Source-linked AI summary
Coverage and Economy of Cellular Networks with Many Base Stations
Seunghyun Lee, Kaibin Huang
TL;DR
The paper asks how deploying many BSs changes cellular-network performance and cost. Using a stochastic-geometry downlink model, it analyzes outage probability and optimizes BS density under hardware, energy, and backhaul costs. Outage decreases inversely with BS density in the many-BS regime, while the optimal density scales sub-linearly with mobile density and depends inversely on cost factors.
Problem
Prior results did not quantify cellular-network performance in the limit of many BSs, despite gains from shorter transmission distances.
Method
The paper models BSs, mobiles, and switching centers with Poisson point processes and analyzes outage while optimizing a cost function covering hardware, energy, cables, and outage.
Results
Outage probability decreases inversely with increasing BS density, while the optimal BS density increases sub-linearly with mobile density and is larger when BS-related prices are lower.
Takeaways & Limitations
Many-BS deployment provides quantifiable outage gains, but the preferred density balances those gains against hardware, energy, and backhaul costs.
Abstract
from arXiv · showhide
The performance of a cellular network can be significantly improved by employing many base stations (BSs), which shortens transmission distances. However, there exist no known results on quantifying the performance gains from deploying many BSs. To address this issue, we adopt a stochastic-geometry model of the downlink cellular network and analyze the mobile outage probability. Specifically, given Poisson distributed BSs, the outage probability is shown to diminish inversely with the increasing ratio between the BS and mobile densities. Furthermore, we analyze the optimal tradeoff between the performance gain from increasing the BS density and the resultant network cost accounting for energy consumption, BS hardware and backhaul cables. The optimal BS density is proved to be proportional to the square root of the mobile density and the inverse of the square root of the cost factors considered.
I. INTRODUCTION
The paper addresses the unclear performance of cellular networks with many base stations using a tractable stochastic-geometry model. It quantifies outage gains from increasing BS density and formulates a cost-performance tradeoff.
- Reducing cell size with more BSs has produced significant throughput gains compared with physical-layer advances.
- Prior work left network performance in the limit of many BSs unclear.
- A homogeneous Poisson point-process model makes mobile-outage analysis tractable compared with simulation-based grid models.
- For fixed mobile density, outage probability diminishes inversely as BS density increases, with simulation validating the asymptotic result at practical densities.
- The paper optimizes BS density against hardware, cable, energy, and outage costs, obtaining square-root scaling with mobile density and inverse square-root scaling with cost factors.
II. NETWORK MODEL
The network model represents BSs, mobiles, and switching centers as independent Poisson point processes and assigns users and cables by nearest-neighbor rules. Outage is defined through the SIR of a typical active mobile.
- BSs, mobiles, and switching centers are independent PPPs with densities λb, λu, and λs, respectively.
- Mobiles connect to nearest BSs, while each BS connects by cable to its nearest switching center.
- Empty-cell BSs are silent; nonempty BSs serve one randomly selected mobile in each time slot.
- BS power consumption is modeled as Pb = Aµ + B, including transmit-power-dependent and offset components.
- Outage for a typical active mobile occurs when its SIR falls below threshold θ: Pout = Pr(SIR < θ).
A. Approximation of the Transmitting BS Process
The transmitting-BS process is approximated by thinning the BS PPP according to the empty-cell probability. As BS density grows relative to mobile density, empty cells become more common and the approximation is simulation-accurate asymptotically.
- The actual transmitting-BS process is not a PPP because each cell’s emptiness depends on the BS configuration.
- The empty-cell probability p is defined as the probability that a typical BS has no assigned mobile.
- The analysis obtains p using the average void probability of the mobile process over a typical Poisson-Voronoi cell.
- As λb/λu increases, p increases because denser BS deployment produces smaller cells.
- The transmitting BSs are approximated by a PPP with density (1 − p)λb, and the resulting analysis is simulation-accurate as λb/λu → ∞.
B. Mobile Outage Probability
The paper derives outage probability for a typical active mobile under the thinned transmitting-BS approximation. In the many-BS regime, outage decreases approximately linearly with BS density because interference remains stable while serving distances shrink.
- The outage-probability derivation uses the approximated transmitting-BS process and the serving-distance distribution.
- The analysis treats aggregate interference as a shot noise process.
- The many-BS result applies to a different regime from prior work, which assumes mobiles significantly outnumber BSs.
- In the many-BS regime, outage probability decreases approximately linearly with increasing λb.
- With λu fixed, transmitting-BS interference remains constant while reduced transmission distances increase received signal power.
IV. OPTIMIZATION OF THE BASE-STATION DENSITY
The paper optimizes BS density by balancing performance gains against hardware, energy, and backhaul-cable costs. The resulting density increases with outage penalty, mobile density, switching-center density, and lower per-BS aggregate prices.
- Cost model: The optimization minimizes a multi-objective cost combining outage penalty with BS hardware, energy consumption, and backhaul-cable costs.The cost function includes cable length, BS density, total power, and outage probability.
- Derivation: The optimal density is obtained by substituting the outage and power expressions into the cost function and minimizing it.The derivation uses the outage approximation and total BS power expression before optimization.
- Optimal density: The optimal BS density increases with the outage penalty and mobile density.The paper interprets this as favoring more BSs when outage is more costly or more mobiles are present.
- Optimal density: The optimal BS density increases with switching-center density because additional BSs require less cable cost.Switching centers are modeled through a homogeneous PPP, which enters the cable-cost tradeoff.
- Optimal density: The optimal BS density is larger when the average aggregate price for one BS is lower.This price aggregates the cost of operating and installing a BS in the optimization.
V. SIMULATION
The simulations compare analytical outage and optimal-density expressions with numerical or simulated values. They show convergence of the outage approximation and small, decreasing relative error for the derived optimal density as K increases.
- Outage probability: The outage probability computed from (5) converges with simulated values as BS density increases.The simulation also compares against the case where all BSs transmit, whose outage probability is insensitive to BS-density changes.
- Outage probability: The all-BS-transmit outage probability is insensitive to changes in BS density.This behavior is reported alongside the comparison between the analytical expression and simulations.
- Optimal density: The derived optimal BS density traces the exact numerical value within a constant gap of approximately 0.07.Figure 3 varies K while keeping λu = 0.02 fixed.
- Optimal density: The percentage error of the derived optimal density decreases as K increases and falls below 10% when K > 10.The absolute gap remains unchanged while the percentage error decreases.
- Optimal density: The derived optimal density is accurate when the outage penalty exceeds the price for operating each BS.This condition is stated as the interpretation of the simulation accuracy.
VI. CONCLUSION
The letter quantifies the gains from deploying many BSs and optimizes BS density against hardware, energy, and backhaul-cable costs.
- Outage probability decreases inversely as BS density increases.
- Optimal BS density grows sub-linearly with mobile density under the outage-probability metric.
- The optimal deployment accounts for BS hardware, energy consumption, and backhaul-cable costs.
- Larger BS density is more desirable when power, cable, and BS-hardware prices are lower.