Performance evaluation of MISO-SDMA in heterogenous networks with practical cell association

In this paper adopting stochastic geometry we investigate the system performance in heterogenous networks including multiple tiers of BSs with multiple-input single output spatial division multiple access (MISO-SDMA) technique. In the related literature on heterogenous systems, ideal cell association (CA) rules are often considered for simplicity, where each user equipment (UE) examines a very large number of pilots across the tiers before choosing its associated base station (BS). Here we consider practical cases where UEs are restricted to examine KH≥1 pilots across all tiers before choosing their associated BS. We then obtain closed-form expressions for the system performance measured by the coverage probability and UE's data rate. Our analytical results provide quantitative insights on the impact of different factors on the system performance including the BS's spatial density, their transmission powers, number of transmit antennas, SIR thresholds, number of UEs served by each BS, and KH. Interestingly, we observe that increasing KH always improves the coverage probability however, it only improves data rate up to a certain point. The data rate is then reduced by further increasing of KH. Given KH pilots in practical cases, the issue is how to allocate the pilots among different tiers. We address this issue by developing an algorithm and show that by careful allocation of available pilots, the network performance is significantly improved even in cases with small KH. Our results also indicate a fundamental tradeoff, as sharing strategies providing the best coverage performance yield very poor capacity and vice versa. Such trade-off provides a new degree of freedom in heterogeneous networks design

Coverage performance in multi-stream MIMO-ZFBF heterogeneous networks

We study the coverage performance of multiantenna (MIMO) communications in heterogenous networks (HetNets). Our main focus is on open-loop and multi-stream MIMO zero-forcing beamforming (ZFBF) at the receiver. Network coverage is evaluated adopting tools from stochastic geometry. Besides fixed-rate transmission (FRT), we also consider adaptive-rate transmission (ART) while its coverage performance, despite its high relevance, has so far been overlooked. On the other hand, while the focus of the existing literature has solely been on the evaluation of coverage probability per stream, we target coverage probability per communication link — comprising multiple streams — which is shown to be a more conclusive performance metric in multi-stream MIMO systems. This, however, renders various analytical complexities rooted in statistical dependency among streams in each link. Using a rigorous analysis, we provide closed-form bounds on the coverage performance for FRT and ART. These bounds explicitly capture impacts of various system parameters including densities of BSs, SIR thresholds, and multiplexing gains. Our analytical results are further shown to cover popular closed-loop MIMO systems, such as eigen-beamforming and space-division multiple access (SDMA). The accuracy of our analysis is confirmed by extensive simulations. The findings in this paper shed light on several important aspects of dense MIMO HetNets: (i) increasing the multiplexing gains yields lower coverage performance; (ii) densifying network by installing an excessive number of lowpower femto BSs allows the growth of the multiplexing gain of high-power, low-density macro BSs without compromising the coverage performance; and (iii) for dense HetNets, the coverage probability does not increase with the increase of deployment densities

Design, Modeling, and Performance Analysis of Multi-Antenna Heterogeneous Cellular Networks

This paper presents a stochastic geometry-based framework for the design and analysis of downlink multi-user multiple-input multiple-output (MIMO) heterogeneous cellular networks with linear zero-forcing transmit precoding and receive combining, assuming Rayleigh fading channels and perfect channel state information. The generalized tiers of base stations may differ in terms of their Poisson point process spatial density, number of transmit antennas, transmit power, artificial-biasing weight, and number of user equipments served per resource block. The spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non-direct moment-generating-function-based methodology with closed-form expressions of the useful received signal and aggregate network interference statistics systematically derived. In addition, the area spectral efficiency is formulated under different space-division multiple-access and single-user beamforming transmission schemes. We examine the impact of different cellular network deployments, propagation conditions, antenna configurations, and MIMO setups on the achievable performance through theoretical and simulation studies. Based on the state-of-the-art system parameters, the results highlight the inherent limitations of baseline single-input single-output transmission and conventional sparse macro-cell deployment, as well as the promising potential of multi-antenna communications and small-cell solution in interference-limited cellular environments

Coverage Analysis of Multi-Stream MIMO HetNets with MRC Receivers

Most of current research on the coverage performance of multi-stream MIMO heterogeneous networks (HetNets) has been focusing on a single data-stream. This does not always provide accurate results as our analysis shows the cross-stream correlation due to interference can greatly affect the coverage performance. This paper analyzes the coverage probability in such systems, and studies the impact of cross-stream correlation. Specifically, we focus on the max-SIR cell association policy, and leverage stochastic geometry to study scenarios whereby a receiver is considered in the coverage, if all of its data-streams are successfully decodeable. Assuming open-loop maximum ratio combining (MRC) at receivers, we consider cases where partial channel state information is available at the receiver. We then obtain an upper-bound on the coverage and formulate crossstream SIR correlation. We further show that approximating such systems based on fully-correlated (non-correlated) datastreams, results in a slight underestimation (substantial overestimation) of the coverage performance. Our results provide insights on the multiplexing regimes where densification improves the coverage performance and spectral efficiency. We also compare MRC with more complex zero-forcing receiver and provide quantitative insights on the design trade-offs. Our analysis is validated via extensive simulations

Coverage Performance in MIMO-ZFBF Dense HetNets with Multiplexing and LOS/NLOS Path-Loss Attenuation

The performance of multiple-input multiple-output (MIMO) multiplexing heterogenous cellular networks are often analyzed using a single-exponent path-loss model. Thus, the effect of the expected line-of-sight (LOS) propagation in densified settings is unaccounted for, leading to inaccurate performance evaluation and/or inefficient system design. This is due to the complexity of LOS/non-LOS models in the context of MIMO communications. We address this issue by developing an analytical framework based on stochastic geometry to evaluate the coverage performance. We focus on the zero-forcing beamforming where the maximum signal-to-interference ratio is used for cell association. We analytically derive the coverage. We then investigate the cross-stream interference correlation, and develop two approximations of the coverage: Alzer Approximation (A-A) and Gamma Approximation (G-A). The former is often used in the single antenna and single-stream MIMO. We extend A-A to a MIMO multiplexing system and evaluate its utility. We show that the inverse interference is well-fitted by a Gamma random variable, where its parameters are directly related to the system parameters. The accuracy and robustness of G-A is higher than that of A-A. We observe that depending on the multiplexing gain, it is possible to attain the best coverage probability by proper densification

Coverage performance of MIMO-MRC in heterogeneous networks:a stochastic geometry perspective

We study the coverage performance of multi-antenna (MIMO) communications with maximum ratio combining (MRC) at the receiver in heterogeneous networks (HetNets). Our main interest in on multi-stream communications when BSs do not have access to channel state information. Adopting stochastic geometry we evaluate the network-wise coverage performance of MIMO-MRC assuming maximum signal- to-interference ratio (SIR) cell association rule. Coverage analysis in MIMO-MRC HetNets is challenging due to inter-stream interference and statistical dependencies among streams' SIR values in each communication link. Using the results of stochastic geometry we then investigate this problem and obtain tractable analytical approximations for the coverage performance. We then show that our results are adequately accurate and easily computable. Our analysis sheds light on the impacts of important system parameters on the coverage performance, and provides quantitative insight on the densification in conjunction with high multiplexing gains in MIMO HetNets. We further observe that increasing multiplexing gain in high- power tier can cost a huge coverage reduction unless it is practiced with densification in femto-cell tier

Design, Modeling, and Performance Analysis of Multi-Antenna Heterogeneous Cellular Networks

Abstract This paper presents a stochastic geometry-based framework for the design and analysis of downlink multi-user multipleinput multiple-output (MIMO) heterogeneous cellular networks (HetNets) with linear zero-forcing (ZF) transmit precoding and receive combining, assuming Rayleigh fading channels and perfect channel state information (CSI). The generalized tiers of base stations (BSs) may differ in terms of their Poisson point process (PPP) spatial density, number of transmit antennas, transmit power, artificial-biasing weight, and number of user equipments (UEs) served per resource block. The spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non-direct moment-generating-function (MGF)-based methodology with closed-form expressions of the useful received signal and aggregate network interference statistics systematically derived. In addition, the area spectral efficiency is formulated under different space-division multiple-access (SDMA) and single-user beamforming (SUBF) transmission schemes. We examine the impact of different cellular network deployments, propagation conditions, antenna configurations, and MIMO setups on the achievable performance through theoretical and simulation studies. Based on state-of-the-art system parameters, the results highlight the inherent limitations of baseline single-input singleoutput (SISO) transmission and conventional sparse macro-cell deployment, as well as the promising potential of multi-antenna communications and small-cell solution in interference-limited cellular environments. Index Terms Multi-antenna communications, downlink heterogeneous cellular networks, stochastic geometry theory