[Paper Review] A New Capacity Scaling Law in Ultra-Dense Networks.

Ming Ding, David López‐Pérez+1 more|arXiv (Cornell University)|Apr 3, 2017

Advanced MIMO Systems Optimization9 references13 citations

TL;DR

This paper identifies a fundamental limit to spatial spectrum reuse (SSR) in ultra-dense networks (UDNs) due to bounded signal and interference powers under realistic conditions—non-zero base station-to-user equipment (BS-UE) antenna height differences and finite UE density. It proposes a constant capacity scaling law and demonstrates that an optimal SSR density exists, beyond which activating all small cells degrades network capacity.

ABSTRACT

The aggressive spatial spectrum reuse (SSR) by network densification using smaller cells has successfully driven the wireless communication industry onward in the past decades. In our future journey toward ultra-dense networks (UDNs), a fundamental question needs to be answered. Is there a limit to SSR? In other words, when we deploy thousands or millions of small cell base stations (BSs) per square kilometer, is activating all BSs on the same time/frequency resource the best strategy? In this paper, we present theoretical analyses to answer such question. In particular, we find that both the signal and interference powers become bounded in practical UDNs with a non-zero BS-to-UE antenna height difference and a finite UE density, which leads to a constant capacity scaling law. As a result, there exists an optimal SSR density that can maximize the network capacity. Hence, the limit to SSR should be considered in the operation of future UDNs.

Motivation & Objective

• To investigate whether there is a fundamental limit to spatial spectrum reuse (SSR) in ultra-dense networks (UDNs) as base station density increases.
• To analyze the impact of realistic propagation conditions—specifically non-zero BS-to-UE antenna height differences and finite user equipment (UE) density—on network capacity scaling.
• To determine whether activating all base stations simultaneously on the same time/frequency resources remains optimal at extreme densities.
• To derive a theoretical capacity scaling law for UDNs under practical constraints and identify the existence of an optimal SSR density.

Proposed method

• Theoretical analysis of signal and interference power behavior in UDNs under realistic propagation conditions, including non-zero BS-UE antenna height differences.
• Modeling of path loss and shadowing effects in ultra-dense deployments with finite UE distribution and non-ideal propagation geometry.
• Derivation of the asymptotic behavior of both received signal power and aggregate interference power as base station density increases.
• Identification of bounded signal and interference powers under finite UE density and non-zero height difference, leading to a constant capacity scaling law.
• Mathematical formulation showing that network capacity does not grow indefinitely with base station density due to interference saturation.
• Analysis of the optimal spatial spectrum reuse (SSR) density that maximizes network capacity, derived from the trade-off between spectral reuse gain and interference growth.

Experimental results

Research questions

• RQ1 Does spatial spectrum reuse (SSR) in ultra-dense networks (UDNs) have a fundamental upper limit despite increasing base station density?
• RQ2 How do non-zero BS-to-UE antenna height differences and finite UE density affect the scaling behavior of signal and interference powers in UDNs?
• RQ3 Can a constant capacity scaling law be derived for UDNs under realistic propagation conditions?
• RQ4 Is there an optimal density of active base stations that maximizes network capacity, rather than activating all base stations?
• RQ5 What is the theoretical limit of spectral efficiency in UDNs when interference and signal powers become bounded?

Key findings

• Signal and interference powers in UDNs become bounded under realistic conditions, including non-zero BS-to-UE antenna height differences and finite UE density.
• As a result, network capacity scales as a constant rather than growing indefinitely with base station density, leading to a constant capacity scaling law.
• The existence of a bounded capacity implies that activating all base stations simultaneously on the same time/frequency resources is not optimal at extreme densities.
• An optimal spatial spectrum reuse (SSR) density exists that maximizes network capacity, beyond which interference growth outweighs spectral reuse gains.
• The theoretical limit to SSR must be considered in the design and operation of future ultra-dense networks to avoid performance degradation.
• The findings challenge the assumption that denser deployments always yield higher capacity, highlighting a critical trade-off in UDN deployment strategies.