We develop a general downlink model for multi-antenna heterogeneous cellular
networks (HetNets), where base stations (BSs) across tiers may differ in terms
of transmit power, target signal-to-interference-ratio (SIR), deployment
density, number of transmit antennas and the type of multi-antenna
transmission. In particular, we consider and compare space division multiple
access (SDMA), single user beamforming (SU-BF), and baseline single-input
single-output (SISO) transmission. For this general model, the main
contributions are: (i) ordering results for both coverage probability and per
user rate in closed form for any BS distribution for the three considered
techniques, using novel tools from stochastic orders, (ii) upper bounds on the
coverage probability assuming a Poisson BS distribution, and (iii) a comparison
of the area spectral efficiency (ASE). The analysis concretely demonstrates,
for example, that for a given total number of transmit antennas in the network,
it is preferable to spread them across many single-antenna BSs vs. fewer
multi-antenna BSs. Another observation is that SU-BF provides higher coverage
and per user data rate than SDMA, but SDMA is in some cases better in terms of
ASE.

研究多天线异构蜂窝网络中的下行链路模型，考虑了不同基站之间在发射功率、目标信干噪比、部署密度、发射天线数量和多天线传输类型等方面的差异，并比较了空分多址、单用户波束成形和单输入单输出传输三种技术的覆盖率概率、用户速率等指标，提出了关于区域频谱效率的统计比较工具。研究发现，为了提高网络的总体性能，将天线分布在多个单天线基站上比分布在少量多天线基站上更为优越；单用户波束成形技术能提供更高的覆盖率和用户速率，但空分多址在某些方面的区域频谱效率更高。

下行 MIMO HetNets: 建模，排序结果和性能分析

Downlink MIMO HetNets: Modeling, Ordering Results and Performance  Analysis

We consider the downlink of a multi-cell system with multi-antenna base
stations and single-antenna user terminals, arbitrary base station cooperation
clusters, distance-dependent propagation pathloss, and general "fairness"
requirements. Base stations in the same cooperation cluster employ joint
transmission with linear zero-forcing beamforming, subject to sum or per-base
station power constraints. Inter-cluster interference is treated as noise at
the user terminals. Analytic expressions for the system spectral efficiency are
found in the large-system limit where both the numbers of users and antennas
per base station tend to infinity with a given ratio. In particular, for the
per-base station power constraint, we find new results in random matrix theory,
yielding the squared Frobenius norm of submatrices of the Moore-Penrose
pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the
cooperation cluster, user distribution, and path-loss coefficients. The
analysis is extended to the case of non-ideal Channel State Information at the
Transmitters (CSIT) obtained through explicit downlink channel training and
uplink feedback. Specifically, our results illuminate the trade-off between the
benefit of a larger number of cooperating antennas and the cost of estimating
higher-dimensional channel vectors. Furthermore, our analysis leads to a new
simplified downlink scheduling scheme that pre-selects the users according to
probabilities obtained from the large-system results, depending on the desired
fairness criterion. The proposed scheme performs close to the optimal
(finite-dimensional) opportunistic user selection while requiring significantly
less channel state feedback, since only a small fraction of pre-selected users
must feed back their channel state information.

该研究旨在探讨多基站系统下行链路的多天线基站和单天线用户终端、任意基站合作集群、距离相关传播路径损耗和一般的 “公平性” 要求，并提出了一种新的简化下行调度方案，根据所需的公平性标准预先选择用户，其性能接近有限维机会用户选择的最优方案，同时需要明显较少的信道状态反馈。