Analysis of Blocking in mmWave Cellular Systems: Application to Relay Positioning

TL;DR

This work addresses the critical issue of blockage in mmWave cellular systems by developing a generalized stochastic-geometric framework for $N$ correlated links, using random shape theory with rectangles of height to capture realistic urban blockers. The authors derive blockage probabilities via $\mathbb{E}[K_{\mathcal{A}}]$ and extend to multi-link scenarios, highlighting how correlation among blockages differs from independent-link assumptions. They then apply the framework to relay-based deployments, formulating an average-coverage objective that accounts for power, sensitivity, and blockage randomness, and show how optimal relay placement depends on height and link-budget constraints. The results demonstrate that blockage correlation materially affects performance and that joint consideration of blocking, path loss, and receiver sensitivity yields practical deployment guidance for mmWave relays. The approach provides a tractable path to evaluate and optimize cell coverage in realistic mmWave environments and can guide generalized relay-placement strategies in next-generation networks.

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.

Figures (15)

• Figure 1: Single-link with one transmitter and one receiver.
• Figure 2: Parallelogram $S_{l\theta}$ corresponding to the line segments model.
• Figure 3: Polygon $S_{lw\theta}$ corresponding to the rectangle model.
• Figure 4: Height effect on the line segments based model.
• Figure 5: Front view (above) and top view (below) of the blocking region $S_{lh\theta}$ (parallelogram) corresponding to the line segments with height model. The figure shows how the size of the parallelogram $S_{lh\theta}$ becomes smaller due to the height of the blocking elements.