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In this article, we advocate for the design of ad hoc artificial intelligence (AI)/machine learning (ML) models to facilitate their usage in future smart infrastructures based on communication networks. To motivate this, we first review key operations identified by the 3GPP for transferring AI/ML models through 5G networks and the main existing techniques to reduce their communication overheads. We also present a novel communication-aware ML framework, which we refer to as Accordion, that enables an efficient AI/ML model transfer thanks to an overhauled model training and communication protocol. We demonstrate the communication-related benefits of Accordion, analyse key performance trade-offs, and discuss potential research directions within this realm.

What will the future of UAV cellular communications be? In this tutorial article, we address such a compelling yet difficult question by embarking on a journey from 5G to 6G and sharing a large number of realistic case studies supported by original results. We start by overviewing the status quo on UAV communications from an industrial standpoint, providing fresh updates from the 3GPP and detailing new 5G NR features in support of aerial devices. We then show the potential and the limitations of such features. In particular, we demonstrate how sub-6 GHz massive MIMO can successfully tackle cell selection and interference challenges, we showcase encouraging mmWave coverage evaluations in both urban and suburban/rural settings, and we examine the peculiarities of direct device-to-device communications in the sky. Moving on, we sneak a peek at next-generation UAV communications, listing some of the use cases envisioned for the 2030s. We identify the most promising 6G enablers for UAV communication, those expected to take the performance and reliability to the next level. For each of these disruptive new paradigms (non-terrestrial networks, cell-free architectures, artificial intelligence, reconfigurable intelligent surfaces, and THz communications), we gauge the prospective benefits for UAVs and discuss the main technological hurdles that stand in the way. All along, we distil our numerous findings into essential takeaways, and we identify key open problems worthy of further study.

In this article, we consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs coexist with the uplink (UL) of cellular ground users (GUEs). Our analysis focuses on comparing two spectrum sharing mechanisms: i) overlay, where the available time-frequency resources are split into orthogonal portions for U2U and GUE communications, and ii) underlay, where the same resources may be accessed by both link types, resulting in mutual interference. We evaluate the coverage probability and rate of all links and their interplay to identify the best spectrum sharing mechanism. Among other things, our results demonstrate that, in scenarios with a large number of UAV pairs, adopting overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance. We also find that increasing the density of U2U links degrades their rates in the overlay-where UAVs only receive interference from other UAVs-, but not significantly so in the underlay -- where the effect of GUE-generated interference is dominant., Comment: Accepted to present at IEEE GLOBECOM 2020. arXiv admin note: substantial text overlap with arXiv:1912.07534

In this article, we evaluate the performance of the parameterized spatial reuse (PSR) framework of IEEE 802.11ax, mainly focusing on its impact on transmission latency. Based on detailed standard-compliant system-level simulations, we provide a realistic analysis of the effects of PSR considering different scenario densities, traffic loads, and access points (APs) antenna capabilities to quantify its performance gains under various scenarios. Our results show that, in medium-density scenarios, PSR can offer up to a 3.8x reduction in the 5% worst-case latencies for delay-sensitive stations with respect to an 802.11ax system without PSR. Moreover, our study demonstrates that, for low-latency communications, providing the network with PSR capabilities may be an appealing alternative to the deployment of more costly multi-antenna APs., Comment: Accepted to IEEE Globecom 2020, SAC - Access Networks and Systems

As hordes of data-hungry devices challenge its current capabilities, Wi-Fi strikes back with 802.11be, alias Wi-Fi 7. This brand-new amendment promises a (r)evolution of unlicensed wireless connectivity as we know it. With its standardisation process being consolidated, we provide an updated digest of 802.11be essential features, vouching for multi-AP coordination as a must-have for critical and latency-sensitive applications. We then get down to the nitty-gritty of one of its most enticing implementations-coordinated beamforming-, for which our standard-compliant simulations confirm near-tenfold reductions in worst-case delays., Comment: 7 pages

Indoor areas, such as offices and shopping malls, are a natural environment for initial millimeter-wave (mmWave) deployments. While we already have the technology that enables us to realize indoor mmWave deployments, there are many remaining challenges associated with system-level design and planning for such. The objective of this article is to bring together multiple strands of research to provide a comprehensive and integrated framework for the design and performance evaluation of indoor mmWave systems. The paper introduces the framework with a status update on mmWave technology, including ongoing fifth generation (5G) wireless standardization efforts, and then moves on to experimentally-validated channel models that inform performance evaluation and deployment planning. Together these yield insights on indoor mmWave deployment strategies and system configurations, from feasible deployment densities to beam management strategies and necessary capacity extensions., Comment: Proceedings of the IEEE

We consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs share the same spectrum with the uplink (UL) of cellular ground users (GUEs). For this setup, we focus on analyzing and comparing the performance of two spectrum sharing mechanisms: (i) underlay, where the same time-frequency resources may be accessed by both UAVs and GUEs, resulting in mutual interference, and (ii)overlay, where the available resources are divided into orthogonal portions for U2U and GUE communications. We evaluate the coverage probability and rate of both link types and their interplay to identify the best spectrum sharing strategy. We do so through an analytical framework that embraces realistic height-dependent channel models, antenna patterns, and practical power control mechanisms. For the underlay, we find that although the presence of U2U direct communications may worsen the uplink performance of GUEs, such effect is limited as base stations receive the power-constrained UAV signals through their antenna sidelobes. In spite of this, our results lead us to conclude that in urban scenarios with a large number of UAV pairs, adopting an overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance., Comment: Related Work: Azari, M. M., Rosas, F., & Pollin, S. (2019). Cellular connectivity for UAVs: Network modeling, performance analysis and design guidelines. IEEE Transactions on Wireless Communications. arXiv admin note: text overlap with arXiv:1904.05104

We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture, wherein a large number of access points (APs) is deployed in place of large co-located massive MIMO arrays. We consider also a variation of the pure cell-free architecture by applying a user-centric association approach, where each user is served only from a subset of APs in the network. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users (GUEs), and the APs follows a Ricean distribution, we derive closed-form spectral efficiency lower bounds for uplink and downlink with linear minimum mean square error channel estimation. We consider several power allocation and user scheduling strategies for such a system, and, among these, also minimum-rate maximizing power allocation strategies to improve the system fairness. Our numerical results reveal that cell-free massive MIMO architecture and its low-complexity user-centric alternative may provide better performance than a traditional multi-cell massive MIMO network deployment., Comment: double-column, 14 pages, 8 figure, journal paper

Reliable and direct communication between unmanned aerial vehicles (UAVs) could facilitate autonomous flight, collision avoidance, and cooperation in UAV swarms. In this paper, we consider UAV-to-UAV (U2U) communications underlaying a cellular network, where UAV transmit-receive pairs share the same spectrum with the uplink (UL) of cellular ground users (GUEs). We evaluate the performance of this setup through an analytical framework that embraces realistic height-dependent channel models, antenna patterns, and practical power control mechanisms. Our results demonstrate that, although the presence of U2U communications may worsen the performance of the GUEs, such effect is limited as base stations receive UAV interference through their antenna sidelobes. Moreover, we illustrate that the quality of all links degrades as the UAV height increases---due to a larger number of line-of-sight interferers---, and how the performance of the U2U links can be traded off against that of the GUEs by varying the UAV power control policy.

Wi-Fi technology is continuously innovating to cater to the growing customer demands, driven by the digitalisation of everything, both in the home as well as the enterprise and hotspot spaces. In this article, we introduce to the wireless community the next generation Wi-Fi$-$based on IEEE 802.11be Extremely High Throughput (EHT)$-$, present the main objectives and timelines of this new 802.11be amendment, thoroughly describe its main candidate features and enhancements, and cover the important issue of coexistence with other wireless technologies. We also provide simulation results to assess the potential throughput gains brought by 802.11be with respect to 802.11ax., Comment: 6 pages, 4 figures

We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users, and the access points follows a Ricean distribution, we derive closed form spectral efficiency lower bounds for uplink and downlink with linear minimum mean square error (LMMSE) channel estimation. We also propose power allocation and user scheduling strategies for such a system. Our numerical results reveal that a cell-free massive MIMO architecture may provide better performance than a traditional multicell massive MIMO network deployment., Comment: Submitted to 2019 ICC Workshop on "Integrating UAVs into 5G and Beyond"

In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band backhaul for the ultra-dense network (UDN) of self-backhauled small cells (SCs), and 2) to provide direct access (DA) to user equipments (UEs). Through comprehensive 3GPP-based system-level simulations and analytical formulations, we show the end-to-end UE rates achievable with these two architectures. Differently from the existing works, we provide results for two strategies of self-backhauled SC deployments, namely random and ad-hoc, where in the latter SCs are purposely positioned close to UEs to achieve line-of-sight (LoS) access links. We also evaluate the optimal backhaul and access time resource partition due to the in-band self-backhauling (s-BH) operations. Our results show that the ad-hoc deployment of self-backhauled SCs closer to the UEs with optimal resource partition and with directive antenna patterns, provides rate improvements for cell-edge UEs that amount to 30% and tenfold gain, as compared to mMIMO DA architecture with pilot reuse 3 and reuse 1, respectively. On the other hand, mMIMO s-BH underperforms mMIMO DA above the median value of the UE rates when the effect of pilot contamination is less severe, and the LoS probability of the DA links improves., Comment: The paper is published at IEEE Transactions on Vehicular Technology (TVT 2019). arXiv admin note: text overlap with arXiv:1806.10969

Uplink power control is an efficient scheme to mitigate pilot contamination in massive multiple-input multiple-output (MIMO) systems. In this work, we provide a comprehensive study on the effects of fractional power control (FPC) on the downlink performance of the most relevant fifth generation (5G) massive MIMO deployments. Specifically, we perform thorough system simulations based on the most recent three dimensional spatial channel model released by the 3rd Generation Partnership Project to evaluate the impact of different deployment-related parameters such as pilot reuse factor, beamforming criterion, and base station array size. Our results indicate the most suitable tuning of the FPC parameters and show that optimized FPC provides huge gains in the cell border throughput when compared to a baseline scheme with all the users transmitting at maximum power. Moreover, our simulations also demonstrate that the effectiveness of FPC grows in scenarios with severe pilot contamination, confirming that implementing this feature is essential in realistic deployments., Comment: Accepted at the IEEE GLOBECOM Workshop on Emerging Technologies for 5G and Beyond Wireless and Mobile Networks, Abu Dhabi (UAE), Dec. 2018

The rapid growth of consumer Unmanned Aerial Vehicles (UAVs) is creating promising new business opportunities for cellular operators. On the one hand, UAVs can be connected to cellular networks as new types of user equipment, therefore generating significant revenues for the operators that can guarantee their stringent service requirements. On the other hand, UAVs offer the unprecedented opportunity to realize UAV-mounted flying base stations that can dynamically reposition themselves to boost coverage, spectral efficiency, and user quality of experience. Indeed, the standardization bodies are currently exploring possibilities for serving commercial UAVs with cellular networks. Industries are beginning to trial early prototypes of flying base stations or user equipments, while academia is in full swing researching mathematical and algorithmic solutions to address interesting new problems arising from flying nodes in cellular networks. In this article, we provide a comprehensive survey of all of these developments promoting smooth integration of UAVs into cellular networks. Specifically, we survey (i) the types of consumer UAVs currently available off-the-shelf, (ii) the interference issues and potential solutions addressed by standardization bodies for serving aerial users with the existing terrestrial base stations, (iii) the challenges and opportunities for assisting cellular communications with UAV-based flying relays and base stations, (iv) the ongoing prototyping and test bed activities, (v) the new regulations being developed to manage the commercial use of UAVs, and (vi) the cyber-physical security of UAV-assisted cellular communications., Comment: Accepted in the JOURNAL OF COMMUNICATIONS SURVEYS AND TUTORIALS, Feb 2019, 26 pages, 9 Tables, 9 Figures Submitted to JOURNAL OF COMMUNICATIONS SURVEYS AND TUTORIALS, June 2018, 20 pages, 9 Tables, 9 Figures

In this paper, we focus on the coexistence between a MIMO radar and cellular base stations. We study the interfering channel estimation, where the radar is operated in the "search and track" mode, and the BS receives the interference from the radar. Unlike the conventional methods where the radar and the cellular systems fully cooperate with each other, in this work we consider that they are uncoordinated and the BS needs to acquire the interfering channel state information (ICSI) by exploiting the radar probing waveforms. For completeness, both the line-of-sight (LoS) and Non-LoS (NLoS) channels are considered in the coexistence scenario. By further assuming that the BS has limited a priori knowledge about the radar waveforms, we propose several hypothesis testing methods to identify the working mode of the radar, and then obtain the ICSI through a variety of channel estimation schemes. Based on the statistical theory, we analyze the theoretical performance of both the hypothesis testing and the channel estimation methods. Finally, simulation results verify the effectiveness of our theoretical analysis and demonstrate that the BS can effectively estimate the interfering channel even with limited information from the radar., Comment: 15 pages, 10 figures. This work has been submitted to the IEEE for possible publication

A key aspect of the fifth-generation wireless communication network will be the integration of different services and technologies to provide seamless connectivity. In this paper, we consider using massive multiple-input multiple-output (mMIMO) to provide backhaul links to a dense deployment of self-backhauling (s-BH) small cells (SCs) that provide cellular access within the same spectrum resources of the backhaul. Through a comprehensive system-level simulation study, we evaluate the interplay between access and backhaul and the resulting end-to-end user rates. Moreover, we analyze the impact of different SCs deployment strategies, while varying the time resource allocation between radio access and backhaul links. We finally compare the above mMIMO-based s-BH approach to a mMIMO direct access (DA) architecture accounting for the effects of pilot reuse schemes, together with their associated overhead and contamination mitigation effects. The results show that dense SCs deployments supported by mMIMO s-BH provide significant rate improvements for cell-edge users (UEs) in ultra-dense deployments with respect to mMIMO DA, while the latter outperforms mMIMO s-BH from the median UEs' standpoint.

What will it take for drones -- and the whole associated ecosystem -- to take off? Arguably, infallible command and control (C&C) channels for safe and autonomous flying, and high-throughput links for multi-purpose live video streaming. And indeed, meeting these aspirations may entail a full cellular support, provided through 5G-and-beyond hardware and software upgrades by both mobile operators and manufacturers of these unmanned aerial vehicles (UAVs). In this article, we vouch for massive MIMO as the key building block to realize 5G-connected UAVs. Through the sheer evidence of 3GPP-compliant simulations, we demonstrate how massive MIMO can be enhanced by complementary network-based and UAV-based solutions, resulting in consistent UAV C&C support, large UAV uplink data rates, and harmonious coexistence with legacy ground users.

The purpose of this article is to bestow the reader with a timely study of UAV cellular communications, bridging the gap between the 3GPP standardization status quo and the more forward-looking research. Special emphasis is placed on the downlink command and control (C&C) channel to aerial users, whose reliability is deemed of paramount technological importance for the commercial success of UAV cellular communications. Through a realistic side-by-side comparison of two network deployments -- a present-day cellular infrastructure versus a next-generation massive MIMO system -- a plurality of key facts are cast light upon, with the three main ones summarized as follows: (i) UAV cell selection is essentially driven by the secondary lobes of a base station's radiation pattern, causing UAVs to associate to far-flung cells; (ii) over a 10 MHz bandwidth, and for UAV heights of up to 300 m, massive MIMO networks can support 100 kbps C&C channels in 74% of the cases when the uplink pilots for channel estimation are reused among base station sites, and in 96% of the cases without pilot reuse across the network; (iii) supporting UAV C&C channels can considerably affect the performance of ground users on account of severe pilot contamination, unless suitable power control policies are in place., Comment: arXiv admin note: text overlap with arXiv:1802.01527

In this article, we provide a much-needed study of UAV cellular communications, focusing on the rates achievable for the UAV downlink command and control (C&C) channel. For this key performance indicator, we perform a realistic comparison between existing deployments operating in single-user mode and next-generation multi-user massive MIMO systems. We find that in single-user deployments under heavy data traffic, UAVs flying at 50 m, 150 m, and 300 m achieve the C&C target rate of 100 kbps -- as set by the 3GPP -- in a mere 35%, 2%, and 1% of the cases, respectively. Owing to mitigated interference, a stronger carrier signal, and a spatial multiplexing gain, massive MIMO time division duplex systems can dramatically increase such probability. Indeed, we show that for UAV heights up to 300 m the target rate is met with massive MIMO in 74% and 96% of the cases with and without uplink pilot reuse for channel state information (CSI) acquisition, respectively. On the other hand, the presence of UAVs can significantly degrade the performance of ground users, whose pilot signals are vulnerable to UAV-generated contamination and require protection through uplink power control.

To guarantee the success of massive multiple-input multiple-output (MIMO), one of the main challenges to solve is the efficient management of pilot contamination. Allocation of fully orthogonal pilot sequences across the network would provide a solution to the problem, but the associated overhead would make this approach infeasible in practical systems. Ongoing fifth-generation (5G) standardisation activities are debating the amount of resources to be dedicated to the transmission of pilot sequences, focussing on uplink sounding reference signals (UL SRSs) design. In this paper, we extensively evaluate the performance of various UL SRS allocation strategies in practical deployments, shedding light on their strengths and weaknesses. Furthermore, we introduce a novel UL SRS fractional reuse (FR) scheme, denoted neighbour-aware FR (FR-NA). The proposed FR-NA generalizes the fixed reuse paradigm, and entails a tradeoff between i) aggressively sharing some UL SRS resources, and ii) protecting other UL SRS resources with the aim of relieving neighbouring BSs from pilot contamination. Said features result in a cell throughput improvement over both fixed reuse and state-of-the-art FR based on a cell-centric perspective.

Providing consistently high wireless capacity is becoming increasingly important to support the applications required by future digital enterprises. In this paper, we propose Eigen-direction-aware ZF (EDA-ZF) with partial coordination among base stations (BSs) and distributed interference suppression as a practical approach to achieve this objective. We compare our solution with Zero Forcing (ZF), entailing neither BS coordination or inter-cell interference mitigation, and Network MIMO (NeMIMO), where full BS coordination enables centralized inter-cell interference management. We also evaluate the performance of said schemes for three sub-6 GHz deployments with varying BS densities -- sparse, intermediate, and dense -- all with fixed total number of antennas and radiated power. Extensive simulations show that: (i) indoor massive MIMO implementing the proposed EDA-ZF provides uniformly good rates for all users; (ii) indoor network densification is detrimental unless full coordination is implemented; (iii) deploying NeMIMO pays off under strong outdoor interference, especially for cell-edge users.

We propose massive MIMO unlicensed (mMIMO-U) as a high-capacity solution for future indoor wireless networks operating in the unlicensed spectrum. Building upon massive MIMO (mMIMO), mMIMO-U incorporates additional key features, such as the capability of placing accurate radiation nulls towards coexisting nodes during the channel access and data transmission phases. We demonstrate the spectrum reuse and data rate improvements attained by mMIMO-U by comparing three practical deployments: single-antenna Wi-Fi, where an indoor operator deploys three single-antenna Wi-Fi access points (APs), and two other scenarios where the central AP is replaced by either a mMIMO AP or the proposed mMIMO-U AP. We show that upgrading the central AP with mMIMO-U provides increased channel access opportunities for all of them. Moreover, mMIMO-U achieves four-fold and seven-fold gains in median throughput when compared to traditional mMIMO and single-antenna setups, respectively., Comment: 6 pages, 5 figures

Nowadays, the demand for wireless mobile services is copious, and will continue increasing in the near future. Mobile cellular operators are therefore looking at the unlicensed spectrum as an economical supplement to augment the capacity of their soon-to-be overloaded networks. The same unlicensed bands are luring internet service providers, venue owners, and authorities into autonomously setting up and managing their high-performance private networks. In light of this exciting future, ensuring coexistence between multiple unlicensed technologies becomes a pivotal issue. So far this issue has been merely addressed via inefficient sharing schemes based on intermittent transmission. In this article, we present the fundamentals and the main challenges behind massive MIMO unlicensed, a brand-new approach for technology coexistence in the unlicensed bands, which is envisioned to boost spectrum reuse for a plethora of use cases., Comment: 6 pages, 6 figures

We consider cellular base stations (BSs) equipped with a large number of antennas and operating in the unlicensed band. We denote such system as massive MIMO unlicensed (mMIMO-U). We design the key procedures required to guarantee coexistence between a cellular BS and nearby Wi-Fi devices. These include: neighboring Wi-Fi channel covariance estimation, allocation of spatial degrees of freedom for interference suppression, and enhanced channel sensing and data transmission phases. We evaluate the performance of the so-designed mMIMO-U, showing that it allows simultaneous cellular and Wi-Fi transmissions by keeping their mutual interference below the regulatory threshold. The same is not true for conventional listen-before-talk (LBT) operations. As a result, mMIMO-U boosts the aggregate cellular-plus-Wi-Fi data rate in the unlicensed band with respect to conventional LBT, exhibiting increasing gains as the number of BS antennas grows., Comment: To appear in Proc. IEEE ICC 2017

We propose to operate massive multiple-input multiple output (MIMO) cellular base stations (BSs) in unlicensed bands. We denote such system as massive MIMO unlicensed (mMIMO-U). We design the key procedures required at a cellular BS to guarantee coexistence with nearby Wi-Fi devices operating in the same band. In particular, spatial reuse is enhanced by actively suppressing interference towards neighboring Wi-Fi devices. Wi-Fi interference rejection is also performed during an enhanced listen-before-talk (LBT) phase. These operations enable Wi-Fi devices to access the channel as though no cellular BSs were transmitting, and vice versa. Under concurrent Wi-Fi and BS transmissions, the downlink rates attainable by cellular user equipment (UEs) are degraded by the Wi-Fi-generated interference. To mitigate this effect, we select a suitable set of UEs to be served in the unlicensed band accounting for a measure of the Wi-Fi/UE proximity. Our results show that the so-designed mMIMO-U allows simultaneous cellular and Wi-Fi transmissions by keeping their mutual interference below the regulatory threshold. Compared to a system without interference suppression, Wi-Fi devices enjoy a median interference power reduction of between 3 dB with 16 antennas and 18 dB with 128 antennas. With mMIMO-U, cellular BSs can also achieve large data rates without significantly degrading the performance of Wi-Fi networks deployed within their coverage area.

In this paper, we explore reduced-connectivity radio frequency (RF) switching networks for reducing the analog hardware complexity and switching power losses in antenna selection (AS) systems. In particular, we analyze different hardware architectures for implementing the RF switching matrices required in AS designs with a reduced number of RF chains. We explicitly show that fully-flexible switching matrices, which facilitate the selection of any possible subset of antennas and attain the maximum theoretical sum rates of AS, present numerous drawbacks such as the introduction of significant insertion losses, particularly pronounced in massive multiple-input multiple-output (MIMO) systems. Since these disadvantages make fully-flexible switching suboptimal in the energy efficiency sense, we further consider partially-connected switching networks as an alternative switching architecture with reduced hardware complexity, which we characterize in this work. In this context, we also analyze the impact of reduced switching connectivity on the analog hardware and digital signal processing of AS schemes that rely on channel power information. Overall, the analytical and simulation results shown in this paper demonstrate that partially-connected switching maximizes the energy efficiency of massive MIMO systems for a reduced number of RF chains, while fully-flexible switching offers sub-optimal energy efficiency benefits due to its significant switching power losses., Comment: 14 pages, 11 figures

In this paper we revisit hybrid analog-digital precoding systems with emphasis on their modelling and radio-frequency (RF) losses, to realistically evaluate their benefits in 5G system implementations. For this, we decompose the analog beamforming networks (ABFN) as a bank of commonly used RF components and formulate realistic model constraints based on their S-parameters. Specifically, we concentrate on fully-connected ABFN (FC-ABFN) and Butler networks for implementing the discrete Fourier transform (DFT) in the RF domain. The results presented in this paper reveal that the performance and energy efficiency of hybrid precoding systems are severely affected, once practical factors are considered in the overall design. In this context, we also show that Butler RF networks are capable of providing better performances than FC-ABFN for systems with a large number of RF chains., Comment: 12 pages, 5 figures