arXiv subjects

Jeffrey G. Andrews

Publications and source records attributed to Jeffrey G. Andrews.

At least 91 records · Page 5Linked to original sources

arXiv2017

Inter-Operator Base Station Coordination in Spectrum-Shared Millimeter Wave Cellular Networks

We characterize the rate coverage distribution for a spectrum-shared millimeter wave downlink cellular network. Each of multiple cellular operators owns separate mmWave bandwidth, but shares the spectrum amongst each other while using dynamic inter-operator base station (BS) coordination to suppress the resulting cross-operator interference. We model the BS locations of each operator as mutually independent Poisson point processes, and derive the probability density function (PDF) of the K-th strongest link power, incorporating both line-of-sight and non line-of-sight states. Leveraging the obtained PDF, we derive the rate coverage expression as a function of system parameters such as the BS density, transmit power, bandwidth, and coordination set size. We verify the analysis with extensive simulation results. A major finding is that inter-operator BS coordination is useful in spectrum sharing (i) with dense and high power operators and (ii) with fairly wide beams, e.g., 30 or higher.

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arXiv2017

Directional Cell Search Delay Analysis for Cellular Networks with Static Users

Cell search is the process for a user to detect its neighboring base stations (BSs) and make a cell selection decision. Due to the importance of beamforming gain in millimeter wave (mmWave) and massive MIMO cellular networks, the directional cell search delay performance is investigated. A cellular network with fixed BS and user locations is considered, so that strong temporal correlations exist for the SINR experienced at each BS and user. For Poisson cellular networks with Rayleigh fading channels, a closed-form expression for the spatially averaged mean cell search delay of all users is derived. This mean cell search delay for a noise-limited network (e.g., mmWave network) is proved to be infinite whenever the non-line-of-sight (NLOS) path loss exponent is larger than 2. For interference-limited networks, a phase transition for the mean cell search delay is shown to exist in terms of the number of BS antennas/beams $M$: the mean cell search delay is infinite when $M$ is smaller than a threshold and finite otherwise. Beam-sweeping is also demonstrated to be effective in decreasing the cell search delay, especially for the cell edge users.

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arXiv2017

Design and Analysis of Initial Access in Millimeter Wave Cellular Networks

Initial access is the process which allows a mobile user to first connect to a cellular network. It consists of two main steps: cell search (CS) on the downlink and random access (RA) on the uplink. Millimeter wave (mmWave) cellular systems typically must rely on directional beamforming (BF) in order to create a viable connection. The beamforming direction must therefore be learned-as well as used-in the initial access process for mmWave cellular networks. This paper considers four simple but representative initial access protocols that use various combinations of directional beamforming and omnidirectional transmission and reception at the mobile and the BS, during the CS and RA phases. We provide a system-level analysis of the success probability for CS and RA for each one, as well as of the initial access delay and user-perceived downlink throughput (UPT). For a baseline exhaustive search protocol, we find the optimal BS beamwidth and observe that in terms of initial access delay it is decreasing as blockage becomes more severe, but is relatively constant (about $π/12$) for UPT. Of the considered protocols, the best trade-off between initial access delay and UPT is achieved under a fast cell search protocol.

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arXiv2017

Macro diversity in Cellular Networks with Random Blockages

Blocking objects (blockages) between a transmitter and receiver cause wireless communication links to transition from line-of-sight (LOS) to non-line-of-sight (NLOS) propagation, which can greatly reduce the received power, particularly at higher frequencies such as millimeter wave (mmWave). We consider a cellular network in which a mobile user attempts to connect to two or more base stations (BSs) simultaneously, to increase the probability of at least one LOS link, which is a form of macrodiversity. We develop a framework for determining the LOS probability as a function of the number of BSs, when taking into account the correlation between blockages: for example, a single blockage close to the device -- including the user's own body -- could block multiple BSs. We consider the impact of the size of blocking objects on the system reliability probability and show that macrodiversity gains are higher when the blocking objects are small. We also show that the BS density must scale as the square of the blockage density to maintain a given level of reliability.

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arXiv2016

Cell-Edge-Aware Precoding for Downlink Massive MIMO Cellular Networks

We propose a cell-edge-aware (CEA) zero forcing (ZF) precoder that exploits the excess spatial degrees of freedom provided by a large number of base station (BS) antennas to suppress inter-cell interference at the most vulnerable user equipments (UEs). We evaluate the downlink performance of CEA-ZF, as well as that of a conventional cell-edge-unaware (CEU) ZF precoder in a network with random base station topology. Our analysis and simulations show that the proposed CEA-ZF precoder outperforms CEU-ZF precoding in terms of (i) aggregate per-cell data rate, (ii) coverage probability, and (iii) 95%-likely, or edge user, rate. In particular, when both perfect channel state information and a large number of antennas N are available at the BSs, we demonstrate that the outage probability under CEA-ZF and CEU-ZF decay as 1/N^2 and 1/N, respectively. This result identifies CEA-ZF as a more effective precoding scheme for massive MIMO cellular networks. Our framework also reveals the importance of scheduling the optimal number of UEs per BS, and confirms the necessity to control the amount of pilot contamination received during the channel estimation phase.

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arXiv2016

A Primer on Cellular Network Analysis Using Stochastic Geometry

This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the signal-to-interference-plus-noise ratio (SINR) distribution, which can be characterized by the coverage probability (the SINR CCDF) or the outage probability (its CDF). We model base stations (BSs) in the network as a realization of a homogeneous Poisson point process of density $λ$, and compute the SINR for three main cases: the downlink, uplink, and finally the multi-tier downlink, which is characterized by having $k$ tiers of BSs each with a unique density $λ_i$ and transmit power $p_i$. These three baseline results have been extensively extended to many different scenarios, and we conclude with a brief summary of some of those extensions.

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arXiv2016

Optimizing The Spatial Content Caching Distribution for Device-to-Device Communications

We study the optimal geographic content placement problem for device-to-device (D2D) networks in which the content popularity follows the Zipf law. We consider a D2D caching model where the locations of the D2D users (caches) are modeled by a Poisson point process (PPP) and have limited communication range and finite storage. Unlike most related work which assumes independent placement of content, and does not capture the locations of the users, we model the spatial properties of the network including spatial correlation in terms of the cached content. We propose two novel spatial correlation models, the exchangeable content model and a Matérn (MHC) content placement model, and analyze and optimize the \emph{hit probability}, which is the probability of a given D2D node finding a desired file at another node within its communication range. We contrast these results to the independent placement model, and show that exchangeable placement performs worse. On the other hand, MHC placement yields a higher cache hit probability than independent placement for small cache sizes.

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arXiv2016

Optimizing Content Caching to Maximize the Density of Successful Receptions in Device-to-Device Networking

Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized opportunistic short-range communication. For D2D to be useful, mobile nodes must possess content that other mobiles want. Thus, intelligent caching techniques are essential for D2D. In this paper we use results from stochastic geometry to derive the probability of successful content delivery in the presence of interference and noise. We employ a general transmission strategy where multiple files are cached at the users and different files can be transmitted simultaneously throughout the network. We then formulate an optimization problem, and find the caching distribution that maximizes the density of successful receptions (DSR) under a simple transmission strategy where a single file is transmitted at a time throughout the network. We model file requests by a Zipf distribution with exponent $γ_r$, which results in an optimal caching distribution that is also a Zipf distribution with exponent $γ_c$, which is related to $γ_r$ through a simple expression involving the path loss exponent. We solve the optimal content placement problem for more general demand profiles under Rayleigh, Ricean and Nakagami small-scale fading distributions. Our results suggest that it is required to flatten the request distribution to optimize the caching performance. We also develop strategies to optimize content caching for the more general case with multiple files, and bound the DSR for that scenario.

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arXiv2016

Are We Approaching the Fundamental Limits of Wireless Network Densification?

The single most important factor behind the data rate increases experienced by users of wireless networks over the past few decades has been densification, namely adding more base stations and access points and thus getting more spatial reuse of the spectrum. This trend is set to continue into 5G and presumably beyond. However, at some point further densification will no longer be able to provide exponentially increasing data rates. Like the end of Moore's Law, this would have massive implications on the entire technology landscape, which depends ever more heavily on wireless connectivity. When and why will this happen? How might we prolong this from occurring for as long as possible? These are the questions explored in this paper.

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arXiv2016

Guard Region Model for Pilot Reuse Analysis in Uplink Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) are expected to significantly enhance the spectrum efficiency (SE) and energy efficiency (EE) of future cellular systems. Since the performance gain of massive MIMO is fundamentally limited by pilot contamination, pilot reuse design is crucial to achieve reasonable cell throughput and user rate. In this paper, we leverage stochastic geometry to model pilot reuse in massive MIMO systems by introducing a guard region model to match realistic pilot allocation strategies. The uplink signal-to-interference-plus-noise ratio (SINR) distribution is analytically derived, based on which the benefits of pilot reuse on cell-throughput and user-rate are investigated. The optimal pilot reuse factor for uplink transmission is obtained. We also find through simulations that increasing the pilot reuse factor beyond a certain value would not improve user-rate, and could even lead to a significant loss of the cell throughput.

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arXiv2016

Modeling and Analyzing Millimeter Wave Cellular Systems

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional Sub-6GHz cellular systems are (i) vulnerability to blocking, and (ii) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: (a) mmWave systems are significantly more noise-limited than at Sub-6GHz for most parameter configurations; (b) initial access is much more difficult in mmWave; (c) self-backhauling is more viable than in Sub-6GHz systems which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and (d) in sharp contrast to Sub-6GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

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arXiv2016

On the Optimal Feedback Rate in Interference-Limited Multi-Antenna Cellular Systems

We consider a downlink cellular network where multi-antenna base stations (BSs) transmit data to single-antenna users by using one of two linear precoding methods with limited feedback: (i) maximum ratio transmission (MRT) for serving a single user or (ii) zero forcing (ZF) for serving multiple users. The BS and user locations are drawn from a Poisson point process, allowing expressions for the signal- to-interference coverage probability and the ergodic spectral efficiency to be derived as a function of system parameters such as the number of BS antennas and feedback bits, and the pathloss exponent. We find a tight lower bound on the optimum number of feedback bits to maximize the net spectral efficiency, which captures the overall system gain by considering both of downlink and uplink spectral efficiency using limited feedback. Our main finding is that, when using MRT, the optimum number of feedback bits scales linearly with the number of antennas, and logarithmically with the channel coherence time. When using ZF, the feedback scales in the same ways as MRT, but also linearly with the pathloss exponent. The derived results provide system-level insights into the preferred channel codebook size by averaging the effects of short-term fading and long-term pathloss.

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arXiv2016

On the Feasibility of Sharing Spectrum Licenses in mmWave Cellular Systems

The highly directional and adaptive antennas used in mmWave communication open up the possibility of uncoordinated sharing of spectrum licenses between commercial cellular operators. There are several advantages to sharing including a reduction in license costs and an increase in spectrum utilization. In this paper, we establish the theoretical feasibility of spectrum license sharing among mmWave cellular operators. We consider a heterogeneous multi-operator system containing multiple independent cellular networks, each owned by an operator. We then compute the SINR and rate distribution for downlink mobile users of each network. Using the analysis, we compare systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost. We show that sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is also favored when there is a low density of users. We also consider a multi-operator system where BSs of all the networks are co-located to show that the simultaneous sharing of spectrum and infrastructure is also feasible. We show that all networks can share licenses with less bandwidth and still achieve the same per-user median rate as if they each had an exclusive license to spectrum with more bandwidth.

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arXiv2016

Gains of Restricted Secondary Licensing in Millimeter Wave Cellular Systems

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. To explain economic trade-offs, we consider a revenue-pricing model for both operators in the presence of a central licensing authority. Our results show that the original operator and central network authority can benefit from secondary licensing when the maximum interference threshold is properly adjusted. This means that the original operator and central licensing authority have an incentive to permit a secondary network to restrictively share the spectrum. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

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arXiv2016

A Comparison of MIMO Techniques in Downlink Millimeter Wave Cellular Networks with Hybrid Beamforming

Large antenna arrays will be needed in future millimeter wave (mmWave) cellular networks, enabling a large number of different possible antenna architectures and multiple-input multiple-output (MIMO) techniques. It is still unclear which MIMO technique is most desirable as a function of different network parameters. This paper, therefore, compares the coverage and rate performance of hybrid beamforming enabled multi-user (MU) MIMO and single-user spatial multiplexing (SM) with single-user analog beamforming (SU-BF). A stochastic geometry model for coverage and rate analysis is proposed for MU-MIMO mmWave cellular networks, taking into account important mmWave-specific hardware constraints for hybrid analog/digital precoders and combiners, and a blockage-dependent channel model which is sparse in angular domain. The analytical results highlight the coverage, rate and power consumption tradeoffs in multiuser mmWave networks. With perfect channel state information at the transmitter and round robin scheduling, MU-MIMO is usually a better choice than SM or SU-BF in mmWave cellular networks. This observation, however, neglects any overhead due to channel acquisition or computational complexity. Incorporating the impact of such overheads, our results can be re-interpreted so as to quantify the minimum allowable efficiency of MU-MIMO to provide higher rates than SM or SU-BF.

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arXiv2016

Modeling and Analyzing the Coexistence of Wi-Fi and LTE in Unlicensed Spectrum

We leverage stochastic geometry to characterize key performance metrics for neighboring Wi-Fi and LTE networks in unlicensed spectrum. Our analysis focuses on a single unlicensed frequency band, where the locations for the Wi-Fi access points (APs) and LTE eNodeBs (eNBs) are modeled as two independent homogeneous Poisson point processes. Three LTE coexistence mechanisms are investigated: (1) LTE with continuous transmission and no protocol modifications; (2) LTE with discontinuous transmission; and (3) LTE with listen-before-talk (LBT) and random back-off (BO). For each scenario, we have derived the medium access probability (MAP), the signal-to-interference-plus-noise ratio (SINR) coverage probability, the density of successful transmissions (DST), and the rate coverage probability for both Wi-Fi and LTE. Compared to the baseline scenario where one Wi-Fi network coexists with an additional Wi-Fi network, our results show that Wi-Fi performance is severely degraded when LTE transmits continuously. However, LTE is able to improve the DST and rate coverage probability of Wi-Fi while maintaining acceptable data rate performance when it adopts one or more of the following coexistence features: a shorter transmission duty cycle, lower channel access priority, or more sensitive clear channel assessment (CCA) thresholds.

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arXiv2016

Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets

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.

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arXiv2016

User Association and Interference Management in Massive MIMO HetNets

Two key traits of 5G cellular networks are much higher base station (BS) densities - especially in the case of low-power BSs - and the use of massive MIMO at these BSs. This paper explores how massive MIMO can be used to jointly maximize the offloading gains and minimize the interference challenges arising from adding small cells. We consider two interference management approaches: joint transmission (JT) with local precoding, where users are served simultaneously by multiple BSs without requiring channel state information exchanges among cooperating BSs, and resource blanking, where some macro BS resources are left blank to reduce the interference in the small cell downlink. A key advantage offered by massive MIMO is channel hardening, which enables to predict instantaneous rates a priori. This allows us to develop a unified framework, where resource allocation is cast as a network utility maximization (NUM) problem, and to demonstrate large gains in cell-edge rates based on the NUM solution. We propose an efficient dual subgradient based algorithm, which converges towards the NUM solution. A scheduling scheme is also proposed to approach the NUM solution. Simulations illustrate more than 2x rate gain for 10th percentile users vs. an optimal association without interference management.

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