Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets

TL;DR

This paper derives a comprehensive closed-form expression for success probability in downlink multiuser MIMO HetNets, revealing key tradeoffs between network density, success probability, and spectral efficiency, with practical algorithms for optimization.

Contribution

It introduces a novel Toeplitz matrix approach for analyzing success probability in MIMO HetNets, including multiuser scenarios, and characterizes the tradeoff between spectral efficiency and link reliability.

Findings

Success probability decreases with increasing network density in MIMO HetNets.

Maximum success probability is achieved by activating only one tier of base stations.

Maximum area spectral efficiency is achieved by activating all base stations.

Abstract

We derive a general and closed-form result for the success probability in downlink multiple-antenna (MIMO) heterogeneous cellular networks (HetNets), utilizing a novel Toeplitz matrix representation. This main result, which is equivalently the signal-to-interference ratio (SIR) distribution, includes multiuser MIMO, single-user MIMO and per-tier biasing for $K$ different tiers of randomly placed base stations (BSs), assuming zero-forcing precoding and perfect channel state information. The large SIR limit of this result admits a simple closed form that is accurate at moderate SIRs, e.g., above 5 dB. These results reveal that the SIR-invariance property of SISO HetNets does not hold for MIMO HetNets; instead the success probability may decrease as the network density increases. We prove that the maximum success probability is achieved by activating only one tier of BSs, while the maximum area spectral efficiency (ASE) is achieved by activating all the BSs. This reveals a unique tradeoff between the ASE and link reliability in multiuser MIMO HetNets. To achieve the maximum ASE while guaranteeing a certain link reliability, we develop efficient algorithms to find the optimal BS densities. It is shown that as the link reliability requirement increases, more BSs and more tiers should be deactivated.