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Age of Information Analysis for NOMA-Assisted Grant-Free Transmissions with Randomly Arrived Packets

Yanshi Sun, Yanglin Ye, Caihong Kai, Zhiguo Ding, Bin Chen

TL;DR

This work tackles the timeliness of uplink status updates by analyzing AoI in a NOMA-assisted grant-free setting with randomly arriving packets. It develops an analytical framework to quantify the average AoI for two retransmission schemes (NOMA-NRT and NOMA-RT) under Bernoulli arrivals, K preconfigured SNR levels, and a fixed power budget, using combinatorial methods and Markov chain analysis. The results show that NOMA substantially reduces AoI compared with OMA, and retransmission improves AoI primarily when the update rate is low or the user density is high, with nuanced regime dependencies. Extensive simulations validate the analysis and provide design guidance on transmission probabilities, SNR-level choices, and system parameters for timeliness in dense IoT networks.

Abstract

This paper investigates the application of non-orthogonal multiple access (NOMA) to grant-free transmissions to reduce the age of information (AoI) in uplink status update systems, where multiple sources upload their {status updates} to {a common} receiver. Unlike existing studies which {adopted} the idealized generate-at-will (GAW) model, {i.e., a status} update data can be generated and transmitted at any time, this paper utilizes a more practical model {to characterize} the inherent randomness of the generation of the status updating data packets. A rigorous analytical framework is established to precisely evaluate the average AoI achieved by the NOMA-assisted grant-free schemes for both {the} cases with and without retransmission. The impact of the choice of the probability {of transmission} on the average AoI is investigated. Extensive simulation results are provided to validate the accuracy of the developed analysis. It is shown that NOMA-assisted schemes are more superior in reducing AoI{, compared} to orthogonal multiple access (OMA) based schemes. In addition, compared to schemes without retransmission, the AoI performance {of} the schemes with retransmission can {be improved} significantly when the status update generation rate is low or the user density is relatively high.

Age of Information Analysis for NOMA-Assisted Grant-Free Transmissions with Randomly Arrived Packets

TL;DR

This work tackles the timeliness of uplink status updates by analyzing AoI in a NOMA-assisted grant-free setting with randomly arriving packets. It develops an analytical framework to quantify the average AoI for two retransmission schemes (NOMA-NRT and NOMA-RT) under Bernoulli arrivals, K preconfigured SNR levels, and a fixed power budget, using combinatorial methods and Markov chain analysis. The results show that NOMA substantially reduces AoI compared with OMA, and retransmission improves AoI primarily when the update rate is low or the user density is high, with nuanced regime dependencies. Extensive simulations validate the analysis and provide design guidance on transmission probabilities, SNR-level choices, and system parameters for timeliness in dense IoT networks.

Abstract

This paper investigates the application of non-orthogonal multiple access (NOMA) to grant-free transmissions to reduce the age of information (AoI) in uplink status update systems, where multiple sources upload their {status updates} to {a common} receiver. Unlike existing studies which {adopted} the idealized generate-at-will (GAW) model, {i.e., a status} update data can be generated and transmitted at any time, this paper utilizes a more practical model {to characterize} the inherent randomness of the generation of the status updating data packets. A rigorous analytical framework is established to precisely evaluate the average AoI achieved by the NOMA-assisted grant-free schemes for both {the} cases with and without retransmission. The impact of the choice of the probability {of transmission} on the average AoI is investigated. Extensive simulation results are provided to validate the accuracy of the developed analysis. It is shown that NOMA-assisted schemes are more superior in reducing AoI{, compared} to orthogonal multiple access (OMA) based schemes. In addition, compared to schemes without retransmission, the AoI performance {of} the schemes with retransmission can {be improved} significantly when the status update generation rate is low or the user density is relatively high.
Paper Structure (20 sections, 5 theorems, 56 equations, 14 figures, 2 tables)

This paper contains 20 sections, 5 theorems, 56 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System model
  3. NOMA assisted grant-free transmission
  4. Retransmission strategies
  5. Without retransmission
  6. With retransmission
  7. Performance metric
  8. Analysis on AoI for NOMA-NRT and NOMA-RT
  9. AoI achieved by grant-free NOMA-NRT scheme
  10. The case with $x=1$, $1\leq i\leq M$, $i\neq x+1$
  11. The case with $2\leq x\leq \Gamma$, $1\leq i\leq M$, $i\neq x+1$
  12. AoI achieved by grant-free NOMA-RT scheme
  13. $i^*=x^*+1$, $x^*\ge0$
  14. $x^*=0$, $1\leq i^*\leq M$, $i^*\neq x^*+1$
  15. $x^*=1$, $1\leq i^*\leq M$, $i^*\neq x^*+1$
  16. ...and 5 more sections

Key Result

Lemma 1

In the considered grant-free NOMA-NRT scheme, the probability of the event that $U_1$ can complete a successful status update in any given time slot, denoted by $P_1$, can be expressed as follows: where $\beta_{(i, x)}$ can be expressed as shown in (beta), $\Gamma=\mathds{1}_{K}(i)i+(1-\mathds{1}_{K}(i))(K-1)$, and $\mathds{1}_{K}(i)$ is an indicator function so that $\mathds{1}_{K}(i)=1$ if $i\

Figures (14)

  • Figure 1: Illustration of the system model.
  • Figure 2: Illustration of the AoI of an status updating process.
  • Figure 3: Illustration the process of transferring the number of users with data in steady state. $M=5$.
  • Figure 4: Illustration of the state transition process from the end instant of the ($j-1$)-th successful transmission to the end instant of the $j$-th successful transmission. The expressions along side the arrow lines denote the corresponding durations spent by the state transitions.
  • Figure 5: Average AoI achieved by the grant-free NOMA-NRT and NOMA-RT schemes. $\lambda=0.5$, $P_{\text{TX}}=0.5$, $P=20$ dB and $q_k=1/K$.
  • ...and 9 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Lemma 2
  • Theorem 2