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PDCCH Scheduling via Maximum Independent Set

Lorenzo Maggi, Alvaro Valcarce Rial, Aloïs Herzog, Suresh Kalyanasundaram, Rakshak Agrawal

TL;DR

The paper addresses the PDCCH candidate selection problem in 5G, casting it as a Maximum Weighted Independent Set (MWIS) on an incompatibility graph G=(C,E,W) to maximize non-overlapping, weighted candidate usage with at most one UL/DL candidate per UE. It analyzes four approaches—Greedy with Weight-to-Degree Ratio (WDR), Feige-Reichmann (FR), an exact recursion, and Optimal-then-Greedy (OtG)—to cope with the NP-hardness and latency constraints. Numerical results across 100 scenarios show FR achieves the highest scheduling and throughput, while WDR-Greedy nearly matches FR with a much lower complexity, and W-Greedy underperforms; OtG offers a fairness-leaning compromise. The findings advocate WDR-Greedy as a practical, efficient method for 5G NR schedulers to alleviate UE blind decoding burdens while maintaining high resource utilization.

Abstract

In 5G, the Physical Downlink Control CHannel (PDCCH) carries crucial information enabling the User Equipment (UE) to connect in UL and DL. UEs are unaware of the frequency location at which PDCCH is encoded, hence they need to perform blind decoding over a limited set of possible candidates. We address the problem faced by the gNodeB of selecting PDCCH candidates for each UE to optimize data transmission. We formulate it as a Maximum Weighted Independent Set (MWIS) problem, that is known to be an NP-hard problem and cannot even be approximated. A solution method called Weight-to-Degree Ratio (WDR) Greedy emerges as a strong contender for practical implementations due to its favorable performance-to-complexity trade-off and theoretical performance guarantees.

PDCCH Scheduling via Maximum Independent Set

TL;DR

The paper addresses the PDCCH candidate selection problem in 5G, casting it as a Maximum Weighted Independent Set (MWIS) on an incompatibility graph G=(C,E,W) to maximize non-overlapping, weighted candidate usage with at most one UL/DL candidate per UE. It analyzes four approaches—Greedy with Weight-to-Degree Ratio (WDR), Feige-Reichmann (FR), an exact recursion, and Optimal-then-Greedy (OtG)—to cope with the NP-hardness and latency constraints. Numerical results across 100 scenarios show FR achieves the highest scheduling and throughput, while WDR-Greedy nearly matches FR with a much lower complexity, and W-Greedy underperforms; OtG offers a fairness-leaning compromise. The findings advocate WDR-Greedy as a practical, efficient method for 5G NR schedulers to alleviate UE blind decoding burdens while maintaining high resource utilization.

Abstract

In 5G, the Physical Downlink Control CHannel (PDCCH) carries crucial information enabling the User Equipment (UE) to connect in UL and DL. UEs are unaware of the frequency location at which PDCCH is encoded, hence they need to perform blind decoding over a limited set of possible candidates. We address the problem faced by the gNodeB of selecting PDCCH candidates for each UE to optimize data transmission. We formulate it as a Maximum Weighted Independent Set (MWIS) problem, that is known to be an NP-hard problem and cannot even be approximated. A solution method called Weight-to-Degree Ratio (WDR) Greedy emerges as a strong contender for practical implementations due to its favorable performance-to-complexity trade-off and theoretical performance guarantees.
Paper Structure (9 sections, 5 equations, 6 figures, 1 table, 4 algorithms)

This paper contains 9 sections, 5 equations, 6 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Algorithms for PDCCH scheduling
  4. Greedy algorithm
  5. Feige-Reichmann (FR) algorithm
  6. Exact solution via recursion
  7. Optimal-then-Greedy (OtG) heuristic balamurali2010optimal
  8. Numerical evaluations
  9. Conclusions

Figures (6)

  • Figure 1: Example of interleaved CCE-to-REG mapping in a CORESET, where CORESET spans 2 OFDM symbol times.
  • Figure 2: Incompatibility graph $G$ and an independent set for a given Search Spaces (SS), considering for simplicity exclusively DL or UL. There is no edge between any pair of vertices in the independent set. Equivalently, only non-overlapping candidates are chosen, and at most one per UE.
  • Figure 3: Greedy algorithm
  • Figure 4: Optimal MWIS for forests
  • Figure 5: Feige-Reichmann (FR) algorithm feige2015recoverable
  • ...and 1 more figures