UNIVERSITÁ DIPISA
DOTTORATO DI RICERCA IN INGEGNERIA DELL’INFORMAZIONE
E
NERGY EFFICIENT CELLULAR NETWORKS FOR
5G
COMMUNICATIONS SYSTEMS
DOCTORAL THESIS
Author
Andrea Pizzo
Tutor (s)
Prof. Luca Sanguinetti Prof. Marco Luise
The Coordinator of the PhD Program
Prof. Marco Luise
Pisa, October 2018 XXXI Cycle
Prof. L. Sanguinetti University of Pisa
Prof. M. Luise University of Pisa
Composition of the doctoral committee:
Prof. M. Moretti (chairman) University of Pisa
Prof. S. Tomasin University of Padova
Prof. O. Simeone King’s College London
External evaluators of the PhD dissertation:
Prof. M. di Renzo University of Paris-Saclay
Prof. E. A. Jorswieck Dresden University of Technology
An electronic version of this dissertation is available at: https://etd.adm.unipi.it/.
“When you change the way you look at things,
the things you look at change.”
– Max Planck
Summary
I
N this thesis, we attempt to solve the problem of optimally design a cellularnet-work in order to maximize the energy efficiency (EE). The problem at hand is addressed considering two potential candidates for future multi-antenna communi-cations systems: Massive multiple-input multiple-output (MIMO) (300 MHz-6 GHz) and millimeter Wave (mmWave) (6 GHz-300 GHz). Both solutions have been proposed by communication theorists to solve the x1000 data challenge for future wireless mo-bile networks, which requires an improvement of the area throughput by three orders of magnitude. In the former, a large number of low power radiating elements serves simultaneously multiple users on the same time-frequency resource offering high mul-tiplexing gain, while the latter exploits the huge amount of spectrum available in the mmWave band to boost channel capacity.
Despite being very different communications paradigms, both technologies require more hardware to be deployed, thus inevitably increasing the overall network energy demand. In the case of mmWave this additional hardware is due to both an increase in the number of base station (BS) antennas, to compensate for the severe path loss, and deployment of more BSs to enhance coverage of a cellular network. The higher inter-ference, resulting from the larger number of users located in the proximity of each other is handled by shifting the carrier frequency up so that narrower radiating beams can be created without increasing the antenna size. Differently, Massive MIMO privileges increasing the number of BS antennas compared with terminals to create additional degrees of freedom which are used to separate the users spatially.
For this reason, when optimizing a cellular network, EE should be considered rather than typical data rate optimization. This is because the communications systems must be evaluated not only in terms of the benefits they bring, e.g., higher data rate, but also by the hardware cost to deploy them and the complexity of the processing that is used to achieve those rates. The EE analysis takes all of these factors into consideration by negatively weighting network architectures that require higher energy consumption than others to work. As a consequence, it is not clear whether these technologies, which are certainly providing higher data rate, could be effectively employed to build future sustainable cellular networks. Our goal is to explore the potential benefits of using
mmWave and Massive MIMO in improving the EE of a cellular network.
Particularly, by changing the focus of the network design, the network operating points obtained considering this different objective cost will reasonably trade-off some of the degrees of freedom available for increasing the data rates (e.g., number of anten-nas per BS, number of BSs, number of users) for decreasing the energy demand of the network. It’s within the scope of this thesis to determine to what extent EE will change the shape of future cellular networks.
Outline
This thesis consists of five chapters. Chapter 1 is the introduction, Chapter 2, 3 and 4 form the main material of the thesis, while Chapter 5 gives our conclusions and recommendations for future research works.
Reproducible research
In order to promote reproducibility of research results, the simulation codes are freely and publicly available for most of my scientific publications at the webpage
https://github.com/lucasanguinetti/. Objectives and contributions
Specifically, with regards to these main chapters, we now briefly summarize the main objectives and list the main contributions per chapter.
Chapter 2: Optimal Design of Energy-Efficient mmWave Wireless Backhaul Wireless backhauling at mmWave band offers to be a cost-efficient alternative to the commonly available wired solutions. This work analyzes a mmWave single-cell net-work, which comprises a macro BS and an overlaid tier of small-cell BSs using a wire-less backhaul for data traffic. Large array gains are needed to compensate for the high channel attenuations at those tiny wavelengths due to, e.g., rain, blockage, penetration and reflection losses. This requires coherent beamforming at each antenna with a ded-icated baseband and radio frequency chain operating at very high frequencies, which poses several implementation challenges mostly because of hardware limitations due to power consumption and components size.
Wireless backhauling at mmWave is first considered in [1], e.g., for a beam align-ment problem in a point-to-point line-of-sight (LoS) deployalign-ment using an analog-only transceiver. Our work differs from that in the following aspects:
• considers hybrid transceiver architecture at the BS, which trades-off some digital signal processing power for improving scalability offered by analog systems. The performances of the chosen hybrid scheme are compared to the corresponding fully-digital;
• looks for the optimal number of antennas at both BS and small-cell BSs that max-imize the EE of the system. To this end, a realistic power consumption model is accurately derived for the considered transceiver architecture that depends non-linearly on the network parameters;
v
• derives closed-form expressions for the EE-optimal values of the number of an-tennas that provide valuable insights into the interplay between the optimization variables and hardware characteristics;
• numerical simulations are conducted to extend the result to a more realistic non-line-of-sight (NLoS) clustered channel model. Both numerical and analytical re-sults show that the maximal EE is achieved by a close-to fully-digital system wherein the number of BS antennas is approximately equal to the number of served small cells.
The results contained in this chapter have been published in:
Pizzo, A., and Sanguinetti, L. (2017, May). Optimal design of energy-efficient millimeter wave hybrid transceivers for wireless backhaul. 2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt). Paris. IEEE.
Chapter 3: Network Deployment for Maximal Energy Efficiency with Multislope Path Loss
In [2] the authors aim to design the uplink (UL) of a cellular network for maximal EE. Each BS is randomly deployed within a given area and is equipped with M antennas to serve K users. A single slope path loss model is used regardless of the distance between the user equipment and the serving BS. Maximum ratio combining is used at the BSs for data detection, under the assumption that channel state information is acquired by using orthogonal pilot sequences (reused across the network). Within this setting, it was found that a cellular network can benefit from the joint usage of small-cells and Massive MIMO. This improvement is justified by the combined effect of pushing the users closer to the serving BSs (lower propagation losses) and the ability of Massive MIMO to handle multi-user interference (high signal to interference and noise ratio).
Our research extends the one in [2] into multiple directions, among which:
• multislope path loss model (where received power decays as d−α(d)over a distance
d) is considered to accurately describe the non-stationarity of the propagating en-vironment instead of a single-slope model (received power decays as d−α);
• different linear detection schemes at the BS, e.g., maximum ratio (MR), zero-forcing (ZF) and multicell minimum mean squared error (M-MMSE);
• probabilistic coordination-free pilot assignment replaces the deterministic pilot sequences use across the network.
The chapter can be divided in two distinct parts:
1. in the first one, we numerically evaluate the optimal BS density and pilot reuse fac-tor for a Massive MIMO network with three different detection schemes, namely, MR, ZF and M-MMSE. A lower bound on the UL spectral efficiency (SE) and a realistic circuit power consumption model are used to evaluate the network EE. Our numerical analysis shows that the EE is a unimodal function of BS density and achieves its maximum for a relatively small density of BS, irrespective of the
employed detection scheme. This is in sharp contrast to the single-slope (distance-independent) path loss model, for which the EE is a monotonic non-decreasing function of BS density.
2. in the second part of this chapter, we concentrate on ZF and use stochastic geom-etry to compute a new lower bound on the average ergodic SE, which is valid for any multi slope path loss model. The provided theoretical formula is then used to optimize, for a given BS density computed numerically in the first part, the pilot reuse factor, number of BS antennas and users. This approach, in fact question the EE-optimality of a Massive MIMO configuration for such cellular networks. Closed-form expressions are computed from which valuable insights into the in-terplay between optimization variables, hardware characteristics, and propagation environment are obtained suggesting that Massive MIMO is the way to be pursued to maximize the EE of a cellular network.
The results contained in this chapter have been published in:
Pizzo, A., Verenzuela, D., Sanguinetti, L. and Björnson, E. (2017, December). Network Deployment for Maximal Energy Efficiency in Uplink with Zero-Forcing. 2017 IEEE Global Communications Conference. Singapore. IEEE.
Pizzo, A., Verenzuela, D., Sanguinetti, L. and Björnson, E. (2018, May). Network Deployment for Maximal Energy Efficiency in Uplink with Multislope Path Loss. IEEE Transactions on Green Communications and Networking. (Vol. 2, pp. 735 - 750). IEEE.
Chapter 4: Solving Fractional Polynomial Problems by Polynomial Optimization Theory
Typically, fractional problems whose objective is given by a concave-convex ratio can be solved by using fractional programming theory, which provides us with convergent algorithms with limited complexity [3]. Alternatively, suboptimal methods may be used, e.g., alternating optimization [4] (requires convexity with respect to the individ-ual variables), semidefinite relaxation [5] (only applies to quadratic polynomials and handles at most two constraints) or sequential fractional programming [6, 7] (difficult to extend to multivariate polynomials).
This chapter aims at addressing a special class of fractional problems wherein the objective is given by a ratio of multivariate polynomials, i.e., fractional polynomial problem (FPPs). The proposed optimization framework uses polynomial optimization theory to solve FPPs, not necessarily defined by concave and/or convex functions.
In particular our work:
• extends the fractional programming theory to work with multivariate polynomially-constrained polynomial rational functions (generally non-convex);
• provides an iterative algorithm that is provably convergent and enjoys asymptotic optimality properties;
• the proposed optimization framework is then applied to a rate-constrained EE maximization problem in multiuser multiple-input multiple-output (MU-MIMO)
vii
communication systems. Numerical results are used to validate its accuracy in the non-asymptotic regime.
The results contained in this chapter have been published in:
Pizzo, A., Zappone, A. and Sanguinetti, L. (2018, October). Solving Fractional Polynomial Problems by Polynomial Optimization Theory. IEEE Signal Processing Letters. (Vol. 25, pp. 1540 -1544). IEEE.
Contents
Summary iii
1 Introduction 1
1.1 Motivations . . . 1
1.2 Energy efficiency . . . 1
1.3 Towards adaptive cellular networks . . . 3
2 Optimal Design of Energy-Efficient mmWave Wireless Backhaul 5 2.1 Introduction . . . 5
2.2 Network model and Problem Statement . . . 7
2.2.1 Network model . . . 7
2.2.2 Problem statement . . . 8
2.3 Power consumption model . . . 8
2.3.1 Transmitted power . . . 9
2.3.2 Transceiver Chain . . . 10
2.3.3 Linear Processing . . . 11
2.3.4 Coding/Decoding and Backhauling . . . 12
2.4 EE optimization . . . 12
2.4.1 Optimum number of small-cell BS antennas . . . 13
2.4.2 Optimum number of BS antennas . . . 13
2.4.3 Sequential Optimization of M, N . . . 14
2.5 Numerical results . . . 14
2.6 Extension to non-LoS (NLoS) channels . . . 16
2.6.1 Network model . . . 16
2.6.2 Numerical results . . . 16
2.7 Conclusions . . . 17
3 Network Deployment for Maximal Energy Efficiency with Multislope Path Loss 19 3.1 Introduction . . . 19
3.1.1 Main literature . . . 19
3.1.2 Contributions and outline . . . 20
3.2 Network Model and Problem Statement . . . 21
3.2.1 Received Signal and Power Control Policy . . . 22
3.2.2 Pilot Reuse Policy and Channel Estimation . . . 22
3.3 Energy Efficiency analysis . . . 24
3.3.1 Area Spectral Efficiency . . . 25
3.3.2 Area Power Consumption . . . 26
3.3.3 Numerical analysis . . . 28
3.4 Energy Efficiency Maximization with ZF . . . 29
3.4.1 Problem Statement . . . 31
3.4.2 Optimal Pilot Reuse Factor . . . 31
3.4.3 Optimal Number of Antennas per BS and Number of UEs . . . . 32
3.5 Numerical results . . . 36
3.6 Conclusions . . . 37
4 Solving Fractional Polynomial Problems by Polynomial Optimization Theory 42 4.1 Introduction . . . 42 4.2 Preliminaries . . . 43 4.3 Optimization framework . . . 44 4.4 Application: EE Maximization . . . 47 4.4.1 Problem statement . . . 47 4.4.2 Numerical validation . . . 48 4.5 Conclusions . . . 49 5 Conclusions 50 5.1 Concluding remarks . . . 50 5.2 Main results . . . 51
5.3 Directions for future research . . . 52
A Proof of Lemma 3.1 – Part 1 55
B Proof of Lemma 3.1 – Part 2 59
C Proof of Lemma 3.5 63 Bibliography 65 List of Abbreviations 70 Notation 72 List of Figures 73 List of Tables 74 List of Publications 75
List of Formation Activities 76
CHAPTER
1
Introduction
1.1
MotivationsK
EEPINGup with the ever-growing demand for higher data throughput is thema-jor ambition of future cellular networks. The annual traffic growth rate is fore-cast to be in the range of 41 − 59%, and consequently, the area throughput will increases by a factor of ×1000 over the next 15 − 20 years [8]. In parallel, the power consumption of the information and communication technology (ICT) industry and the corresponding energy related pollution have become primary ecological and economi-cal concerns, in the last decade. Although the ICT contribution to the global emissions still is and will probably remain a rather small percentage of the global figures (ap-proximately 3% with mobile communication networks accounting for 0.5% [9]), the general trend of a 10 − 15% annual increase in ICT-related carbon emission is alarm-ing. Reducing the energy consumption is also an economical issue with cost for the cellular operators of approximately 15$billion on their annual energy use. Thus, it is no surprise that energy consumption reduction is a strategic priority for them globally.
Therefore, offering higher network area throughput on the one hand and using less energy on the other are the trends for future cellular networks. An important question is how to evolve communications technologies to meet those contradictory requirements.
1.2
Energy efficiencyA physically sound performance metric that considers both requirements jointly is the energy efficiency (EE). Broadly, the EE refers to how much energy it takes to achieve a certain amount of work. In the wireless communications, this benefit-cost ratio is represented, e.g., by the number of bits that can be reliably transmitted per unit of
energy [10], that is,
EE [bit/Joule] = Area throughput [bit/s/km
2]
Area power consumption [W/km2]
where the benefit (area throughput) is compared with the associated costs (area power consumption). Most of the research efforts are devoted to developing theoretical tools to characterize the area throughput of a cellular network. However, the EE metric as defined in [10], is affected by changes in the numerator and denominator since both are variable. Therefore, modelling accurately the total power consumption of a network is of primary importance to obtain reliable guidelines for the EE optimal design. The wrong model might lead to misleading conclusions on how the cellular network may look like.
There is a broad consensus that this EE goal of mobile networks cannot be achieved by incremental evolution of nowadays networks but it rather requires wireless commu-nication engineers to come up with some theoretical novelties and profound changes in the system architecture.
Area throughput
Massive multiple-input-multiple-output (MIMO) and millimeter wave (mmWave) are wireless communications technologies that envision boosting the area throughput of future cellular networks.
Massive MIMO represents a clear change towards the evolution of sustainable cel-lular networks, due to its capability of improving the data rate without severely impact-ing the overall network power consumption. This has been studied both in a central-ized [10–12] and distributed manner [13]. The enhancement is achieved at the base station (BS) by using arrays with a hundred or more small low-cost dipole antenna ele-ments, each one transmitting with low power. Despite the increased power consumption cost due to the deployment of more hardware, the use of a large number of radiating elements enables coherent processing at the BSs, which can be utilized to reduce the total radiated power with respect to standard multiuser multiple-input-multiple-output (MU-MIMO) communications systems. The logarithmic loss in terms of data rate in-curred by reducing the transmitted power is more than compensated with the linear gain obtained by multiplexing multiple users in the same time-frequency channel re-source. This linear multiplexing gain is made possible by the so-called asymptotic
favorable propagationthat makes wireless channels {hk} ∈ CM orthogonal to each
other 1 Mh
H
khj → 0, j 6= k almost surely. This happens in the asymptotic regime, that
is, when the number of antennas M grows large. Another promising research track in the wireless communications field is the mmWave technology [14–16]. In mmWave systems we push the carrier frequency up to tens of GHz in order to exploit the huge bandwidth available in that area of the frequency spectrum. Consequently, since in multi-antenna systems the radiating elements are typically separated by fractions of wavelength, it is possible to collect (radiate) more energy in the same physical area with respect to µWave systems. The current main use cases are line-of-sight (LoS) outdoor-to-outdoor or indoor-to-indoor configurations over relatively short distances like wireless backhaul in the unlicensed 60 GHz band, as a cost-efficient alternative to wired solutions in urban environment, and wireless local area networks (WLANs)
1.3. Towards adaptive cellular networks 3
based on the IEEE 802.11ad standard. This is mainly due to the very high atmospheric absorption, rain and foliage attenuation, strong penetration and reflection losses, and little diffraction. Nevertheless, recent theoretical considerations and measurement cam-paigns have proved its applicability to mid-range outdoor scenarios and use cases, e.g., small cells.
Area power consumption
As anticipated, besides the evaluation of the area throughput, particular attention should be paid to accurately model the energy consumption of a cellular network. Tradition-ally, in cellular systems a quite remarkable research effort has been devoted to reducing the energy consumption of mobile terminals, in order to enhance their battery lifetime. However, according to figures from Vodafone [17, 18], BSs account for almost 60% of total mobile network power consumption, while just 20% is consumed by mobile switching equipment and around 15% by the core infrastructure. Also, in order for the mobile operators to produce smaller and lighter products there is the tendency for the hardware and wireless engineers to move the complexity of the network to the BS rather than the users. These are the reasons why the communications society has recently ex-tended its attention towards BSs rather than user equipments (UEs) only. In view of this critical power consumption at the BS, and considering the fact that both Massive MIMO and mmWave increases the hardware to be deployed per BS than current cel-lular networks based on nowadays technology, it is rather difficult to claim that these solutions can be employed to efficiently build future sustainable cellular networks.
1.3
Towards adaptive cellular networksThe main contribution to BSs power consumption is given by the fixed power consump-tion needed to run the entire mobile network, which accounts for around one fourth of the total mobile network consumption (i.e., air conditioning, power supply). The total energy demand depends on the traffic load that is determined by many factors, e.g., number of active UEs, throughputs and channel conditions to name a few. The vari-ability of these large number of factors during the day makes the traffic load, and so the network energy demand, time varying quantities. Nevertheless, current cellular net-works are mainly designed to meet the peak traffic demands. Consequently, the energy available at a cellular network is not efficiently used during non-peak traffic hours or, even worse, it is completely wasted in the limit case when no UE is active within the coverage BS area (e.g., in rural regions), inevitably. Surprisingly, recent data in [19] shows that this load variability of mobile networks can reach peaks in the order of 200− 1000% with respect to the daily minimum loads. Hence, the BS with no load waste at least half of the energy it requires to serve the network at its peak load traffic condition. This calls for efficient mechanisms able to adapt the future cellular networks to the daily mobile network load variations.
One way current cellular networks may be made adaptive to this time-varying load variation is given by either switching off some of the hardware or changing the oper-ating point of the network dynamically, e.g., the number of BS antennas, number of scheduled UEs per cell, pilot reuse factor and BS density. The mobile network can be seen as a time-varying system that adapt itself to certain traffic inputs (e.g., quality
of service, data demand, latency), which may lead to turning off some of the active BSs, scheduling less UEs, or even adjust the number of BS antennas when sufficient to achieve the required spatial multiplexing. This requires the network designer to select some of the parameters that impact the network performance most and optimize them in order to meet the EE-maximization goal we set beforehand.
CHAPTER
2
Optimal Design of Energy-Efficient mmWave
Wireless Backhaul
2.1
IntroductionThe mmWave communications suffer from high atmospheric absorption, rain and fo-liage attenuation, penetration and reflection losses, which essentially restrict their use to LoS indoor-to-indoor or outdoor-to-outdoor communications over relatively short distances [20]. Nevertheless, recent theoretical considerations and measurement cam-paigns have provided evidence that outdoor cells with up to 200 m cell radii are viable if transmitters and receivers are equipped with sufficiently large antenna arrays along with beamforming [21], [22]. However, large arrays beamforming poses several imple-mentation challenges mostly because of hardware limitations that make impractical to have a dedicated baseband and radio frequency (RF) chain for each antenna. Analog solutions arise in early works for mmWave systems for their ease of implementation and power saving [1, 23] at the price of single-stream transmissions that substantially limit the system spectral efficiency. To combine the benefits of analog and digital ar-chitectures, hybrid beamforming schemes have gained a lot of interest [24].
A hybrid beamformer is made up of a low-dimensional baseband precoder followed by a high-dimensional RF beamformer. The latter is fully implemented by low-cost and power efficient analog phase shifters. Interestingly, in [25] the authors provide neces-sary and sufficient conditions to realize any fully-digital beamformer by using a hybrid one. The literature on hybrid beamforming schemes is relatively vast. In [26] and [27], a point-to-point MIMO system is considered while the downlink of a multi-user setting is investigated in [28] using single-antenna receivers and a single-stream transmitter with a RF chain per user. In [29], the authors consider the more realistic case of imper-fect channel state information due to the limited feedback of the return channel. All the
BB pre-coder HPA HPA RF chain LNA LNA fRF 1 fRF K FBB DAC DAC DAC DAC N N N K sK s1 RF chain ADC ADC M K wH 1 wH K LNA LNA RF chain M RF chain H1 H K LPF LPF LPF LPF LPF LPF ADC ADC LPF LPF
Figure 2.1: Transceiver chain architecture.
aforementioned works are mainly focused on increasing the system spectral efficiency. There exist also some literature looking at reducing the power consumption. Exam-ples towards this direction can be found in [30] and [31]. In particular, [30] proposes the use of low-cost switches for implementing antenna selection schemes whereas [31] provides algorithms for selecting a subset of antennas. In [32], different hybrid archi-tectures are compared in terms of both spectral and EE, defined as the ratio between throughput and power consumption. Switching-based solutions are found to performs poorly compared to both fully-digital and hybrid schemes.
In addition to mobile communications, the main use cases of mmWave communica-tions are WLANs based on the IEEE 802.11ad standard as well as wireless backhaul in the unlicensed 60 Ghz band as a cost-efficient alternative to wired solutions. Wireless backhaul at mmWave bands is considered in [1], wherein the design of beam alignment techniques is investigated for a single-cell point-to-point network using an analog-only transceiver. Along this line of research, this chapter focuses on the downlink of a single-cell network in which a given number of multiple small-cell BSs exchange data with a macro BS through wireless backhaul, using a low-cost hybrid transceiver ar-chitecture [28, 29]. Our goal is to find respectively the optimal number N and M of antennas at the BS and each small-cell BS in order to maximize the EE. To this end, we first model the consumed power of a hybrid transceiver architecture at mmWave and then derive closed-form EE-optimal values for M and N. These expressions provide valuable design insights into the interplay between system parameters and different components of the consumed power model. This research is inspired to the framework developed in [33], which however deals with the EE of massive MIMO networks and thus does not fit networks operating at mmWave frequencies.
The remainder of this chapter is organized as follows. Next section introduces the system model under a LoS channel propagation model and formulates the EE maxi-mization problem. Section 2.3 develops the power consumption model of the hybrid transceiver network as a function of different system parameters. The EE-optimal num-ber of antennas are computed in Section 2.4. Numerical results are given in Section 2.5 to validate the theoretical analysis. The numerical results are then extended to a more realistic clustered mmWave channel model in Section 2.6. Conclusions are drawn in Section 2.7.
2.2. Network model and Problem Statement 7
2.2
Network model and Problem Statement 2.2.1 Network modelWe consider a two-tier network, which comprises a macro BS equipped with N an-tennas and an overlaid tier of K small-cell BSs (selected from a larger set) endowed with M antennas and using a mmWave wireless backhaul link over a bandwidth B. We assume that the small-cell BSs are deployed so as to be in visibility with the macro BS. Due to the high absorption of scattered rays and the use of large antenna arrays (that create very narrow beam) at mmWave bands, a LoS model can be reasonably adopted for the propagation channel of each transmission link.1 In these circumstances, the
channel matrix Hk ∈ CN ×M between the BS and small-cell BS k can be modeled as:
Hk=√αkaN(φk)aHM(θk) (2.1)
where aN ∈ CN and aM ∈ CM account, respectively, for the array manifolds of the
BS and small-cell BSs with φkand θk being the angle of departure (AoD) and angle of
arrival (AoA) of the LoS link k. The parameter αkdescribes the macroscopic pathloss
and is computed as αk = 10−lk,dB/10with [1]
lk,dB= 32.5 + 20 log10fc+ 10 log10(dk)β+ Adk+ ξ (2.2)
where fc [GHz] is the carrier frequency, β is the pathloss exponent, dk [km] denotes
the distance between the BS and small-cell BS k, A accounts for the oxygen absorption and rainfall effect whereas ξ ∼ CN (0, σ2
ξ) is the shadowing being complex circularly
symmetric Gaussian with variance σ2 ξ.
Channel acquisition at mmWave bands is generally a challenging task due to the large number of antennas and the high bandwidth. However, if an uniform linear array (ULA) is adopted at both sides, the channel acquisition problem simply reduces to estimating the sets of directions {θk, φk} and pathlosses {αk} cutting down the number
of unknowns from (NM)K to 3K. If mmWave communications are used for wireless backhaul, then channel estimation simplifies further due to the absence of mobility and the favorable deployment of the macro BS and small-cell BSs. In these circumstances, perfect channel state information seems to be a reasonable assumption (e.g., [1] and [35]). Based on this observation, we assume perfect knowledge of {θk, φk, αk}. To
limit the implementation costs [29], we assume that a two-stage linear hybrid precoding scheme is employed at the BS and that a RF linear combiner is used at each small-cell BS (see Fig. 2.1). In particular, the BS employs a baseband precoder FBB =
[fBB
1 ,· · · , fKBB] ∈ CR×K followed by a RF precoder FRF = [f1RF,· · · , fRRF] ∈ CN ×R
with K ≤ R ≤ N being the number of RF chains. The transmitted vector x ∈ CN
is thus given by x = FRFFBBswhere s ∈ CK is the data vector such that E{ssH} =
P/NIK with P being the transmitted power. Hereafter, we assume that R = K, i.e.
one stream per small-cell BS is allocated.
At small-cell BS k, the received signal is linearly processed through the RF com-biner wkto obtain: yk = wHkH H kx+ w H knk (2.3)
1Observe that the LoS condition is also valid in highly dense mmWave networks, where having links in visibility is more likely
where nk ∼ CN (0, σ2IM) is the thermal noise with σ2 = BN0NF [W] while N0
[W/Hz] and NF being the noise power spectral density and noise figure, respectively.
The RF combiners {wk} and precoders {fkRF} are implemented using analog phase
shifters. Under the assumption of perfect knowledge of {θk, φk}, we have that wk =
aM(θk) and fkRF= aN(φk). Therefore, ykreduces to:
yk = (MN)¯hHkFBBs+ aHM(θk)nk (2.4) where ¯hH k = √α k N a H
N(φk)FRF is the effective channel seen from small-cell BS k after
receive combining. The BB precoder FBBis designed according to a ZF criterion so as
to completely remove the interference among small-cell BSs [29]. This leads to FBB =
( ¯HH
)−1 where ¯HH
= [¯h1, . . . , ¯hK]H = N1D1/2(FHRFFRF) with D =diag(α1, . . . , αK).
Plugging FBB = ( ¯HH)−1 into (2.4) yields
yk = (MN)sk+ aHM(θk)nk. (2.5)
Note that the inverse of ¯HHexists as long as φl− φk 6= 0 for k, l = 1, . . . , K, which
always occurs in practice if the served small-cell BSs are properly selected. 2.2.2 Problem statement
The aim of this research is to compute the values of (N, M) that, for a given number K of small-cell BSs, maximize the EE of the network given by:
EE = Throughput
Consumed Power [bit/Joule] (2.6)
which stands for the number of bits that can be reliably transmitted per unit of energy. From (2.5), the throughput of the considered network is easily found as:
Throughput = BK log2(1 + MNγ) [bit/s] (2.7) with γ = P/σ2. Observe that we have neglected the pre-log factor that should take
into account the signaling overhead for channel estimation, due to the stationarity of the investigated network [33]. The consumed power is computed as [33]
Consumed Power = η−1P
x+ PCP [W] (2.8)
where Pxis the transmit power, η ≤ 1 is the high power amplifier (HPA) efficiency and
PCPaccounts for the power consumed by the circuitry.
2.3
Power consumption modelA reasonable circuit power consumption model for a generic BS in a cellular network is as follows [33]
PCP = PFIX+ PTC+ PLP+ PCE+ PC/BH (2.9)
where PFIXaccounts for the fixed power consumption of the system, PTCof the transceiver
chain (at both BS and small-cell sides), PCEof the channel estimation process, PLPof
the linear processing, PC/BH of the coding at BS and of the load-dependent
backhaul-ing cost. Next all the above terms will be explicated as a function of all the system parameters in Table 2.1 taken for a reference carrier frequency of fc = 60 Ghz.
2.3. Power consumption model 9
Table 2.1: Network and system parameters at 60GHz.
Parameter Description Value References
PLNA Power consumed by low noise amplifier 39 [mW] [36] PHPA Power consumed by the high-power-amplifier 138 [mW] [36, 37]
PDC Power absorbed by the down conversion stage 47.3 [mW] [38] PUC Power absorbed by the up conversion stage 49 [mW] [37] PADC Power needed to run the analog-to-digital converter 200 [mW] [30] PDAC Power needed to run the digital-to-analog converter 110 [mW] [39] PC Power consumed by the combiner 19.5 [mW] [36] PPS Power required to commute phase shifter 30 [mW] [36] LBS Computational efficiency at the BS 20 [Gflops/W] [33] LSC Computational efficiency at the small-cell BSs 5 [Gflops/W] [33] LC Power consumed performing coding per bit/s 100 [mW/Gbit/s] [33] LD Power consumed performing decoding per bit/s 800 [mW/Gbit/s] [33] LBH Power used by backhauling per bit/s 250 [mW/Gbit/s] [33]
Tc Coherence time 10 [s] [40]
∆ Normalized antenna separation 0.5 [1]
σ2
ξ Shadowing variance 8 [dB] [1]
A Oxigen and rainfall absorption 25 [dB] [1]
κ Path-loss exponent 2.2 [1]
N0 Noise power spectral density -174 [dBm] [1]
d Distance BS to small-cell BSs 150 [m] [1]
NF Noise figure 6 [dB] [1]
B Transmission bandwidth 2 [Ghz] [1]
fc Carrier frequency 60 [Ghz] [1]
η High power amplifier efficiency 0.375 [33]
2.3.1 Transmitted power
The average transmit power is given by Px = E{kxk22} where the expectation is taken
with respect to the set of distances d = [d1,· · · , dK] and AoDs φ = [φ1,· · · , φK], and
thus, can be computed as
Px= tr (E{ssH} E {FHBBF H RFFRFFBB}) = P Ntr E ( ¯HH )−1(ND−1/2H¯H )( ¯HH )−1 = NP tr ED−1(FH RFFRF)−1 = NP K X k=1 Ed{α−1 k }Eφ n (FH RFFRF)−1 k,k o (a) = NP K ¯αEφ n P−1 k,k o (2.10) where (a) follows from assuming that any small-cell location is drawn from the same spatial distribution such that ¯α = Ed{αk−1}. Also, we have defined for notational
simplicity P = FH
RFFRF ∈ CK×K. A possible way to deal with the computation of
EφP−1
k,k is to make use of the Kantorovic inequality [29], which reads (exploiting
the fact that [P]k,k = 1)
P−1 k,k ≤ 1 4[P]k,k κ(P) + κ(P)−1+ 2 = 1 4N κ(P) + κ(P) −1+ 2 (2.11) where κ(P) = κ2(F
RF) and κ(FRF)=kFRFkkF†RFk stands for the 2-norm condition
number of the Vandermonde matrix with entries [FRF]n,k = zkn for n = 0, · · · , N − 1
and nodes {zk}Kk=1= ejπ sin(φk)for normalized antenna spacing ∆/(2πfc) = 1/2.
entire range of antennas. Vandermonde matrices with positive real nodes zk ∈R+ are
well-known to be ill-conditioned [41] - the condition number grows at least exponen-tially with the number of nodes K. However, if the nodes are complex-valued, it is possible to lower this growth to polynomial [42] and even achieve perfect conditioning choosing the nodes to be roots of unity [43]. In [44], the authors generalize this result to nodes that are close enough to the unit circle (not necessarily on the unit circle) and not so close to each other, while having N large enough. In particular, it turns out that if |zk|= 1 and N > 2K−1δ then [44] 1≤ κ(FRF)≤ 1 + 2 δK−1N 1− 2 δK−1N (2.12) with δ = minj6=k|zj−zk| accounting for the worst-case node separation. Thus, in order
for the Vandermonde matrix FRFto be nearly perfect conditioned we better impose
N ≫ 2K − 1
δ . (2.13)
To get some insight into how much large N should be, we consider a uniformly spaced small-cell deployment on the right side quadrants and evaluate δ. If the small-cell BSs are such that {φk}Kk=1 =−Kπ⌊K/2⌋ +
π K then δ =|z⌊K 2⌋− z⌊ K 2⌋−1| = |1 − e jπ sin(φ1)| = 2 sin π 2 sin π K (2.14)
from which it follows that, when K grows large, δ can be well-approximated with π2/K (using first order Taylor expansion). Plugging π2/K into (2.13) leads to N ≫ 2K(K− 1)/π2. This means that, for K sufficiently large, the value of N for achieving
good conditioning for FRFis given by
N ≥ 2λ π2K
2 = µ
K (2.15)
with λ ≥ 1 being a design parameter. Under this condition, by using (2.11) and (2.15) into (2.10) we have that Pxcan be reasonably approximated as
Px= P K ¯α for N ≥ µK. (2.16)
Fig. 2.2 illustrates κ(FRF) as a function of N for different values of K and uniformly
spaced nodes, i.e. {φk}Kk=1 = −Kπ⌊ K
2⌋ + π
K. As seen, κ(FRF) tends to unity when
N grows for any K. Also, it can be seen numerically that λ = 1 is already enough to satisfy condition (2.15) when the nodes (small-cell BSs) are properly selected. A similar behavior is observed for AoDs uniformly distributed φk ∼ U[−π/2, π/2] [45].
2.3.2 Transceiver Chain
The transceiver architecture of the investigated network is sketched in Fig. 2.1. We assume that both the BS and the set of small-cell BSs make use of (at least) 5-bit passive phase shifters (PSs) that emulate the arbitrary angles matching at RF [30]. Each small-cell BS consists of a single RF chain connected through a combiner to M parallel front-end (FE) receivers, one for each receive antenna. Each FE receiver is composed
2.3. Power consumption model 11 10 15 20 25 30 2 4 6 8 10 12 14 16 18 20 κ (F R F ) Number of antennas N K = 2 K = 6 K = 8
Figure 2.2: Condition number of FRF(φ) versus N for K = 2, 6 and 8.
of a low-noise amplifiers (LNAs) followed by a phase shifter, while an RF chain hosts a couple (I/Q) of analog-to-digital converters (ADCs), and a down conversion stage that includes a mixer, a voltage controlled oscillator and a baseband buffer [38]. Therefore, the power consumption of the transceiver chain at each small-cell BS can be computed as PTCSC = M (PLNA+ PPS) | {z } Front-end + PDC+ PADC+ PC | {z } RF chain (2.17) where PLNA accounts for the power consumption of each LNA, PPS of each PS, PDC
of the down-conversion, PADCof the ADC and PC of the combiner.
On the other hand, the BS transceiver consists of K RF chains each one fetching a rake of N PSs that drive the phases of N antennas, each one with a HPA. Each RF chain has a pair (I/Q) of digital-to-analog converters (DACs) plus a combiner as well as an up-conversion stage including filtering and amplifying. Therefore, we have that
PTCBS= N (KPPS+ PHPA+ PC) | {z } Front-end + K(PUC+ PDAC) | {z } RF chain (2.18)
Therefore, the total amount of consumed power in the transceiver chain is
PTC = PTCBS+ KPTCSC = pRF+ pSCFEM + pBSFEN (2.19)
where pRF= K(PDC+PADC+PC+PUC+PDAC) accounts for the power consumption
of the RF chain at both sides, whereas pSC
FE = K(PLNA + PPS) and pBSFE = KPPS +
PHPA+ PC of the FEs at the small-cells BS and BS, respectively.
2.3.3 Linear Processing
The power consumed by linear processing accounts for all the operations performed in the digital domain at the macro BS. This be quantified as
PLP= PLP−T | {z } Transmission + PLP−P | {z } Precoder computation (2.20)
where PLP−Taccounts for the total power consumed by downlink transmission of pay-load samples whereas PLP−P is the power required for the computation of FBB. Due
to the stationarity of the investigated network, the latter can be neglected since it is computed once for all. This amounts to saying that PLP−P = 0. The computation of FBBsrequires a total of K(2K − 1) complex operations per sample. Denoting by LBS
the computational efficiency of the BS [flops/W], we have that PLP= B
K(2K− 1) LBS
. (2.21)
2.3.4 Coding/Decoding and Backhauling
Load-dependent power costs are given by coding/decoding and backhauling. In the downlink, the BS applies channel coding and modulation to K sequences of informa-tion symbols and each small-cell BS applies some suboptimal fixed-complexity algo-rithm for decoding its own sequence. The opposite is done in the uplink. The power consumption accounting for these processes is proportional to the number of bits. The backhaul is used to transfer uplink/downlink data between the BS and the core network. The power consumption of the backhaul is commonly modeled as the sum of two parts: one load-independent (included in the fix power consumption) and one load-dependent (proportional to the throughput). Therefore, the power consumption for coding/decod-ing and backhaulcoding/decod-ing processes can be computed as
PC/BH = LBBK log2(1 + MNγ) (2.22)
where LB = LC/D+ LBHwith LC/Dand LBHbeing the operational costs for
coding/de-coding and backhauling, respectively.
2.4
EE optimizationPlugging (2.7)-(2.9) and (2.16)-(2.22) into (2.6), the EE optimization problem can thus be formulated as arg max (M,N )∈Z++ EE(M, N, K) s.t. N ≥ µK (2.23) with EE = ¯BK log2(1 + γMN) PFIX+ pSCFEM + pBSFEN (2.24) and ¯ PFIX = pRF+ PFIX+ Pxη−1+ PLP. (2.25)
In the following, we aim at solving (2.23) for fixed system parameters as given in Table 2.1. In doing so, we first derive a closed-form expression for the EE-optimal value of both M and N when the other one is fixed. This does not only bring indispensable insights into the interplay between (M, N) and the system parameters, but provides the means to solve the problem by a sequential optimization algorithm.
2.4. EE optimization 13
2.4.1 Optimum number of small-cell BS antennas
We begin by deriving the optimal number of small-cell BS antennas M while N is fixed. Applying [33, Lemma 3], it readily follows that:
Lemma 2.1. AssumeN is given, then the optimal M can be computed as M⋆ =⌊x⋆⌉ with x⋆ = e W γec1c2− 1 e +1 − 1 γN (2.26) andc1 = N ¯ PFIX+ pBSFEN
,c2 = pSCFEand⌊·⌉ as the nearest integer projector.
The above result provides explicit guidelines on how to select M in a hybrid mmWave system for maximal EE. Notice that the term c1 depends, through ¯PFIX, on pRF, which
accounts for the RF chain power consumption of the transceiver architecture, and also on the front-end power consumption pBS
FE at the BS. Using the typical values of
Ta-ble 2.1, it turns out that c1 is on the order of hundreds of Watt for a relatively small
number of antennas N. Larger values are obtained if N increases. On the other hand, c2 does not depend on N and takes values in the range of Watt, since it depends only
on the power consumed by the small-cell BSs for the front-end. Therefore, we can reasonably assume that, for typical values of system parameters, c1/c2 ≫ 1 such that
eW(r)+1can be approximated2with r and x⋆reduces to
x⋆ ≈ 1 N 1 e c1 c2 = P¯FIX+ p BS FEN e pSC FE . (2.27)
Using the above result and the power consumption expressions provided in Section 2.3, the following Corollary is found:
Corollary 2.1. IfN and K grow large, then M⋆ increases monotonically as:
M⋆ ≈ ξ + p BS FE pSC FE N (2.28) withξ = pRF+ PFIX+L2BBSK2 /pSC
FE,pSCFEandpBSFEas in(2.17) and (2.18), respectively.
From Corollary 2.1, it follows that M⋆is monotonically increasing with P
FIXas well
as with K and N. Using the values reported in Table 2.1, it turns out that pBS
FE/pSCFE < 1,
meaning that M⋆ grows at a slower pace than N. Also, the term ξ indicates that M⋆
increases linearly with pRF, i.e., the power consumed by the FE at both the BS and
small-cell BSs.
2.4.2 Optimum number of BS antennas
We now look for the value of N that maximizes the EE in (2.23). Still, by using [33, Lemma 3] and exploiting the pseudo concavity of the objective function, the following result is obtained:
2The interested reader is referred to [46] for further details on the inequalities and approximations involving the Lambert
Lemma 2.2. AssumeM is given, then the optimal N is given by N⋆ =⌊z⋆⌉ with z⋆ = max eW γ e d1 d2− 1 e +1 − 1 γM , µK (2.29) andd1 = M ¯ PFIX+ pSCFEM
,d2 = pBSFE,µK as in(2.15) and ⌊·⌉ as the nearest integer projector.
As for M, we have that z⋆ can be reasonably approximated as z⋆ ≈ 1 N
1 e
d1
d2 from
which it follows that:
Corollary 2.2. IfM and K grow large, then N⋆ increases monotonically as:
N⋆ ≈ max ξ + p SC FE pBS FE M, µK (2.30) In agreement with the results of Corollary 2.1, we have that N⋆ grows at faster pace
than M since pSC
FE/pBSFE > 1 as it follows using the values of Table 2.1. Therefore, using
larger arrays at the BS rather than at small-cell BSs seems to be a more natural choice for maximal EE.
2.4.3 Sequential Optimization ofM, N
Using Lemma 2.1 and Lemma 2.2, an alternating optimization algorithm to solve (2.23) operates as follows:
1. Optimize M for a fixed N using Lemma 2.1; 2. Optimize N for a fixed M using Lemma 2.2; 3. Repeat 1)–2) until convergence is achieved.
The EE is a non-decreasing monotone function of (M, N) and bounded above. The monotonicity is ensured by the pseudo concavity of (2.24). Indeed, the numerator is non-negative, differentiable, and concave, while the denominator is differentiable and affine, and so convex. Thus, the proposed alternating optimization algorithm returns a sequence {M∗
k, Nk∗}kof optimizers that converges to the global maximizer of (2.23).
2.5
Numerical resultsNumerical results are now used to validate the analysis. We consider a single-cell scenario as described in Section 2.2 with a macro BS, operating at fc = 60 GHz over
a bandwidth of B = 2 GHz placed at the center of the cell and serving simultaneously K small-cell BSs, with a distance d = 150 m from the BS. To avoid ambiguity in the spatial domain, the small cells are angularly displaced on the right half-space centered on the BS. The channel parameters and all of the terms introduced in Section 2.3 are listed in Table 2.1. To make the numerical results as realistic as possible, the same fabrication technology (65nm CMOS3) is used for the circuit parameters (e.g. [36] and
3CMOS technology promises higher levels of integration and reduced cost with respect to other solutions on the market such
2.5. Numerical results 15 250 400 450 200 20 500 40 150 550 60 100 80 600 100 50 120 Number of antennas N Number of antennas M E E [M bi t/J ou le ] EE-optimal EE⋆=620 Mbit/Joule, (M⋆,N⋆)=(19,32) Sequential optimization (a)pBS FEandpSCFEas in Table 2.1 500 550 250 20 600 200 40 650 150 60 700 80 100 100 50 120 Number of antennas N Number of antennas M E E [M bi t/J ou le ] EE-optimal EE⋆=710 Mbit/Joule, (M⋆,N⋆)=(108,163) Sequential optimization (b)pBS
FEandpSCFEas in Table 2.1 scaled by a factor10×
Figure 2.3: Energy Efficiency [Mbit/Joule] for different combination ofM and N (with K = 10).
[30]), while the linear processing and the traffic-dependent parameters are from [33]. The channel model parameters are taken from [48] and [1]. Results are obtained for a signal-to-noise ratio of γ = 0 dB.
Fig. 2.3a shows the EE as a function of M and N when K = 10. We see that there is a global maximizer for (M⋆, N⋆) = (19, 32) to which corresponds an EE⋆ = 620
Mbit/Joule and a throughput of 18.4 Gbit/s per small-cell BS. The total power con-sumed by circuitry is approximately PCP = 290 W. The sequential optimization
algo-rithm described in Section IV converges after a few iterations to the global optimizer validating (2.16). As seen, the optimal configuration is characterized by a relatively small N⋆ = 30, which is slightly larger than the number of served small cells, i.e.
K = 10. In other words, the output of the optimization problem suggests to use a num-ber of BS antennas that is on the same order of magnitude of K. This is in contrast to what it is usually required in mmWave communications for maximal spectral efficiency, namely, a large antenna array at both sides of the link to cope with the severe propaga-tion condipropaga-tions. To be energy-efficient, the so-called doubly massive MIMO paradigm4
requires either better beamforming schemes (increasing the throughput) or more power efficient electronic devices (reducing the power consumption). This latter case is inves-tigated in Fig. 2.3b in which the power consumed by front-end devices is decreased by an order of magnitude, both at the BS (pBS
FE) and at the small-cell BSs (pSCFE). We see
that in this case a doubly massive MIMO setup with (M⋆, N⋆) = (108, 163) naturally
arises at the EE-optimal. The throughput is also increased by a factor 1.5× with respect to the EE-optimal in Fig. 2.3a. Based on the above results, it follows that, to improve the EE and throughput of mmWave communications, the hardware components (such as PSs, LNAs and HPAs) have to be more efficient than todays.
4In literature doubly massive MIMO is referred to a system equipped with very large antenna arrays at both transmitter and
2.6
Extension to non-LoS (NLoS) channelsIn this section, we investigate to what extent the major conclusions can be extended to a NLoS scenario.
2.6.1 Network model
We adopt a time-invariant clustered channel model composed of a LoS path and Ncl
scattering clusters, each one contributing with Nr rays accounting for the NLoS
com-ponent. This leads to the following channel matrix Hk ∈ CN ×M between the BS and
small-cell BS k [49]: Hk = Ncl X i=1 Nr X j=1 √α i,j,k √ NclNr
aN(φi,j,k)aHM(θi,j,k) + ILoS(dk)√αkaN(φk,LoS)aHM(θk,LoS)
(2.31) where φi,k and θi,k are the mean AoD and AoA of each link between BS and the
i-th scatterer. The angle spread wii-thin each cluster is also taken into account by using Laplacian distribution, φi,j,k ∼ L(φi,k, µi,k) and θi,j,k ∼ L(θi,k, µi,k). The parameter
αi,j,kincludes both the small-scale and the large-scale fading effect and is computed as
αi,j,k = ˜αi,j,k10−li,k,dB/10with li,k,dBas in (2.2) and ˜αi,j,kaccounting or the small-scale
effects. The set of NLoS distances can be evaluated by geometrical considerations as di,k= dcli,k+
q (dcl
i,ksin ¯φi,k)2+ (dk− dcli,kcos ¯φi,k)2 (2.32)
where dcl
i,k and dk are the distances cluster i (when pointing small cell k) and
BS-small cell k, respectively and ¯φi,k = φi,k− φk,LoS, ¯θi,k = θi,k− θk,LoS. Besides, in the
LoS component, ILoS ∼ B(p) is a Bernoulli random variable indicating the presence
or not of the LoS link5. Unlike the NLoS component, θ
k,LoS and φk,LoS are related as
θk,LoS=mod(π + φk,LoS, 2π). We refer to [48] and [22] for further details. Hereafter, to
dimension the precoder/combiner we use the same eigenmode beamforming approach used in Section 2.2, in the analog domain, along with a digital ZF precoder. In par-ticular, let HH
k = UkΣkVkH be the singular value decomposition (SVD) of HHk, the
k-th user precoding and combining vectors, fRF,k and wk, are chosen as the columns
of the matrices Vk and Uk corresponding to the largest eigenvalue of Σk, i.e. vk,1
and uk,1. We then project the beamforming matrices FRF and W onto the analog set
Sp,q = {X ∈ Cp×q :|Xi,j| = 1, (i, j) = {p} × {q}}. This simply results in scaling
each entry of those matrices by its magnitude [26]. The precoder FBB is designed
ac-cording to a ZF criterion to cope with the effective interference after analog precoding-combining.
2.6.2 Numerical results
Fig. 2.4a shows numerically how the EE behaves as a function of M and N using the NLoS channel model described above. The optimal operating point is found at (M⋆, N⋆) = (5, 30) to which corresponds an EE = 709 Mbit/Joule, an aggregate
5Reasonably, p(d
k) i.e. the probability to have LoS link, it is modeled with a monotonic non-increasing function of its
2.7. Conclusions 17 560 600 250 20 40 200 650 60 150 700 80 100 100 50 120 Number of antennas N Number of antennas M E E [M bi t/J ou le ] EE-optimal EE⋆=709 Mbit/Joule, (M⋆,N⋆)=(5,30)
(a) Hybrid precoder
0 250 200 5 200 400 10 600 150 15 100 20 50 25 Number of antennas N Number of antennas M E E [M bi t/J ou le ] EE-optimal EE⋆=714 Mbit/Joule, (M⋆,N⋆)=(1,24) (b) Fully-digital precoder
Figure 2.4: Energy Efficiency [Mbit/Joule] for different combination ofM and N (with K = 10) for
hybrid and fully-digital precoder.
throughput and circuit power consumption are respectively 29.2 Gbit/s per small-cell BS and 412 W. The above network configuration is far from being considered as doubly-massive MIMO. This supports our conclusion that such systems, when used with hybrid architectures, are not optimal from an EE perspective. Fig. 2.4b illustrates the EE of a fully-digital system, which applies the ZF precoder entirely in the baseband, that is FRFFBB = F = ¯H†. In addition, to fairly compare the performance of the fully-digital
to that of the hybrid scheme in Fig. 2.1, constant transmit power at BS is ensured, i.e. kxk2
2= ksk22. The transmitted vector of symbols must be changed accordingly so as
s′ = (1M ⊗ IK) s. At the small cell side, linear combining is performed by matching
the most significant left eigenvector of the channel wk = uk,1associated to the highest
eigenvalue. Fig. 2.4b further validates the tendency encountered for the hybrid system, which is to avoid the use of large arrays at both network sides. Here, the EE-optimal point is at (M⋆, N⋆) = (1, 24) achieving a throughput of 27.2 Gbit/s per small-cell BS
with 381 W of consumed power. Although the precoders perform similarly, the hybrid solution leads to a smoother EE function that is preferable for its robustness to system changes. Moreover, Table 2.2 shows how much the circuit power terms contribute to the overall consumed power at the EE-optimal, both for the hybrid and fully-digital case. As we can see, in the hybrid case, the major contribution comes from the fixed power, while in the fully-digital one it comes from the power drawn by the FE chain at the BS. This is due to the high power required by one DAC per antenna. Those costs scale linearly with N instead of with K, becoming prohibitive in the large array domain.
2.7
ConclusionsThis chapter focused on a two-tier network in which a given number K of small-cell BSs uses a mmWave wireless backhaul to communicate with a macro BS. In particular, we analyzed how to select the number of BS antennas N and number of receive
anten-Table 2.2: Power consumption of different components at the operating point (M⋆, N⋆) with PFIX= 50W.
Power parameters Hybrid Fully-digital
PFIX 68% 17%
PRF 5% 16%
PFE 24% 65%
PLP 3% 2%
nas M at each small-cell BS under the assumption that a hybrid transceiver architecture is employed, with the number of RF chains equal to K. To this end, we developed a realistic power consumption model that explicitly describes how the total power con-sumption of the hybrid scheme depends non-linearly on M, K, and N. Our analytical and numerical results showed that deploying a hybrid scheme with a large number of antennas N is not the EE-optimal solution with today’s technology. Alternative so-lutions must be developed in order to exploit the promising advantages (in terms of spectral efficiency) of using large values of N at mmWave bands and at the same time to maximize the EE.
CHAPTER
3
Network Deployment for Maximal Energy
Efficiency with Multislope Path Loss
3.1
IntroductionKeeping up with the ever-growing demand for higher data throughput is the major am-bition of future cellular networks [50]. An important question is how to evolve commu-nication technologies to deliver higher throughput without prohibitively increasing the power consumption [51]. This calls for new design mechanisms that provide the UE with high spectral efficiency at moderate energy costs. There is a broad consensus on that this wireless capacity growth can only be achieved with a substantial network den-sification [52] [53]. The main approaches for this denden-sification are twofold: small-cell networks [54–56] and Massive MIMO [10–12, 57, 58]. The former relies on a massive deployment of small cells that guarantees lower propagation losses [54–56]. The latter makes use of a massive number of BS antennas to simultaneously serve a relatively large number of UEs by means of spatial multiplexing. A combination of both has also received a lot of interest in the research literature (e.g., [2, 13]). Despite being potentially effective in increasing spectral efficiency, both solutions tend to increase the power consumed by the network; small cells increase the number of deployed BSs, whereas Massive MIMO requires more hardware per BS. The aim of this research is to design a cellular network from scratch to achieve maximal EE, without any a priori assumption on the number of BS antennas, UEs, cell pilot reuse or BS density.
3.1.1 Main literature
The optimal deployment of cellular networks has received great attention in the liter-ature. The first attempts were based on the simple Wyner model [59] wherein both BSs and UEs are located on a line at fixed positions. Next, more complex 2D
sym-metric grid-based deployments (e.g., hexagonal lattice) were considered [60]. Both approaches are not suited for modeling and studying networks characterized by a very irregular and dense structure, as envisioned in future cellular networks. To address this problem, advanced mathematical tools based on stochastic geometry have been em-ployed in the last years (e.g., [61–63]). Within the stochastic geometry framework, the locations of BSs form a point process in a compact set whose cardinality is a Pois-son distributed random variable that is independent among different disjoint sets. The performance of a cellular network can be measured in many different ways such as cov-erage probability, throughput and EE [64]. Earlier works on the design of EE-optimal cellular networks, equipped with multiple antenna BSs, can be found in [57] and [33] where closed-form expressions are derived for a single-cell scenario and numerical re-sults are given for a multicell setting. The EE analysis of a multicell network is devel-oped in [64–66] by using stochastic geometry. In [65], the optimization is done while satisfying a quality-of-service requirement per UE. In [64, 66], the use of small-cells together with sleeping strategies is proved to be a promising solution for increasing the EE. Generally speaking, small-cells lead to a higher EE but this gain saturates quickly as the density of small cells increases. In [2], it has been shown that further benefits can be achieved by using Massive MIMO.
As the majority of works in the literature, all the aforementioned ones use the stan-dard path loss model where received power decays like d−α over a distance d, where
α is called the "path loss exponent". This standard path loss model is quite ideal-ized, and in most scenarios α is itself a function of distance, typically an increasing one [67]. For example, three distinct regimes could be easily identified in a practi-cal environment [68]: a distance-independent "near field" where α0 = 0, a free-space
like regime where α1 = 2, and finally some heavily-attenuated regime where α2 > 2.1
What happens if densification pushes many BSs into the near-field? An answer to this question can be found in [67, 69, 70] (among others), wherein the authors show that the propagation environment and fading distribution play a key role in identifying network operating regimes for which an increase, saturation, or decrease of the throughput is ob-served as the network densifies. In the extreme case, ultra BS-densification may even lead to zero throughput. Despite all this, multislope path loss models are not frequently used in the analysis of cellular networks because, in general, they make the theoretical analysis much more demanding. This research attempts to solve this issue for the EE maximization problem at hand.
3.1.2 Contributions and outline
We consider a cellular network in which the BSs are independently and uniformly dis-tributed in a given area according to a homogeneous Poisson point process (H-PPP) of intensity λ. Each BS is equipped with an arbitrary number M of antennas and serves simultaneously K UEs. Statistical channel inversion power-control is employed in the UL to achieve a uniform average signal to noise ratio (SNR) across all the UEs. A multislope (distance-dependent) path loss model is considered. Three different linear combining schemes, namely, MR, ZF and MMMSE, are used under the assumption that channel state information is acquired by using pilots, which are reused across the network with a factor ζ. The EE of the network is computed by using a lower bound
1Such a situation results even with a simple 2-ray ground reflection, with α
3.2. Network Model and Problem Statement 21
on the average UL spectral efficiency (valid for any combining scheme) as well as a polynomial power consumption model, thoroughly developed in [10]. Numerical re-sults are used to evaluate the impact of BS density λ and pilot reuse factor ζ on the EE of a Massive MIMO network such that M ≫ K ≫ 1. The results show that the EE with a multislope path loss is a unimodal2function of λ. Irrespective of the employed
detection scheme, the optimal EE is achieved for relatively small values of λ and ζ. This is in sharp contrast to [2] where the adoption of a single-slope path loss model leads to the conclusion that densification is always beneficial for EE; the EE is shown to be a monotonic increasing function of λ in [2]. The results show also that, although the “optimal” M-MMSE combiner provides the highest EE, the three different schemes behave similarly in terms of EE and area throughput as BS density increases.
Motivated by the above analysis, we concentrate on ZF and compute a new closed-form lower bound on the average UL SE. This lower bound is used to analytically find in closed-form the EE-optimal network configuration with respect to M, K and ζ while satisfying a signal-to-interference-plus-noise ratio (SINR) constraint. The closed-form expressions reveal the fundamental interplay between the three design parameters, which are also illustrated numerically. It turns out that ZF allows a higher densification of the network while using a smaller pilot reuse factor and achieving a higher EE than with MR. Both schemes employ almost the same optimal number of antennas per BS to ap-proximately serve the same number of UEs, with a ratio M/K between 4 and 19 when using ZF and between 4 and 27 for MR depending on the SINR constraint. In addition, ZF is characterized by a smoother EE function, which is more robust to system changes and thus makes it a better choice.
Compared to the preliminary version in [71], this chapter: (i) provides the EE anal-ysis for MR, ZF and MMMSE; (ii) is based on a multislope path loss model and aims at showing its impact on EE when the network is densified; (iii) gives more details and insights into the effect of network parameters and circuit power model are given.
The remainder of this chapter is organized as follows. Section 3.2 introduces basic notation and describes the cellular network with the underlying assumptions and trans-mission protocols. Section 3.3 analyzes the EE of MR, ZF, and MMMSE based on a realistic circuit power model. In Section 3.4, we consider the ZF scheme and compute a lower bound on the achievable EE, which is then maximized analytically with respect to M, K and ζ. The resulting expressions reveal the fundamental interplay between the three design parameters. Numerical results are used in Section 3.5 to validate an alter-nating optimization algorithm, which allows of optimally design the network. Finally, the major conclusions and implications are drawn in Section 3.6.
3.2
Network Model and Problem StatementWe consider the UL of a cellular network wherein the BSs are spatially distributed at locations {xi} within a compact geographic area according to a HPPP Φλ = {xi; i ∈
N} ⊂ R2 of intensity λ [BS/km2]. Let A be the deployment area of interest, the average number of deployed BSs is simply E{xi}{Φλ} = λA. Each BS has M antennas and
serves K single-antenna UEs over a bandwidth of Bw[MHz]. These K UEs are selected
at random from a very large set according to some scheduling algorithm. We assume
that each UE is connected to the closest BS such that the coverage area of a BS is its Poisson-Voronoi cell (see Fig. 3.1). The K UEs are assumed to be uniformly distributed in the Poisson-Voronoi cell. Without loss of generality, we assume that the “typical UE”, which is statistically representative for any other UE in the network [72], has an arbitrary index k and is connected to an arbitrary BS j. The network operates according to a synchronous time-division-duplex protocol. We denote by Bc [Hz] and Tc[s] the
coherence bandwidth and time, respectively. Then, the coherence block is composed of τc = BcTc [complex samples]. In each coherence block, τp samples are used for
acquiring channel state information by means of UL pilot sequences, whereas τu and
τd samples (such that τc= τp+ τu+ τd) are used for payload transmission in the UL
and downlink (DL), respectively. We assume that τp = ζK with ζ ≥ 1 being the pilot
reuse factor and τu = ξ(τc− ζK) with ξ ≤ 1 accounting for the payload UL fraction
transmission [10].
3.2.1 Received Signal and Power Control Policy
We call sli ∼ NC(0, pli) the UL payload signal transmitted from UE i of cell l to its
serving BS l with power pli = Es{|sli|2}. The signal yj ∈ CM received at BS j is
yj = hjjksjk | {z } desired signal + K X i=1,i6=k hjjisji | {z } intra-cell interference + X l∈Φλ\{j} K X i=1 hjlisli | {z } inter-cell interference + nj |{z} noise (3.1)
where nj ∼ NC(0, σ2IM) is the additive Gaussian noise, hjli ∈ CM is the channel
re-sponse between UE i in cell l and BS j modeled as uncorrelated Rayleigh fading [12], i.e., hj
li ∼ NC(0, βlijIM), where βlij is the large-scale fading coefficient. We call d j lithe
distance of UE i in cell l from BS j and compute βj
li according to a general multislope
path loss model, which is given by:
βlij(djli) = Υn (djli)−αn (3.2)
for dj
li ∈ [Rn−1, Rn) [km], for n = 1, . . . , N. The coefficients{Υn}, {αn} are design
parameters. Specifically, 0 ≤ α1 ≤ · · · ≤ αN are the power decay factors, 0 = R0 <
· · · < RN =∞ denote the distances at which a change in the power decadence occurs.
Setting N = 1 yields the widely used single-slope path loss model βj
li = Υ1(djli)−α1.
Following [73], we assume the UEs use a statistical channel inversion power-control policy such that pli = P0/βlil where P0 is a design parameter. This ensures a
uni-form ergodic per-antenna received SNR at BS l to all the UEs, which it is given by E{khl
lik2pli}/(Mσ2) = P0/σ2 = SNR0 and it is assumed to be constant over the
co-herence block.
3.2.2 Pilot Reuse Policy and Channel Estimation We assume that a pilot book Φ ∈ Cτp×τp of τ
p mutually orthogonal UL sequences is
used for channel estimation and call φjk∈ Cτp the pilot sequence assigned to the
typ-ical UE k in cell j. It is assumed to have normalized UL pilot sequences, to obtain a constant power level, and this implies that kφjkk2 = 1. To avoid cumbersome pilot
