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 zeroforcing 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. Index Terms-Poisson point process, MIMO heterogeneous networks, area spectral efficiency, link reliability.
Li et al. REF have developed a semi-closed expression for the success probability using the Toeplitz matrix representation in a multiuser MIMO HCN, where the tradeoff between the link reliability and the area spectrum efficiency has been discussed.
Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets
IEEE Transactions on Communications
IEEE Transactions on Communications
Mathematics Computer Science