[Paper Review] Analysis of Blocking in mmWave Cellular Systems: Application to Relay Positioning

Cristian García Ruiz, Antonio Pascual‐Iserte+1 more|arXiv (Cornell University)|Feb 5, 2020

Millimeter-Wave Propagation and Modeling30 references29 citations

TL;DR

This paper develops a statistical framework using stochastic geometry and random shape theory to model correlated blockages across multiple mmWave links, demonstrating that independence assumptions significantly underestimate blockage probability. It applies this model to optimize relay positioning in mmWave cellular networks, showing that both blockage correlation and link budget constraints critically impact optimal relay placement for minimizing communication failure probability.

ABSTRACT

Within the framework of 5G, blockage effects occurring in the mmWave band are critical. Previous works describe the effects of blockages in isolated and multiple links for simple blocking objects, modeled with mathematical tools such as stochastic geometry and random shape theory. Our study uses these tools to characterize a scenario with $N$ links, including the possible correlation among them in terms of blocking for several models of blocking objects. We include numerical evaluations highlighting that assuming independence among the links' blocking elements is a too-brief simplification and does not accurately describe the real scenario. This paper also applies the formulation developed for the case of $N$ links to optimize the relay positioning in mmWave cells for coverage enhancement, that is, to minimize the communication failure probability. We also show that both link budget and blockages affect the optimum positioning of the relays as they are both essential for successful transmission.

Motivation & Objective

• To model correlated blockage effects across N mmWave links using stochastic geometry and random shape theory.
• To challenge the common assumption of independent blockages across links, showing it leads to overly optimistic failure probability estimates.
• To apply the derived blockage model to optimize relay positioning in mmWave cellular systems for coverage enhancement.
• To jointly consider blockage correlation and link budget constraints in evaluating relay deployment performance.

Proposed method

• Uses a 3D rectangular blocking object model with random size, orientation, and height to represent urban buildings.
• Applies Poisson point process (PPP) to model the spatial distribution of blocking elements.
• Derives the joint probability of blockage across N links by accounting for statistical dependence through geometric probability and random shape theory.
• Incorporates link budget constraints (transmit power, antenna gain, receiver sensitivity) to compute effective path loss limits.
• Uses Monte Carlo simulations to validate analytical expressions and evaluate failure probability under various relay configurations.
• Optimizes relay position by minimizing the average communication failure probability across user locations.

Experimental results

Research questions

• RQ1 How does correlation between blockages on multiple mmWave links affect the overall communication failure probability compared to independent blockage assumptions?
• RQ2 What is the optimal placement of relays in an mmWave cellular cell to minimize the average failure probability due to blockage and path loss?
• RQ3 How do link budget constraints (transmit power, sensitivity) interact with blockage effects in determining the true failure probability?
• RQ4 To what extent does exploiting spatial diversity in blockage patterns improve system reliability?
• RQ5 How do blocking object dimensions and orientations influence the correlation structure of blockages across links?

Key findings

• Assuming independent blockages leads to a significant underestimation of failure probability—correlation increases blockage probability, especially when links are closely aligned.
• The optimal relay position is not at the cell center (e.g., 150 m from BS) but closer to the cell edge, due to reduced path loss and better spatial diversity in blockage patterns.
• Including link budget constraints increases the average communication failure probability by over 5% compared to blockage-only analysis.
• The minimum failure probability occurs at a relay distance r ≈ 120 m from the BS when sensitivity and power limits are considered, compared to r ≈ 150 m without them.
• Blockage correlation is most pronounced when links are aligned (e.g., φ = 0°), where a blockage on one link implies a high likelihood of blockage on the other.
• The visual LOS probability (based on line-of-sight geometry) is a highly accurate approximation of the actual LOS probability (error <1% for f > 20 GHz), justifying its use in the analysis.