogeneous and imperfectly estimated. It develops an importance-weighted stochastic gradient approach to optimize slot allocation under activity estimation errors, proving almost-sure convergence to a stationary point. The method demonstrates robustness across symmetric, asymmetric, and GAMP-based error models with substantial throughput gains over error-unaware baselines. The results support practical deployment by enabling reliable, high-throughput GFRA in IoT networks despite realistic activity estimation imperfections.

Abstract

Grant-free random access (GFRA) is now a popular protocol for large-scale wireless multiple access systems in order to reduce control signaling. Resource allocation in GFRA can be viewed as a form of frame slotted ALOHA, where a ubiquitous design assumption is device homogeneity. In particular, the probability that a device seeks to transmit data is common to all devices. Recently, there has been an interest in designing frame slotted ALOHA algorithms for networks with heterogeneous activity probabilities. These works have established that the throughput can be significantly improved over the standard uniform allocation. However, the algorithms for optimizing the probability a device accesses each slot require perfect knowledge of the active devices within each frame. In practice, this assumption is limiting as device identification algorithms in GFRA rarely provide activity estimates with zero errors. In this paper, we develop a new algorithm based on stochastic gradient descent for optimizing slot allocation probabilities in the presence of activity estimation errors. Our algorithm exploits importance weighted bias mitigation for stochastic gradient estimates, which is shown to provably converge to a stationary point of the throughput optimization problem. In moderate size systems, our simulations show that the performance of our algorithm depends on the type of error distribution. We study symmetric bit flipping, asymmetric bit flipping and errors resulting from a generalized approximate message passing (GAMP) algorithm. In these scenarios, we observe gains up to 40\%, 66\%, and 19\%, respectively.
Paper Structure (25 sections, 1 theorem, 23 equations, 5 figures, 4 algorithms)

This paper contains 25 sections, 1 theorem, 23 equations, 5 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Main Contributions
  4. Organization of the Paper
  5. System Model
  6. Device Activity and Resource Selection
  7. Grant-Free Random Access Protocols and Device Identification
  8. Device Identification in the Preamble
  9. Device Identification in the Data
  10. Feedback of the Allocation Matrix $\mathbf{A}$
  11. Stochastic Resource Allocation Problem
  12. Objective
  13. Stochastic Optimization Problem
  14. Mitigating Errors in Activity Estimation
  15. Impact of Activity Estimation Error
  16. ...and 10 more sections

Key Result

Theorem 1

The iterates $\mathbf{A}^t$ of Alg. alg:SGA_bias_reduced converge almost surely as $t \rightarrow \infty$ to a stationary point provided that the step size sequence $\{\gamma^t\}$ satisfies and $w(\mathbf{x}) < \infty$ for all $\mathbf{x} \in \{0,1\}^N$.

Figures (5)

  • Figure 1: Expected throughput with user identification errors for a network of $3$ devices sharing two slots. Baseline, in blue, corresponds to $\epsilon=0$. Drawing samples $\mathbf{X}_t$ with probability $\epsilon$ from $\hat{\mathbf{p}}$ instead of $\mathbf{p}$ (in orange) can reduce the throughput by up to $35\%$.
  • Figure 2: Resulting throughput after 10000 frames for different values of $p_{\mathrm{flip}}$.
  • Figure 3: Trajectories of the different method presented in Fig. \ref{['fig:bsc']} with $p_\mathrm{flip}=0.35$.
  • Figure 4: Resulting throughput after 10000 frames for different values of $p_{miss}$.
  • Figure 5: Resulting throughput after 10000 frames for different values of SNR.

Theorems & Definitions (3)

  • Example 1
  • Theorem 1
  • proof