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Performance Guarantees of Cellular Networks with Hardcore Regulation and Scheduling

Ke Feng, François Baccelli, Catherine Rosenberg

TL;DR

This work investigates how hardcore spatial regulation of base-station locations, combined with base-station scheduling, influences downlink performance guarantees in cellular networks. Using spatial network calculus, it derives a tighter interference upper bound that accounts for the exclusion region created by hardcore regulation, and translates this into lower bounds on the normalized rate for Always Active and periodic scheduling, including reduced-power variants. A key concept is the critical hardcore distance $H_K^*$ that delineates when scheduling improves rate guarantees, with hexagonal deployments illustrating concrete thresholds and power-saving opportunities. The results offer design guidelines for deploying spatial regulations and scheduling to meet target performance while potentially reducing power consumption in dense cellular networks.

Abstract

Providing performance guarantees is one of the {critical} objectives of {recent and future} communication networks, toward which regulations, {i.e., constraints on key system parameters,} have played an indispensable role. This is the case for large wireless communication networks, where spatial regulations (e.g., constraints on intercell distance) have recently been shown, through a spatial network calculus, to be essential for establishing provable wireless link-level guarantees. In this work, we focus on performance guarantees for {the downlink of} cellular networks where we impose a hardcore (spatial) regulation on base station (BS) locations and evaluate {how BS scheduling (which controls which BSs can transmit at a given time) impacts performance}. Hardcore regulation is the simplest form of spatial regulation that enforces a minimal distance between any pair of transmitters in the network. Within this framework of spatial network calculus, we first provide an upper bound on the power of total interference for a spatially regulated cellular network, and then, identify the regimes where scheduling BSs yields {better} link-level rate guarantees compared to scenarios where base stations are always active. The hexagonal cellular network is analyzed as a special case. The results offer insights into what spatial regulations are needed, when to choose scheduling, and how to potentially reduce the network power consumption {to provide a certain target performance guarantee}.

Performance Guarantees of Cellular Networks with Hardcore Regulation and Scheduling

TL;DR

This work investigates how hardcore spatial regulation of base-station locations, combined with base-station scheduling, influences downlink performance guarantees in cellular networks. Using spatial network calculus, it derives a tighter interference upper bound that accounts for the exclusion region created by hardcore regulation, and translates this into lower bounds on the normalized rate for Always Active and periodic scheduling, including reduced-power variants. A key concept is the critical hardcore distance that delineates when scheduling improves rate guarantees, with hexagonal deployments illustrating concrete thresholds and power-saving opportunities. The results offer design guidelines for deploying spatial regulations and scheduling to meet target performance while potentially reducing power consumption in dense cellular networks.

Abstract

Providing performance guarantees is one of the {critical} objectives of {recent and future} communication networks, toward which regulations, {i.e., constraints on key system parameters,} have played an indispensable role. This is the case for large wireless communication networks, where spatial regulations (e.g., constraints on intercell distance) have recently been shown, through a spatial network calculus, to be essential for establishing provable wireless link-level guarantees. In this work, we focus on performance guarantees for {the downlink of} cellular networks where we impose a hardcore (spatial) regulation on base station (BS) locations and evaluate {how BS scheduling (which controls which BSs can transmit at a given time) impacts performance}. Hardcore regulation is the simplest form of spatial regulation that enforces a minimal distance between any pair of transmitters in the network. Within this framework of spatial network calculus, we first provide an upper bound on the power of total interference for a spatially regulated cellular network, and then, identify the regimes where scheduling BSs yields {better} link-level rate guarantees compared to scenarios where base stations are always active. The hexagonal cellular network is analyzed as a special case. The results offer insights into what spatial regulations are needed, when to choose scheduling, and how to potentially reduce the network power consumption {to provide a certain target performance guarantee}.
Paper Structure (16 sections, 6 theorems, 21 equations, 5 figures)

This paper contains 16 sections, 6 theorems, 21 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Spatial Regulations: Background and Extensions
  3. System Model
  4. System Model
  5. Scheduling Schemes with Maximum Transmit Power
  6. Always Active
  7. Periodic Scheduling
  8. Scheduling with Reduced Power
  9. Performance Guarantees of Cellular Networks
  10. Conditional Upper Bounds on Interference
  11. Scheduling Schemes with Maximum Transmit Power
  12. Always Active (AA)
  13. Periodic Scheduling
  14. Scheduling Schemes with Reduced Power
  15. Hexagonal Cellular Networks
  16. ...and 1 more sections

Key Result

Lemma 1

Let $\Phi$ be $(K,H_K)$-hardcore regulated. Then there exists a stationary marking such that $\forall i\in\{1,2,...,K\}$, $\{x\in\Phi\colon M(x)=i\}$ is strongly $(1,\rho_{H_K},\nu_{H_K})$-ball regulated; further, for all non-negative, bounded, and non-increasing functions $\ell\colon \mathbb{R}^{+} .

Figures (5)

  • Figure 1: Comparison on the new upper bound on the total interference in Lemma \ref{['lemma: conditional reg']} versus the previous bound in FengBaccelli2024spatial with path loss exponent $\alpha=2.5, 3, 4$, $P=1$, and $\ell(r)=\min\{1,r^{-\alpha}\}$.
  • Figure 2: For $K=3$, guaranteed normalized rates for scheduling and always active (AA) vs. $H_3$. $H_1=2$. $d=4/\sqrt{3}$. $\ell(r)=\min\{1,r^{-4}\}$.
  • Figure 3: For $K=4$, guaranteed normalized rates for scheduling and always active (AA) vs. $H_4$. $H_1=2$. $d=4/\sqrt{3}$. $\ell(r)=\min\{1,r^{-4}\}$.
  • Figure 4: Reduced power $P_K^*$ vs. hardcore distance $H_K$ as in Eq (\ref{['eq: P_critical']}). $P=1$. SNR = 0dB. $H_1=2$. $d=4/\sqrt{3}$. $\ell(r)=\min\{1,r^{-4}\}$.
  • Figure 5: Normalized rate guarantees for scheduling and always active (AA) for the hexagonal cellular structure vs. SNR. $a=4/\sqrt{3}, H_1=2$. $\ell(r)=\min\{1,r^{-4}\}$.

Theorems & Definitions (17)

  • Definition 1: Strong $(\sigma,\rho,\nu)$-Ball Regulation FengBaccelli2024spatial
  • Definition 2: $(K,H_K)$-Hardcore Regulation
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Corollary 1
  • proof
  • Example 1
  • Corollary 2
  • ...and 7 more