Massive MIMO for Internet of Things (IoT) Connectivity

TL;DR

This paper explores how massive MIMO technology can be adapted for IoT connectivity in 5G, addressing unique challenges and opportunities for supporting diverse IoT applications like mMTC and URLLC.

Contribution

It investigates the applicability of massive MIMO to IoT, identifying opportunities, challenges, and proposing suitable communication schemes for heterogeneous IoT requirements.

Findings

Massive MIMO can benefit IoT connectivity with proper integration.

Trade-offs exist between spectral efficiency and reliability for IoT.

Network slicing with massive MIMO supports diverse IoT needs.

Abstract

Massive MIMO is considered to be one of the key technologies in the emerging 5G systems, but also a concept applicable to other wireless systems. Exploiting the large number of degrees of freedom (DoFs) of massive MIMO essential for achieving high spectral efficiency, high data rates and extreme spatial multiplexing of densely distributed users. On the one hand, the benefits of applying massive MIMO for broadband communication are well known and there has been a large body of research on designing communication schemes to support high rates. On the other hand, using massive MIMO for Internet-of-Things (IoT) is still a developing topic, as IoT connectivity has requirements and constraints that are significantly different from the broadband connections. In this paper we investigate the applicability of massive MIMO to IoT connectivity. Specifically, we treat the two generic types of IoT connections envisioned in 5G: massive machine-type communication (mMTC) and ultra-reliable low-latency communication (URLLC). This paper fills this important gap by identifying the opportunities and challenges in exploiting massive MIMO for IoT connectivity. We provide insights into the trade-offs that emerge when massive MIMO is applied to mMTC or URLLC and present a number of suitable communication schemes. The discussion continues to the questions of network slicing of the wireless resources and the use of massive MIMO to simultaneously support IoT connections with very heterogeneous requirements. The main conclusion is that massive MIMO can bring benefits to the scenarios with IoT connectivity, but it requires tight integration of the physical-layer techniques with the protocol design.

Tables

Table 1. Table I: Classification of random access protocols according to three features: type of pilot sequence, grant mode and device identification.

o —X—X—X—X—X—	Pilot sequences	Grant mode	Device ID
SUCRe	Orthogonal	Grant-based	yes
pilot RA	Orthogonal	Grant-free	yes
coded RA	Orthogonal	Grant-free	yes
CS-RA	Pseudo-random	Grant-free	yes
Unsourced RA	none	Grant-free	no

Equations

$$P_{\text{outage}}=\mathrm{Pr}\left[R>{\log }_2(1+\gamma )\right].$$

$$P_{\text{outage}}=\mathrm{Pr}\left[\gamma <{\gamma }_{\text{th}}\right].$$

$$\hat{\mathbf{h}}=\frac{1}{t}{\mathbf{Y}}_t{\mathbf{p}}^H$$

$$\displaystyle\gamma^{\text{DL}}_{\text{MRT}}=\dfrac{\rho}{\sigma_{n}^{2}}\dfrac{\mathinner{\!\left\lvert\widehat{\mathbf{h}}^{H}\mathbf{h}\right\rvert}^{2}}{\big{\lVert}\widehat{\mathbf{h}}\big{\rVert}^{2}},$$

$$\mathbf{h}=\sum _{i=1}^{N_P}{\alpha }_i{\mathbf{s}}_i.$$

$$\mathbf{R}=\mathbf{V}\Lambda {\mathbf{V}}^H.$$

$$\displaystyle\mathbf{w}_{\text{SV}}=\dfrac{\mathbf{VV}^{H}\widehat{\mathbf{h}}^{*}}{\big{\lVert}\mathbf{VV}^{H}\widehat{\mathbf{h}}^{*}\big{\rVert}}.$$

$${\gamma }_{\text{SV}}^{\text{DL}}=\frac{\rho }{{\sigma }_n^2}\frac{{\left|{\mathbf{h}}^T{\mathbf{VV}}^H{\hat{\mathbf{h}}}^{\ast }\right|}^2}{{\Vert {\mathbf{VV}}^H{\hat{\mathbf{h}}}^{\ast }\Vert }^2}.$$

$${\gamma }_1=\frac{{\left|{\mathbf{h}}_1{\mathbf{w}}_1\right|}^2}{{\sigma }_n^2\left|{\mathbf{h}}_1{\mathbf{w}}_1\right|+{\left|({\mathbf{h}}_1{\mathbf{w}}_1{)}^H{\mathbf{h}}_1{\mathbf{w}}_2\right|}^2}$$

$${\gamma }_{\text{FDD}}=\frac{\rho }{{\sigma }_n^2}\frac{{\left|{\mathbf{h}}^T{\mathbf{V}}_{N_s}{\hat{\mathbf{\beta }}}^H\right|}^2}{{\Vert {\mathbf{V}}_{N_s}{\hat{\mathbf{\beta }}}^H\Vert }^2},$$

Full text

I Introduction

I-A The Heterogeneous 5G services

Future 5G New Radio (NR) networks will support a variety of connections with heterogeneous requirements, built upon three generic types of connectivity illustrated on Figure 1: extended mobile broadband (eMBB), ultra-reliable low-latency communication (URLLC) and massive machine-type communication (mMTC). eMBB is a natural unfolding of LTE, where the primary goal is to increase the user data rates and network spectral efficiency. The enhancements provided by eMBB target mainly human-type traffic, such as high-speed wireless broadband access, ultrahigh-quality video streaming, Virtual Reality and Augmented Reality.

The other two services, URLLC and mMTC, are the cornerstones of machine-type traffic and thus enablers of various types of Internet of Things (IoT) connectivity. URLLC, also known as mission-critical IoT, envisions transmission of moderately small data packets (in the order of tens of bytes) with extremely high-reliability, ranging between $99.999\%$ and $99.9999999\%$, i.e. down to $10^{-9}$ packet error probability [1]. The user plane latency requirement is most commonly defined to be $1\text{\,}\mathrm{m}\mathrm{s}$, including uplink (UL) and downlink (DL) roundtrip transmission [2]. In URLLC the device activity pattern is often not deterministic, but rather intermittent. However, it is generally assumed that it is likely that only a few URLLC devices that are active simultaneously. URLLC is seen as an enabler of safety systems, wireless industrial robots, autonomous vehicles (cars, trucks, drones), immersive virtual reality with haptic feedback, tactile Internet, and many others which may not even be foreseen at this point.

mMTC aims to provide service to a vast number of devices, out of which only a certain fraction are active at a given time. The packet lengths in mMTC are comparable to URLLC, being assumed to be rather short, in the range of tens of bytes. The main challenge of mMTC is to enable access for sporadically active devices, such that at any given instant an unknown subset out of the massive set of devices wishes to send messages. Most mMTC applications do not have strict delay requirements. The performance is assessed in terms of how many devices can be served within a certain time-frequency resource grid, assuming a certain predefined level of reliability that is much lower compared to URLLC. Spectral efficiency (SE) becomes critical, as the overhead of transmitting very small, sporadic payloads from a large set of devices in a typical LTE-type network becomes considerable [3]. Energy efficiency is critical at the device side, as a large proportion of the mMTC devices are expected to be low-power sensors that are battery-driven. Therefore, even if access latency is not critical, collisions occurring in the access will affect the energy consumption of the devices. Furthermore, the deployment of some of these sensors can be in very remote or in low-coverage areas, which brings up the need of having extended coverage capabilities. Any massive deployment of connected devices falls into the category of mMTC, where devices are mainly sensors used to gather measurements from various environments, such as weather, industry, energy, agriculture, transport, etc. Note that the term IoT may be encountered as an umbrella term for mMTC, but we emphasize that in the context of 5G, IoT is also extended to cover mission-critical IoT, associated with URLLC.

I-B The Three Services in the Context of Massive MIMO

A massive antenna array is seen as a distinctive technology in the context of the next-generation wireless systems [4, 5]. The large number of spatial degrees of freedom (DoFs) created by the massive arrays contribute to achieving two important features: channel hardening and favorable propagation [6, 7]. The occurrence of channel hardening essentially means that the massive multi-antenna pre- or post-processing transforms the channel into almost deterministic quantities, making the links quasi-immune to small-scale variations of the instantaneous channel. The occurrence of favorable propagation means that as the size of the antenna array grows, the propagation channels to different users become more separable. Therefore, the many-antenna BS becomes more efficient in mitigating inter-user interference through the use of spatial multiplexing techniques.

The large array gain, coupled with these two features ensure that massive MIMO is the main enabler of high user throughput and high spectral efficiency for eMBB [8], [9]. In fact, the majority of works have optimized the use of massive MIMO in the context of the high-rate eMBB service. The use of massive MIMO for IoT connectivity has received significantly less attention in the research literature. Massive MIMO holds a potential to support transmission techniques that are suitable for both URLLC and mMTC. However, the massive MIMO techniques used for eMBB are not directly transferable to URLLC and mMTC due to vastly different requirements of these IoT-related services. This paper fills this important gap by identifying the opportunities, challenges and tradeoffs of exploiting massive MIMO for URLLC and mMTC.

In URLLC, the spatial DoFs are essential in attaining the high reliability requirements, as the low-latency requirement severely reduces the time diversity. The large number of spatial DoFs contribute to the channel hardening, reducing the odds of having a low energy channel realization that might result in an outage event. Furthermore, the large number of spatial DoFs combined with favorable propagation, enable good spatial separation of devices and thereby efficient spatial multiplexing. However, the efficient use of the large number of spatial DoFs is critically dependent on the channel estimation process, which in massive MIMO can be time-consuming and therefore not directly suited for low latency services. Thus, in supporting URLLC, massive MIMO operation should depart from its eMBB-optimized operation, in which the objective is to estimate the channel as fully as possible and then load the spatially multiplexed channels with highest possible rate. In URLLC, low latency dictates a shorter estimation period, which means that massive MIMO should either operate in a non-coherent mode or shorten the estimation process by relying on a structure present in the channel. Such structure can be manifested through, fro example, the second-order statistics. Furthermore, imperfect channel estimation affects inter-user interference, such that sometimes Time-Division Mutliple Access (TDMA) may be preferable to imperfect spatial multiplexing of users. Channel estimation complexity in the case of massive MIMO has lead also to a preference towards time-division duplexing (TDD), since in this case one can rely on the channel reciprocity between UL and DL channels. This is in contrast to frequency-division duplexing (FDD), where the task of estimating the DL channel becomes tedious.

The requirements of mMTC pose an entirely different set of problems, such as activity detection [10, 11, 12, 13], collision resolution [14, 15, 16, 17] and wide-area low-rate coverage. Massive MIMO can be used to efficiently support mMTC due to the following two features: (i) the favorable propagation property enables multi-user detection (MUD) for a large number of devices; (ii) the array gain can boost the signal-to-noise ratio (SNR) for extended coverage requirements. Considering the fact that the central problem in mMTC is the detection of the activity and decoding of the data for an unknown subset of sporadically active devices, the primary benefit from massive MIMO for mMTC is likely to be in the large spatial multiplexing capability. The large number of antennas are instrumental in utilizing the sparsity in activity detection. Furthermore, in the event of sudden, large number of correlated arrivals, the large array is capable to absorb and resolve a large number of devices as well as decode the associated data packets.

This paper addresses the means through which massive MIMO enables URLLC and mMTC. Besides the support of the individual services, we also discuss the suitability of massive MIMO to support a mix of different services through slicing of the wireless resources [18]. This will reveal interesting tradeoffs that arise due to interaction among the services while trying to exploit the massive number of antennas. As this paper shows, massive MIMO can be a powerful instrument in the quest of fulfilling the requirements of IoT connectivity. However, in order to fully reap its benefits, physical layer signal processing techniques need to be integrated with protocol design, with techniques such as channel estimation, retransmission, random access, scheduling, etc.

The paper is organized as follows. The next section discusses the related work. Section II-B discusses 5G standardization aspects and the 3GPP approach to MTC and mMIMO. Sections III and IV discuss specific aspects of employing mMIMO to achieve URLLC and mMTC, respectively. Section V provides considerations on network slicing in a mMIMO network, and Section VI provides conclusions and offers further research directions.

II Related works

II-A Research Literature

II-A1 Massive MIMO for eMBB

The quest for maximizing SE in eMBB is considered to be the main motivation of using massive MIMO [5, 8]. In order to achieve high SE, careful optimization of the number of spatially multiplexed users, as well as channel training overhead needs to be considered. As the number of antennas increase, channel hardening becomes more effective [19]. On the other hand, as the channel exhibits more spatially correlated scattering, the channel hardening effect occurs to a smaller extent [6, 19]. Therefore, the trade-off between array size and the number of DoFs per user has been investigated [9] from the perspective of the achievable rate.

Pilot contamination in a multi-cell massive MIMO system is largely considered as the most severe limiting factor in achieving high SE [20, 21, 22]. However, recent developments [23] show that even in the presence of pilot contamination, the capacity of massive MIMO systems is unbounded as the number of antennas grow, for the case of spatially correlated channels.

II-A2 URLLC and massive MIMO

The general principles of achieving URLLC have been discussed in [24], where the importance of optimizing the reliability of the signaling information is highlighted, as well as efficient utilization of the diversity sources. URLLC is treated from a massive MIMO perspective in [25], where the authors emphasize the requirements of tactile Internet and how many antennas are needed to meet the requirements for a given number of simultaneous users, using maximum-ratio transmission (MRT) and zero-forcing (ZF) beamforming, and assuming ideal channel estimation. However, in practice, channel estimation is rarely ideal, being affected by imperfections or pilot interference between users. In this sense, [26] proposes exploiting the forward error correction (FEC) code diversity in order to assign unique user signatures, which allow separating the pilot-interfering users.

Coherent and non-coherent UL transmissions are compared in [27] for the case of multi-antenna base-station (BS) and single- or two antennas at the transmitting device. The authors conclude that non-coherent transmission requires higher SNR to achieve the target reliability, and that the single-antenna at the transmitter is not a limiting factor in achieving high reliability.

A stochastic network calculus approach is adopted in [28], where the authors evaluate the latency-reliability trade-off using the delay violation probability. It is shown that increasing number of antennas (however, only up to $M=10$) considerably reduces the delay violation probability. A similar approach is taken in [29] with respect to the evaluated metric, where the authors model the latency-reliability trade-off by imposing a probabilistic constraint on the length of the queue at the BS. The end-to-end delay, comprising queueing delay, frame transmission and backhaul latency has been considered in [30], where the authors consider the joint optimization of transmit power, bandwidth and number of active antennas for a given number of active users in order to maximize the energy efficiency under Quality-of-Service (QoS) constraints of a massive MIMO network.

II-A3 mMTC

In [31], authors focus on the massive mMTC service within a multi-service air interface. Authors discuss in a broad sense the different physical and medium access techniques to tackle the problem of a massive number of access attempts in mMTC. The main conclusion is that, in order for mMTC to take place, there is a need for efficient access protocols capable of withstanding a massive number of devices that contend for network access. Physical layer techniques include a) multi-user detection using compressive sensing (CS) techniques, b) collision resolution and harnessing of interference using physical layer network coding, and c) non-orthogonal access with relaxed time-alignment. In terms of medium access layer, techniques include a) coded random access and signature based access, b) one/two-stage random access and fast uplink access protocols with a focus on latency reduction.

Grant-free mMTC activity and data detection is tackled in [32], where the authors consider a massive MIMO scenario and employ compressed sensing to retrieve the device activity and the short messages. Another approach of solving the activity detection and collision resolution is the grant-based strongest-user collision resolution (SUCR) protocol described in [14]. The reason for using such an approach is to be able to solve the collisions prior to the channel training phase and data transmission, with a limited number of orthogonal pilot sequences which is much lower than the total number of devices. In an mMTC scenario, the number of devices can easily exceed the number of orthogonal pilots; therefore, collision resolution methods have been proposed in the literature, and are summarized in [33].

Throughout the paper we will use boldface small ($\mathbf{x}$) and boldface capital letters ($\mathbf{X}$) to denote vectors and matrices, respectively. The superscripts $(\cdot)^{*}$, $(\cdot)^{T}$ and $(\cdot)^{H}$ denote the conjugate, transpose and the conjugate transpose operations, respectively, and $\mathinner{\!\left\lvert\cdot\right\rvert}$ and $\left\lVert\cdot\right\rVert$ denote the absolute value and the $\ell_{2}$ vector norm. The notations $\Pr[\cdot],\mathbb{E}[\cdot]$ and $\text{RSD}[\cdot]$ denote the probability of an event, the expectation and the relative standard deviation of a random variable, respectively.

II-B *3GPP standardization *

5G NR will include the key aspects of massive MIMO, namely advanced antennas with complex digital beamforming, or hybrid analog/digital beamforming, and large antenna arrays. In 2018, 3GPP froze the first 5G NR specification, Release 15 [34], focusing on early commercial deployments and a subset of the 5G requirements, mainly related to eMBB. 5G NR R15 supports a maximum of 256 antenna elements, compared to the 64 elements in Release 13. With massive MIMO, beamforming is exploited by combining multiple antenna elements to focus the power in a specific direction. 5G NR specifies new initial access techniques for beamforming that will utilize beams sweeping so that the BS can identify the strongest beam and establish a connection. The MIMO implementations in NR support frequencies below and above 6 GHz, and FDD and TDD.

The second phase of the standardization, to be finalized at the end of 2019, targets fulfillment of the full set of 5G requirements. Particularly, there is a work item dedicated to the MIMO improvements that includes, among others, enhancements to the multi-beam and multi-transmission point operation and to the multi-user MIMO (MU-MIMO). Physical layer enhancements for URLLC and the industrial IoT are also part of the on-going work.

One remarkable feature for the support of massive MIMO was the introduction, already in LTE-A, of Full-Dimension MIMO (FD-MIMO). FD-MIMO utilizes an active antenna system (AAS) with a 2D plannar array structure, which allows for a large number of antenna elements to be packed. Even more important is the possibility of adaptive electronic beamforming, to form a beam in both horizontal and vertical direction and cover any point in the 3D space.

The 5G NR frame [35] has been designed with the premise of providing the necessary flexibility to support a heterogeneity of 5G services and requirements. Figure 2 illustrates some possible configurations. The general design principle is that static and/or strict timing relations are avoided. For example, asynchronous hybrid automatic repeat request (HARQ) is used instead of predefined retransmission time. A slot is defined as 7 or 14 orthogonal frequency-division multiplexing (OFDM) symbols for subcarriers up to 60 kHz, and 14 OFDM symbols for subcarrier spacing higher than 60 kHz. Data transmission can span multiple slots, to increase the coverage or reduce the overhead due to switching and control information. The TDD DL/UL scheme is much more flexible than in LTE: a slot can contain all DL, all UL, or almost any other DL/UL ratio, and the pattern can be changed in each slot or subframe. A faster TDD switching allows for a more flexible capacity allocation. The possibility of having sounding reference symbols (SRS) in every slot allows a more optimized TDD channel reciprocity and therefore more efficient massive MIMO. Low-latency for URLLC cases is possible thanks to faster TDD turn-around and the self-contained concept, such that data and ACK can be scheduled in the same slot. For low latency transmissions, a mini-slot has a flexible start position (it can start at any time) and a duration shorter than a regular slot duration. The mini-slot can be as short as one OFDM symbol and it constitutes the smallest scheduling unit.

For the Channel State Information (CSI), 5G NR introduces Type I and Type II CSI [35]. The former is the normal codebook-based CSI feedback where the device sends back a precoder matrix indicator (PMI) to the gNB, and it supports multi-panel scenarios by having a co-phasing factor across antenna panels. The Type II is an enhanced scheme that enables explicit feedback and/or codebook-based feedback with higher spatial resolution. It can report the wideband and sub-band amplitude information of the selected beams, such that better precoded MIMO transmission can be employed by the network.

Release 15 has prioritized eMBB services, while the full support for URLLC and mMTC services is expected to be completed in Release 16 and beyond. Specifically, there are on-going activities in the form of work and study items on physical layer enhancements for NR URLLC, channel modelling for indoor industrial scenarios, and NR Industrial Internet of Things (IoT).

Another important feature in NR is the efficient support of a mix of services. Network slicing is the virtualized technology framework that will accommodate the high requirements heterogeneity of 5G MTC networks [18]. Significant progress has been done in 3GPP with regard to the core network and the functional aspects with, e.g., the definition of the network slice identifiers, and procedures and functions for slice selection. However, the exploitation of network slicing in the Radio Access Network (RAN) is not mature in the specification yet. In the research domain, the authors in [36] propose a functional framework for the realization of network slicing management in the RAN, whereas [18] discusses the communication-theoretic limits. As it will be discussed in Section V, the implementation of network slicing in a massive MIMO deployment presents additional challenges and opportunities.

III Massive MIMO solutions for URLLC

This section presents an overview of the latency and reliability metrics of URLLC, and discusses how the properties of massive MIMO can enable achieving these strict constraints. Downlink transmission is considered for the most part, as the acquisition of the CSI is more critical at the massive antenna transmitter, especially under a strict latency constraint. Beamforming methods with imperfect CSI are studied in a single-user TDD system, then extended to the two-user multiplexing case with a varying constraint on the latency. Feasibility of low-latency FDD operation is also discussed in the DL scenario of URLLC, as well as a few methods for UL transmissions with deteriorated CSI.

III-A URLLC Metrics: Physical Layer Reliability and Latency

In URLLC, the most important metrics are latency and reliability. Several types of latency are encountered in the context of URLLC. The most common is the user-plane radio latency, defined in [37, 38] as the time duration between a packet arriving at the transmitting layer-2 radio protocol and its delivery at the receiving layer-3 protocol. The reliability is defined by 3GPP as the probability of successfully transmitting a number of bytes within a certain user-plane delay. More specifically, a general requirement for URLLC is a reliability of ${1-10^{-5}}$ for transmitting a 32-byte packet within 1 ms user-plane latency. Within the user-plane delay, the user-plane reliability can be increased if retransmissions are performed. In this case, the physical layer latency must be smaller than the user-plane latency, whereas the physical layer reliability may be lower than the target user-plane reliability, which would be compensated by retransmissions.

For the remainder of this section, we will only focus on the physical layer latency, which we will simply refer to as latency. In a communication theoretic sense, the physical layer latency of a packet is commonly expressed in terms of the number of symbols (or channel uses) it takes to transmit it. For a fixed data size, the more symbols available, the lower the rate and the higher the reliability becomes. Therefore, in a scenario where we have a certain number of bits to transmit, we can aim for a target reliability under varying latency, or for a target latency with unconstrained reliability. Let us consider the latter option for now, such that $b$ bits need to be transmitted within a certain latency of $N$ symbols. Note that the conversion of the latency into actual time requires specification of the bandwidth user in the system [38]. Unless explicitly stated otherwise, here we assume a normalized bandwidth and focus on the rate in terms of bits per channel use. This imposes a transmit rate $R=b/2N$ for a complex channel, where one symbol can be regarded as two channel uses in a real channel. The physical layer reliability can be expressed as the complementary event to achieving an outage in the transmission, that is ${1-P_{\text{outage}}}$. Considering the fact that the impact of quasi-static fading dominates the effect of the finite blocklength [3], the outage probability is defined as follows:

[TABLE]

Provided that the rate is fixed, as well as that transmissions are scheduled and are thereby free of interference, from (1) it follows that there exists a threshold SNR $\gamma_{\text{th}}=2^{R}-1$ such that a packet encoded with rate $R$ can be reliably decoded. Therefore, the outage probability can be expressed as:

[TABLE]

III-B Favorable Massive MIMO Properties and CSI Acquisition

Due to the low-latency constraint, it is very challenging to use time diversity in order to support URLLC. At the physical layer URLLC can benefit from frequency diversity provided by the wideband OFDMA, as well as from space diversity offered by the massive antenna arrays. Space diversity manifests through the two phenomena mentioned previously: channel hardening and favorable propagation [6, 19]. Channel hardening is particularly important for URLLC, as it diminishes the impact of small-scale fading in a similar fashion as time diversity would do over multiple coherence intervals. Favorable propagation is important when performing spatial multiplexing of several URLLC devices, as it ensures that the streams to the devices can be well separated at the massive array BS, provided that the BS has obtained CSI from the devices.

In order to make use of downlink precoding schemes, the massive array transmitter must be aware of the CSI. The task of acquiring DL CSI at the transmitter is challenging in FDD systems, since the training length is dependent on the number of BS antennas. In contrast, in TDD systems channel reciprocity is assumed between UL and DL, and therefore, UL training can be utilized to estimate the channel coefficients at all antennas simultaneously, i.e. the training length is independent of the number of antennas. This mode of operation alleviates the CSI acquisition procedure, such that massive MIMO is commonly based on TDD operation.

III-C Imperfect full CSI

Assuming the case of one single-antenna device, the BS can estimate the channel coefficient for each antenna based on the UL pilots sent by the device by using the least squares (LS) method. The $M\times 1$ vector estimate of the channel coefficients can be expressed as

[TABLE]

where $t$ is the training length, $\mathbf{p}$ is the $1\times t$ pilot vector fulfilling $\mathbf{p}^{H}\mathbf{p}=t\mathbf{I}$, and $\mathbf{Y}_{t}$ is the $M\times t$ received training signal. The noisy LS estimates for the channel coefficients at each BS antenna $\widehat{\mathbf{h}}$ are then used to perform DL MRT. The transmitter uses the precoding filter $\mathbf{w}_{\text{MRT}}=\widehat{\mathbf{h}}^{H}/\lVert\widehat{\mathbf{h}}\rVert$, and the DL MRT SNR at the device is then:

[TABLE]

where $\rho$ and $\sigma_{n}^{2}$ denote the transmit power and the noise variance, their ratio being the pre-processing SNR.

III-D Exploiting channel sparsity

In reality, fading channels are not seen as i.i.d. coefficients from the massive array BS. Instead, the coefficients experience a certain correlation, based on the spatial structure of the propagation environment. Let us consider the case of a cluster-based channel model, in which each cluster is characterized by a set of propagation paths based on their angle of departure (AoD) and their angle of arrival (AoA) [6, 9]. In addition, each propagation path incurs an attenuation given by an independent fading coefficient following a zero-mean circularly symmetric complex Gaussian distribution, with exponentially distributed power, decreasing with a power decay factor, defining the maximum decrease between the strongest and weakest path.

In a simplified form, for a single-antenna user, the channel can be expressed as the following column vector

[TABLE]

Here, $N_{P}$ is the total number of paths, $\alpha_{i}$ is the fading coefficient of path $i$, and $\mathbf{s}_{i}$ is the normalized steering vector for each path.

This spatial structure of the channel can be captured using second order statistics, more specifically, by estimating the channel correlation matrix of each device at the BS [6], which is defined as $\mathbf{R}=\mathbb{E}[\mathbf{h}\mathbf{h}^{H}]$, where the expectation is taken over the channel realizations. In addition to the TDD channel reciprocity, let us assume that the the correlation matrix of the device is perfectly known at the BS. This sets the context to discuss how the precoding can be enhanced using the second-order statistics of the channel.

The correlation matrix takes the following form when expressed based on the singular value decomposition:

[TABLE]

Here, $\mathbf{V}$ is an $M\times N_{p}$ matrix containing the singular vectors of the channel and $\Lambda$ is the diagonal matrix containing the $N_{P}$ eigenvalues of the channel. Both the instantaneous estimated channel coefficients $\widehat{\mathbf{h}}$ and the channel second-order statistics in the form of the singular vectors (SV) $\mathbf{V}$ can be utilized in forming the DL precoding vector $\mathbf{w}_{\text{SV}}$.

The procedure [39] consists in projecting the instantaneous channel estimate vector $\widehat{\mathbf{h}}$ on the subspace spanned by the singular vectors $\mathbf{V}$. The result is $\widehat{\mathbf{h}}^{T}\mathbf{V}$, which represents the instantaneous fading coefficients for each singular vector, thereby being a refined instantaneous estimate, as the noise lying outside of the subspace of the singular vectors is eliminated. This result is then used to form the projected estimated channel $\widehat{\mathbf{h}}^{T}\mathbf{VV}^{H}$, its matched filter being the beamforming vector

[TABLE]

The DL SNR has then been showed [39] to be

[TABLE]

Compressed sensing methods could potentially be employed as well, however, at the expense of higher complexity and latency.

III-E Impact of training duration

The training length is an important parameter, especially when dealing with low-latency transmissions. Figure 4 shows the dependence of the mean and relative standard deviation (RSD) of the DL SNR $\gamma$ on the training length, for the MRT scheme and for the SV-based precoding. It can be seen that increasing the number of training symbols for the SV-based scheme provides minimal increase in average SNR and minimal decrease in RSD. However, it can be noticed that MRT is more sensitive to the training length, such that increasing the training length can be beneficial. Figure 5 shows how the outage varies in a latency constrained scenario where the total number of channel uses are limited, as the training symbols are increased. It can be seen that for the case of 28 symbols (2 slots of 14 symbols with one subcarrier of 60 kHz, corresponding to 0.5 ms duration), the optimal number of training symbols is slightly different for the two schemes. Note that as more symbols are used for training, fewer symbols remain for data, therefore, a higher rate and SNR threshold being required to successfully decode the packet. Furthermore, it can be seen that the scheme relying on projecting the channel estimate on the singular vector subspace achieves between 1 and 2 magnitudes lower outage probability. It is, therefore, worthwhile to consider such a precoder which can exploit the channel correlation in order to refine the instantaneous CSI.

III-F Multi-user setting: SDM vs TDM

In a multi-user setting, another trade-off arises in terms of how to allocate the DoFs between the multiplexed devices. If spatial multiplexing, or space division multiplexing (SDM), is employed, the spatial DoFs are shared, whereas if time division multiplexing (TDM) is employed, the devices use the full spatial DoFs, but share the time resources.

SDM can be particularly suitable when the devices share the same latency requirements, as they can be served simultaneously with a fixed physical layer latency. Therefore, in SDM, the average device latency is equal to the system level latency. Here, by system level latency we consider the total latency required to serve the devices.

TDM, on the other hand, may be suitable when the latency requirements may differ, or when traffic is prioritized. In TDM, the devices experience different latency, depending on the transmission priority. Therefore, the average device latency is smaller than the system level latency.

The effects of the two multiplexing strategies can be observed in Figure 6. TDM requires higher system latency to serve both devices with the same reliability as SDM with ZF. This is due to the increased data rate caused by the sharing of time resources, which, in turn, causes the threshold SNR $\gamma_{\text{th}}$ to soar. However, the first device experiences lower latency and, for this reason, the average device latency is similar for the two schemes, despite the overall system latency being higher in the case of TDM than SDM. This further states that SDM is more suitable when multiplexing devices with the same latency requirement, and that TDM is suitable for multiplexing devices with distinct latency characteristics.

The efficiency of spatially multiplexing the devices depends on several factors, such as which multiplexing technique is used (here MRT and ZF) and the channel estimation accuracy. The signal-to-interference-and-noise ratio (SINR) when multiplexing two devices can be expressed, regardless of the multiplexing technique, as:

[TABLE]

where $\mathbf{w}_{i}$ is the beamforming vector for each device, depending on the beamforming method. If MRT is used, the numerator is maximized, without taking into account the interference term in the denominator. If ZF is used, the interference term in the denominator is minimized. The extent to which this can be performed is dictated by the accuracy of the channel estimate which is used in $\mathbf{w}_{2}$. For low-SNR scenarios, several pilot symbols per device or estimation refinement using second order statistics are beneficial in order to improve the multiplexing efficiency.

III-G Feasibility of FDD in URLLC

Legacy systems benefit from operating in FDD for two main reasons: lower latency and no need for guard-time when switching between UL and DL. However, due to the channel estimation procedures, massive MIMO is generally assumed to operate in TDD. FDD operation is possible in massive MIMO only when the channel is assumed to be sparse, such that the BS is able to estimate the instantaneous coefficients of the dominant paths in the DL by transmitting orthogonal pilots, and then receiving the coefficients as a feedback from the device. This operation incurs considerable overhead, which increases with the number of dominant propagation paths, as the number of DL orthogonal pilots and the number of symbols used for UL feedback scale with the number of dominant paths.

Let us assume that the correlation matrix is known at the BS, therefore the BS knows the dominant singular vectors and their relative power, represented by the diagonal eigenvalue matrix. With this knowledge, the BS constructs an orthogonal set of pilots equal to the number of singular vectors to be estimated. Note that the number of singular vectors to be estimated does not necessarily have to be the full size of the dominant eigenspace ($N_{s}<N_{P}$). The DL SNR can be expressed similarly to (8) as:

[TABLE]

where $\widehat{\bm{\beta}}=\widehat{\mathbf{h}_{\text{DL}}^{T}\mathbf{V}_{N_{s}}}$ are the estimated coefficients for each singular vector which are in the simplest case fed back in an analog manner [40].

The trade-off between the outage probability and the number of singular vectors to estimate is shown in Figure 7. It can be seen that for $N_{P}=4$, all the singular vector instantaneous coefficients should be estimated in order to minimize the outage. However, as the channel diversity increases, the optimal $N_{s}$ becomes as low as 6 for a channel with a total of $N_{P}=16$ paths. This is due to the increasing overhead required to estimate additional SVs.

Figure 8 shows the latency-reliability trade-off for TDD and FDD. It can be seen that in TDD, utilizing the SV-based scheme provides considerable improvements over MRT. For both schemes, the number of training symbols is optimized such that the reliability is maximized for each latency. The training varies between 1-3 and 1-2 symbols for TDD-MRT and TDD-SV, respectively, out of a total of between 20 and 40 channel uses defining the latency. For FDD, the performance is degraded compared to TDD schemes, due to the increased overhead required to estimate the SVs. The optimal number of DL training symbols that maximizes the reliability for the same 20 to 40 channel uses is varying between 3-9 symbols, being therefore up to 3 times higher than in TDD. However, this is not to say FDD is infeasible, but only to highlight that in a massive MIMO scenario it becomes less efficient than TDD.

III-H Non-coherent massive MIMO

For scenarios where the channel may vary rapidly throughout a packet transmission due to high mobility, schemes that do not rely on channel acquisition have been investigated from a reliability perspective [41, 42, 43]. Non-coherent energy detection (ED) in the UL at a large antenna array has been proposed [41], as it does not rely on the instantaneous channel coefficients. The procedure exploits the channel and noise hardening phenomena, which make the channel more deterministic, such that the pulse amplitude modulated signals can be decoded reliably based on the received energy, only with the knowledge of long-term statistics of the channel. An extension of this idea has been considered in [42], where a constellation allowing both coherent and non-coherent reception of symbols has been proposed. The reliability is shown to be increased for a 2 bit/symbol rate compared to the case of QPSK, when channel estimation proves to be inaccurate. Depending on whether training symbols have been invested in obtaining an instantaneous channel estimate, one of these schemes can be employed in the UL in order to increase reliability in severe fading conditions when CSI is unavailable or degraded.

IV Massive MIMO for mMTC

The challenges brought by mMTC stem from the massive number of deployed MTC devices. The MTC traffic is usually sporadic and unpredictable, as the MTC devices transmit in an uncoordinated way whenever they have data to transmit. The main question is how to detect the activity and successfully decode the data from a maximal number of transmitting mMTC devices in the uplink within a limited bandwidth.

The general model used for random access in mMTC is that a very large number of devices operate in an uncoordinated fashion. At any time, only a small subset of the total are active, i.e., with some payload to be sent. Massive MIMO plays an important role in mMTC random access. The fundamental benefit offered by massive MIMO is the large spatial multiplexing gain, allowing accommodation of a large number of devices transmitting simultaneously, resolution of collisions and efficient data decoding, such as compressed sensing. Enhanced array gain and channel hardening are important features as well. In particular, channel hardening enables a simple collision resolution procedure in section IV-B and grant-free coded-random access transmission in section IV-C.

IV-A Random Access Protocols with Massive MIMO

This section treats several random access protocols models for massive MTC. The protocols differ according to the resource that is randomly accessed, how training is performed, as well as how data is transmitted and decoded.