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Sensing Models and Its Impact on Network Coverage in Wireless Sensor Network

Ashraf Hossain, S. Chakrabarti, P. K. Biswas

arXiv:0812.2409v1cs.ITmath.IT

TL;DR

The paper examines how sensing models affect wireless-sensor-network coverage and compares regular with random placement. It presents analyses for Boolean, shadow-fading, and Elfes sensing, and reports that regular placement uses fewer nodes than random placement for the stated coverage fraction.

  • Problem

    Coverage depends on the nodes’ sensing models, so the paper examines how different sensing models affect how well a WSN monitors an area.

    Source: §I · p. 1

  • Method

    The paper analyzes Boolean, shadow-fading, and Elfes sensing models and compares coverage under regular and random node placement.

    Source: §I · p. 1, §II · p. 2, §IV · p. 3

  • Results

    For 90.69% coverage, regular placement requires 363 nodes while random placement requires 949 nodes.

    Source: §V · p. 5

  • Takeaways & Limitations

    Regular placement uses fewer nodes for the stated coverage, but placing nodes at specified positions may be infeasible in some settings.

    Source: §V · p. 5, §VI · p. 5

Abstract

from arXiv · show

Network coverage of wireless sensor network (WSN) means how well an area of interest is being monitored by the deployed network. It depends mainly on sensing model of nodes. In this paper, we present three types of sensing models viz. Boolean sensing model, shadow-fading sensing model and Elfes sensing model. We investigate the impact of sensing models on network coverage. We also investigate network coverage based on Poisson node distribution. A comparative study between regular and random node placement has also been presented in this paper. This study will be useful for coverage analysis of WSN.

I. INTRODUCTION

Network coverage measures how well a WSN monitors an area, with sensing range and boundary effects shaping what nodes can observe. The paper compares sensing models and node-placement strategies to examine their impact on coverage.

I. INTRODUCTION

  • A node near the area boundary covers less of the area of interest than one in its central zone because part of its sensing area falls outside the area.This is the boundary or border effect.Source: §I · p. 1
  • Earlier coverage studies,, considered only the Boolean sensing model, while later work examined shadow fading and Elfes sensing.The paper positions its comparison as extending coverage analysis across deterministic and probabilistic sensing models.Source: §I · p. 1
  • The paper investigates how sensing models affect network coverage and compares regular with random node placement.Its stated scope includes deterministic and probabilistic sensing models.Source: §I · p. 1

II. SYSTEM MODEL AND SENSING MODELS

The paper assumes individual event detection and presents Boolean, shadow-fading, and Elfes sensing models. These models differ in whether detection is deterministic or probabilistic and in how environmental conditions and sensor properties enter detection.

II. SYSTEM MODEL AND SENSING MODELS

  • Nodes are assumed uniformly distributed over area A with homogeneous density ρ = N/A.The detection setup assumes each sensor independently detects an event.Source: §II · pp. 1–2
  • Boolean sensing treats an event within a node’s sensing range as detected and ignores environmental conditions and emitted-signal strength.The sensing area is described as a circle whose radius equals the node’s sensing radius.Source: §II · p. 2
  • Shadow-fading sensing accounts for environmental factors and nonuniform directional sensing using a log-normal shadowing path-loss model.Its parameters include path-loss exponent n, sensing radius without fading r_s, and fading parameter σ.Source: §II · p. 2
  • The Elfes model gives detection probability as a function of distance, with R1 marking the onset of uncertainty and λ and γ set according to sensor properties.The paper states that the model becomes Boolean when R1 = Rmax and gives an approximation for R1 = 0 and γ = 1.Source: §II · p. 2

III. NETWORK COVERAGE

Network coverage is the fraction of the area of interest covered by the network. The section frames coverage as dependent on sensing model, node count, and placement strategy.

III. NETWORK COVERAGE

  • Network coverage is the ratio of covered area to the area of interest.Source: §III · p. 2
  • Coverage depends on the sensing model, the number of nodes, and the node-placement strategy.Source: §III · p. 2
  • The section examines how the sensing model affects network coverage in a WSN.Source: §III · p. 2

A. Network coverage for Boolean sensing model

For random placement, the Boolean-model coverage fraction is derived from the probability that an event is detected by at least one node. The derivation neglects boundary effects.

A. Network coverage for Boolean sensing model

B. Network coverage for Elfes sensing model

The section develops a probabilistic coverage expression and states that coverage depends on the sensing model. Equation (6) is presented as the formula for probabilistic sensing, whose expression is more complex than the Boolean-model expression.

B. Network coverage for Elfes sensing model

  • Equation (6) provides the coverage formula for probabilistic sensing, whose expression is more complex than the Boolean-model formula.The section says the Boolean-model expression is simple, while the probabilistic-model expression is somewhat more complex.Source: B. Network coverage for Elfes sensing… · p. 3
  • The derivation considers the probability of an event remaining undetected across annular rings around the event location.It describes a sensor at distance x and an annular ring of thickness dx, then uses integration for the Poisson case.Source: B. Network coverage for Elfes sensing… · pp. 2–3
  • For Poisson node distribution, the coverage expression is derived as a closed form and identified as the same as equation (6).The text connects the Poisson derivation to the coverage fraction obtained from equation (6).Source: B. Network coverage for Elfes sensing… · p. 3

IV. NODE PLACEMENT AND COVERAGE ANALYSIS

The section compares regular and random placement for network coverage and analyzes regular placement using one node per regular hexagonal cell. Under the stated typical parameters, maximum coverage is 90.69% at r = rsmax, with an estimated 363 cells.

IV. NODE PLACEMENT AND COVERAGE ANALYSIS

  • The section compares regular and random placement in terms of network coverage, within trade-offs in node count, deployment cost, time, and placement feasibility.The cited figure depicts the scheme for regular node placement.Source: §IV · p. 3, Figure 3 · p. 4
  • Regular placement divides the area into hexagonal cells, each with one node at its center and sensing radius from 0 to rsmax.The coverage fraction is approximated for R >> rsmax.Source: §IV · p. 4, Figure 3 · p. 4
  • 90.69% is the maximum coverage fraction, attained when r = rsmax.The regular-placement analysis uses variable sensing radius up to rsmax.Source: §IV · p. 4
  • 363 hexagonal cells are estimated for R = 1000 m, rsmax = 50 m, and fa = 90.69%.The required node count for regular placement equals the number of hexagonal cells.Source: §IV · p. 4

V. RESULTS AND DISCUSSIONS

Coverage depends on the sensing model: Boolean sensing gives the best coverage, while probabilistic models show degradation. Coverage also rises with sensing radius, and regular placement reaches a stated coverage level with fewer nodes than random placement.

V. RESULTS AND DISCUSSIONS

  • Boolean sensing achieves the best coverage, while higher Elfes λ requires more nodes for a given coverage and shadow fading degrades coverage.The comparison uses a 1000 m-radius area and maximum sensing radius of 50 m, with the figure showing the model and parameter settings.Source: §V · p. 4, Figure 4 · p. 4
  • Coverage fraction increases with sensing radius, with less variation at smaller normalized sensing radii.Fig. 5 compares random placements using different node counts with regular placement.Source: §V · p. 4, Figure 5 · p. 5
  • 90.69% coverage is achieved with 363 nodes in regular placement, compared with 949 nodes in random placement.Regular placement reaches 90.69% at normalized sensing ratio 1; the study notes that placing nodes at specified positions may be infeasible in some settings.Source: §V · p. 5, Figure 5 · p. 5

VI. CONCLUSION

The conclusion addresses the trade-off between node count and deployment strategy and reports analytical coverage results for sensing-model impacts and Poisson node distribution.

VI. CONCLUSION

  • Regular placement uses fewer nodes than random placement to cover an area of interest, framing a trade-off between node count and deployment strategy.The results also identify specified node positions as a practical concern for regular placement.Source: §VI · p. 5
  • The paper provides analytical results on how sensing models affect network coverage.The conclusion also reports investigation of coverage based on Poisson node distribution.Source: §VI · p. 5
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