Toward 6G Sidelink Reliability: MAC PRR Modeling for NR Mode 2 SPS and ns-3 Validation

This paper presents an analytical MAC-layer model for 5G NR Sidelink Mode 2 that explicitly incorporates standardized Semi-Persistent Scheduling features to derive closed-form expressions for packet reception ratio, which are validated against ns-3 simulations to provide design insights for enhancing 6G sidelink reliability.

The Gist

Imagine a busy highway where cars (User Equipment, or UEs) need to talk to each other directly to avoid accidents, without asking a traffic cop (a cell tower) for permission every time they speak. This is the world of 5G and 6G Sidelink communication.

In this paper, the authors are trying to solve a very specific problem: How do we make sure these cars don't crash into each other when they try to speak at the same time?

Here is a breakdown of the paper using simple analogies.

1. The Setting: The "Self-Driving" Highway

In the old days, cars had to wait for a traffic light (the base station) to tell them when to go. But in Mode 2, cars are like self-driving vehicles in a remote area with no traffic lights. They have to decide for themselves: "Okay, I'm going to send a message now. Which lane (frequency) and which second (time slot) should I use?"

They use a system called SPS (Semi-Persistent Scheduling). Think of it like this:

• The Sensing: Before you pick a lane, you look around to see which lanes are already occupied by other cars.
• The Reservation: You pick a free lane and say, "I'm going to use this lane for the next 10 seconds."
• The Counter: You have a little countdown timer (the Reselection Counter). Every second, the timer goes down. When it hits zero, you have to look around again and pick a new lane.

2. The Problem: The "Double-Booking" Crash

The main issue the paper tackles is Collisions. A collision happens when two cars pick the exact same lane and time slot. When that happens, neither message gets through.

The authors realized that existing math models were too simple. They treated collisions like isolated accidents. But in reality, these collisions are more like traffic jams that last for a while.

They identified two main ways these "traffic jams" happen:

• Collision Event 1: The "Simultaneous Re-Entry"
  Imagine two cars, Car A and Car B, both finish their 10-second reservation at the exact same moment. They both look at the map, see the same empty lane, and both decide to grab it. Crash! They are now stuck fighting for that lane for the next several seconds.
• Collision Event 2: The "Stubborn Driver"
  Imagine Car A and Car B crashed in the last round. Car A's timer hits zero, and it decides to stick with the same lane it was using before (because the rules say it can keep the lane with some probability). Car B is still using that same lane because its timer hasn't hit zero yet. They are now stuck in a loop, crashing into each other repeatedly until one of them finally decides to switch lanes.

3. The Solution: A New "Traffic Law" Calculator

The authors built a new mathematical model (a calculator) to predict exactly how often these crashes happen.

• The "Resource Keeping" Knob ($p_k$): There is a setting that decides how likely a car is to keep its current lane vs. switching to a new one.

  • Analogy: If you set the knob to "Always Switch," cars are constantly looking for new lanes. This causes a lot of chaos (Event 1) because everyone is looking at the same map at the same time.
  • If you set the knob to "Always Stay," cars rarely switch. This reduces the chaos of switching, but if two cars do crash, they get stuck in that crash for a very long time (Event 2).
  • The Finding: The authors found a "Goldilocks" zone. You need a mix of switching and staying to minimize crashes.

• The "Duplicate Message" Trick ($N_{Se}$):
  To make sure a message gets through, you can send the same message twice (like shouting the same thing twice in a noisy room).

  • Good News: In a lightly crowded highway, sending duplicates works great. If one copy crashes, the other might get through.
  • Bad News: In a super crowded highway (Saturation), sending duplicates actually makes things worse! It's like everyone shouting twice; the noise level becomes so high that nothing gets heard. The math shows that once the road is too full, sending duplicates hurts reliability.

• The "Minimum Lane Requirement" ($X$):
  The rules say: "You must only pick a lane if at least 20% of the lanes are empty."

  • The authors tested if raising this requirement (e.g., "Wait until 50% of lanes are empty") would help.
  • The Surprise: It didn't help! In fact, it just made cars wait longer without actually reducing crashes. It's like telling drivers to only drive when the highway is half-empty; you just end up with a lot of cars sitting in the parking lot, but the ones on the road are still crashing.

4. The Proof: The Video Game Simulation

To prove their math was right, the authors didn't just do equations on a whiteboard. They built a video game simulation (using a tool called ns-3) that mimics a real 5G network.

• They created a virtual world with up to 200 cars.
• They let the cars drive and talk for 100 seconds.
• The Result: Their math predictions matched the video game results almost perfectly when the road wasn't too crowded. When the road got super crowded, the math started to drift a little (because real-world physics like signal interference start to matter more than just the "lane selection" rules).

The Big Takeaway

This paper gives engineers a manual for tuning 6G networks.

1. Don't be too stubborn: If cars stay on the same lane too long, they get stuck in crashes.
2. Don't be too jittery: If cars switch lanes too often, they bump into each other while looking for new spots.
3. Don't over-send: Sending duplicate messages is a great safety net, but only when the network isn't already full.
4. Keep the rules simple: Raising the minimum requirement for "empty lanes" doesn't actually make the network safer.

By understanding these "traffic laws," we can design 6G networks that are incredibly reliable, ensuring that critical messages (like "Brake!" or "Turn!") get through even in chaotic, infrastructure-less environments.

Technical Summary

Here is a detailed technical summary of the paper "Toward 6G Sidelink Reliability: MAC PRR Modeling for NR Mode 2 SPS and ns-3 Validation."

1. Problem Statement

The paper addresses the challenge of ensuring ultra-reliable communication in 5G New Radio (NR) Sidelink (SL) Mode 2, a decentralized, infrastructure-less communication mode critical for 6G applications like Vehicle-to-Everything (V2X) and industrial IoT.

• The Core Issue: NR SL Mode 2 relies on Sensing-based Semi-Persistent Scheduling (SPS) for channel access. While widely studied, existing analytical models often abstract or omit specific 3GPP-standardized NR features (e.g., resource keeping, asynchronous reselection timing, and duplicate transmissions).
• The Gap: Current models fail to explicitly capture the temporal evolution of MAC-layer collision events. Collisions in SPS are not isolated one-shot events; they can persist across multiple Resource Reservation Intervals (RRIs) due to "resource keeping" and asynchronous counter decrements. Without an explicit event-level model, it is difficult to analytically quantify the steady-state Packet Reception Ratio (PRR) as a function of SPS parameters.

2. Methodology

The authors propose a novel analytical MAC-layer model to derive closed-form expressions for collision probability and PRR, validated against high-fidelity simulations.

A. System Model & Assumptions

• Scenario: A fully connected network of static User Equipments (UEs) using periodic traffic.
• Protocol: NR SL Mode 2 SPS (Release 16/17 features).
• Assumptions: Perfect PHY layer (collisions are the only cause of failure, aside from Half-Duplex constraints); UEs are half-duplex.
• Key Mechanism: UEs sense the channel, exclude occupied Physical Resource Blocks (PRBs), and select resources. A Reselection Counter ($R_c$) is decremented every RRI. When $R_c=0$, the UE enters a "selection window" to either keep the current resource (with probability $p_k$) or reselect (with probability $1-p_k$).

B. Collision Event Decomposition

The paper formally defines two dominant collision mechanisms occurring in the selection window:

1. Collision Event 1 (Simultaneous Reselection): Occurs when the reference UE and one or more other UEs simultaneously enter their selection windows ($R_c=0$) and independently reselect the same available PRB. This leads to a sequence of consecutive collisions lasting $\min(R_{c,init}^{UE0}, R_{c,init}^{UE1})$ intervals.
2. Collision Event 2 (Persistent Collisions): Occurs when a UE that previously collided with the reference UE does not reselect (keeps the resource) while the reference UE enters its selection window. This includes sub-events based on the relative state of the reselection counters ($R_c$) of the colliding UEs.

C. Analytical Derivation

• State Diagram: A Markov-like state diagram is used to model the probability ($\pi_i$) of a UE having a specific $R_c$ value.
• Probability Formulation:
  • Derives the probability of $n$-fold collisions using binomial distributions based on the number of UEs ($N_{UE}$) and the probability of entering the selection window ($2\pi_0$).
  • Calculates the number of available PRBs ($N_a$) as a function of total PRBs, occupied PRBs, and collision probability.
  • Derives closed-form expressions for Total MAC Collision Probability ($P_{COL}$) and Packet Reception Ratio (PRR).
• Model Extensions:
  • Packet Duplication ($N_{Se}$): Extends the model to account for PDCP duplication (sending multiple copies of a packet).
  • Minimum Resource Availability ($X$): Analyzes the impact of the 3GPP constraint requiring a minimum proportion of available PRBs ($X \cdot N_r$) for reselection.

D. Validation

• Simulation Tool: The analytical results are validated using ns-3 simulations based on the 5G-LENA framework.
• Setup: Linear topology with 20 to 200 UEs, varying $p_k$ (resource keeping probability) and $N_{Se}$ (number of duplicates).
• Metrics: Comparison of $P_{COL}$, $P_{COL,1}$, $P_{COL,2}$, and PRR between the analytical model and simulation traces.

3. Key Contributions

1. First Complete Analytical Model for NR Mode 2: Provides the first analytical framework that explicitly models NR-specific SPS collision events (asynchronous reselection and resource keeping) to derive MAC PRR.
2. Closed-Form Expressions: Derives numerically solvable closed-form equations for steady-state collision probability and PRR, linking reliability directly to parameters like $p_k$, $N_{UE}$, and $N_{Se}$.
3. Insight into NR Features: Quantifies the impact of under-explored features:
   • Resource Keeping ($p_k$): Shows how increasing $p_k$ reduces new collisions (Event 1) but increases persistent collisions (Event 2).
   • Packet Duplication ($N_{Se}$): Analyzes the trade-off between redundancy and increased channel contention.
   • Minimum Availability ($X$): Evaluates the constraint on available PRB selection.
4. Validation & Saturation Boundary: Identifies the under-saturated operating region where the pure MAC model is accurate. It demonstrates that the model deviates in saturated conditions due to PHY-layer effects (e.g., RSRP thresholding behavior in dense networks).

4. Key Results

• Collision Dynamics:
  • $P_{COL,1}$ (Simultaneous reselection) decreases as the resource keeping probability ($p_k$) increases because UEs reselect less frequently.
  • $P_{COL,2}$ (Persistent collisions) increases with $p_k$ because UEs are more likely to stick to a colliding resource.
  • The total collision probability ($P_{COL}$) generally increases with $p_k$ because the reduction in Event 1 is outweighed by the increase in Event 2.
• Packet Duplication ($N_{Se}$):
  • In under-saturated conditions ($N_{UE} \le 80$), increasing $N_{Se}$ (e.g., from 1 to 2) significantly improves PRR.
  • In saturated conditions ($N_{UE} \ge 100$), increasing $N_{Se}$ degrades PRR because the additional traffic causes excessive collisions, negating the diversity gain.
• Minimum Availability ($X$):
  • Increasing the minimum proportion of available PRBs ($X$) from 0.2 to 0.5 does not improve PRR. In fact, forcing UEs to include occupied PRBs in their selection pool (when $N_a < X \cdot N_r$) can increase collision probability.
• Model Accuracy:
  • The analytical model matches ns-3 simulation results closely in under-saturated regimes.
  • Deviations occur in saturated regimes ($N_{UE} \approx N_r$) because the model assumes a perfect PHY layer, whereas in reality, dense networks cause RSRP measurements to cluster, altering the actual number of available resources in ways the MAC-only model cannot predict.

5. Significance

• Design Guidance for 6G: The paper provides a mechanistic understanding of how SPS parameters shape reliability, offering a tool for network engineers to tune parameters (like $p_k$) for specific 6G reliability targets without relying solely on time-consuming simulations.
• Parameter Optimization: It suggests that for safety-critical messages, the minimum resource availability parameter ($X$) should be kept at its lowest allowable value (0.2) rather than increased, as higher values offer no benefit and may hurt performance.
• Operational Limits: It clearly defines the boundary between under-saturated and saturated operation, warning that pure MAC analysis is insufficient for dense, saturated networks where PHY-layer effects dominate.
• Foundation for Future Work: The model serves as a baseline for future research incorporating PHY-layer imperfections and extending the analysis to LTE Mode 4 or more complex mobility scenarios.