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Traffic-Aware Mean-Field Power Allocation for Ultra-Dense NB-IoT Networks

Sami Nadif, Essaid Sabir, Halima Elbiaze, Abdelkrim Haqiq

TL;DR

This work provides a consistent and distributed uplink power allocation solution under spatiotemporal fluctuation incorporating NB-IoT features, such as the number of repetitions and the data rate, as well as the IoT device’s energy budget, packet size, and traffic intensity, by leveraging stochastic geometry analysis and mean-field game (MFG) theory.

Abstract

The Narrowband Internet of Things (NB-IoT) is a cellular technology introduced by the Third Generation Partnership Project (3GPP) to provide connectivity to a large number of low-cost IoT devices with strict energy consumption limitations. However, in an ultra-dense small cell network employing NB-IoT technology, inter-cell interference can be a problem, raising serious concerns regarding the performance of NB-IoT, particularly in uplink transmission. Thus, a power allocation method must be established to analyze uplink performance, control and predict inter-cell interference, and avoid excessive energy waste during transmission. Unfortunately, standard power allocation techniques become inappropriate as their computational complexity grows in an ultra-dense environment. Furthermore, the performance of NB-IoT is strongly dependent on the traffic generated by IoT devices. In order to tackle these challenges, we provide a consistent and distributed uplink power allocation solution under spatiotemporal fluctuation incorporating NB-IoT features such as the number of repetitions and the data rate, as well as the IoT device's energy budget, packet size, and traffic intensity, by leveraging stochastic geometry analysis and Mean-Field Game (MFG) theory. The effectiveness of our approach is illustrated via extensive numerical analysis, and many insightful discussions are presented.

Traffic-Aware Mean-Field Power Allocation for Ultra-Dense NB-IoT Networks

TL;DR

This work provides a consistent and distributed uplink power allocation solution under spatiotemporal fluctuation incorporating NB-IoT features, such as the number of repetitions and the data rate, as well as the IoT device’s energy budget, packet size, and traffic intensity, by leveraging stochastic geometry analysis and mean-field game (MFG) theory.

Abstract

The Narrowband Internet of Things (NB-IoT) is a cellular technology introduced by the Third Generation Partnership Project (3GPP) to provide connectivity to a large number of low-cost IoT devices with strict energy consumption limitations. However, in an ultra-dense small cell network employing NB-IoT technology, inter-cell interference can be a problem, raising serious concerns regarding the performance of NB-IoT, particularly in uplink transmission. Thus, a power allocation method must be established to analyze uplink performance, control and predict inter-cell interference, and avoid excessive energy waste during transmission. Unfortunately, standard power allocation techniques become inappropriate as their computational complexity grows in an ultra-dense environment. Furthermore, the performance of NB-IoT is strongly dependent on the traffic generated by IoT devices. In order to tackle these challenges, we provide a consistent and distributed uplink power allocation solution under spatiotemporal fluctuation incorporating NB-IoT features such as the number of repetitions and the data rate, as well as the IoT device's energy budget, packet size, and traffic intensity, by leveraging stochastic geometry analysis and Mean-Field Game (MFG) theory. The effectiveness of our approach is illustrated via extensive numerical analysis, and many insightful discussions are presented.
Paper Structure (22 sections, 2 theorems, 52 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 22 sections, 2 theorems, 52 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contributions
  4. Preliminaries
  5. NB-IoT Deployment Modes
  6. Resource Unit
  7. Repetition Protocol
  8. Data Rate
  9. System Model
  10. Spatial Model
  11. Transmission Model
  12. IoT Traffic
  13. Problem Formulation
  14. Mean Field Game
  15. Mean Field Regime
  16. ...and 7 more sections

Key Result

Theorem 1

Let us consider $n$ independent renewal processes with independent and identically distributed inter-arrival times $S_k$, $k=1,\dots,n$. The expected inter-arrival time for each process is $\mathbb{E}[S_k]=1/\lambda_k$ where $\lambda_k$ is the arrival intensity. If the following assumptions hold: 1)

Figures (7)

  • Figure 1: Logarithmic Convergence Error of the iterative $\textbf{Algorithm 1}$ (power allocation, mean-field, Lagrange multiplier) as a function of number of iterations for two different SBS densities and for the same starting point $p_0(e,b) = P_{max}$ for all $(e,b) \in \Omega$
  • Figure 2: Optimal power allocation strategy as a function of energy and bit numbers for various MCS levels.
  • Figure 3: The mean-field interference as a function of SBS density for various arrival rates (MCS level = 8, $R_{safe} = 4$ m).
  • Figure 4: The mean-field interference as a function of MCS level for various arrival rates ($\beta_s = 30000$ SBS / $km^2$, $R_{safe} = 4$ m).
  • Figure 5: The average SINR as a function of the distance for various energy budgets, packet sizes, and MCS levels ($\beta_s = 30000$ SBS / $km^2$, $R_{safe} = 4$ m, $\lambda_u = 1$ packet / $15$ min).
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1: Palm–Khintchine theorem
  • Proposition 1