Massive MIMO Networks:
Spectral, Energy, and Hardware Efficiency
Emil Björnson
Linköping University
emil.bjornson@liu.se
Jakob Hoydis
Bell Labs, Nokia
jakob.hoydis@nokia.com
Luca Sanguinetti
University of Pisa
luca.sanguinetti@unipi.it
c
2017 E. Björnson, J. Hoydis and L. Sanguinetti
Version of record:
Emil Björnson, Jakob Hoydis and Luca Sanguinetti (2017), “Massive
MIMO Networks: Spectral, Energy, and Hardware Efficiency”, Foundations and Trends
R
in Signal Processing: Vol. 11, No. 3-4, pp 154–655. DOI: 10.1561/2000000093.
Simulation code and supplementary material: https://massivemimobook.com
Printed books: Available from now Publishers Inc., http://www.nowpublishers.com
This is the authors’ version of the manuscript. See the above version of record for the
final published manuscript. Date of this version: February 26, 2020.
“Massive MIMO is an essential topic in the field of future cellular
networks. I have not seen any other book which can compete at that
level of detail and scientific rigor. I liked the didactic style, coming back
to root definitions (cellular networks, spectral efficiency, channel models,
and so forth) which will be very useful to PhD students and others
starting in this area. The models are very well explained and justified
as opposed to being imposed out of nowhere. This makes the reading
particularly pleasant and rich. Overall, a great tool to researchers and
practitioners in the field.”
David Gesbert, EURECOM
“This book provides a modern presentation of the state-of-the-art for
Massive MIMO communication. It includes a comprehensive treatment
of mathematical tools for analyzing and understanding Massive MIMO
networks. The authors provide an enlightening introduction to the topic,
suitable for graduate students and professors alike. The book starts
with the basic definitions and culminates in a systematic treatment of
spectral and energy efficiency. Of particular interest, the book provides
an updated assessment of the performance limiting factors, showing for
example that pilot contamination is not a fundamental limitation.”
Robert W. Heath Jr., The University of Texas at Austin
Contents
1 Introduction and Motivation 158
1.1 Cellular Networks . . . . . . . . . . . . . . . . . . . . . . 160
1.2 Definition of Spectral Efficiency . . . . . . . . . . . . . . . 167
1.3 Ways to Improve the Spectral Efficiency . . . . . . . . . . 173
1.4 Summary of Key Points in Section 1 . . . . . . . . . . . . 214
2 Massive MIMO Networks 216
2.1 Definition of Massive MIMO . . . . . . . . . . . . . . . . 216
2.2 Correlated Rayleigh Fading . . . . . . . . . . . . . . . . . 222
2.3 System Model for Uplink and Downlink . . . . . . . . . . 226
2.4 Basic Impact of Spatial Channel Correlation . . . . . . . . 228
2.5 Channel Hardening and Favorable Propagation . . . . . . . 231
2.6 Local Scattering Spatial Correlation Model . . . . . . . . . 235
2.7 Summary of Key Points in Section 2 . . . . . . . . . . . . 243
3 Channel Estimation 244
3.1 Uplink Pilot Transmission . . . . . . . . . . . . . . . . . . 244
3.2 MMSE Channel Estimation . . . . . . . . . . . . . . . . . 248
3.3 Impact of Spatial Correlation and Pilot Contamination . . 254
3.4 Computational Complexity and Low-Complexity Estimators 264
3.5 Data-Aided Channel Estimation and Pilot Decontamination 271
3.6 Summary of Key Points in Section 3 . . . . . . . . . . . . 274
4 Spectral Efficiency 275
4.1 Uplink Spectral Efficiency and Receive Combining . . . . . 275
4.2 Alternative UL SE Expressions and Key Properties . . . . . 301
4.3 Downlink Spectral Efficiency and Transmit Precoding . . . 316
4.4 Asymptotic Analysis . . . . . . . . . . . . . . . . . . . . . 335
4.5 Summary of Key Points in Section 4 . . . . . . . . . . . . 351
5 Energy Efficiency 353
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 354
5.2 Transmit Power Consumption . . . . . . . . . . . . . . . . 357
5.3 Definition of Energy Efficiency . . . . . . . . . . . . . . . 362
5.4 Circuit Power Consumption Model . . . . . . . . . . . . . 375
5.5 Tradeoff Between Energy Efficiency and Throughput . . . 390
5.6 Network Design for Maximal Energy Efficiency . . . . . . . 395
5.7 Summary of Key Points in Section 5 . . . . . . . . . . . . 401
6 Hardware Efficiency 403
6.1 Transceiver Hardware Impairments . . . . . . . . . . . . . 404
6.2 Channel Estimation with Hardware Impairments . . . . . . 413
6.3 Spectral Efficiency with Hardware Impairments . . . . . . 419
6.4 Hardware-Quality Scaling Law . . . . . . . . . . . . . . . 439
6.5 Summary of Key Points in Section 6 . . . . . . . . . . . . 449
7 Practical Deployment Considerations 451
7.1 Power Allocation . . . . . . . . . . . . . . . . . . . . . . . 452
7.2 Spatial Resource Allocation . . . . . . . . . . . . . . . . . 468
7.3 Channel Modeling . . . . . . . . . . . . . . . . . . . . . . 482
7.4 Array Deployment . . . . . . . . . . . . . . . . . . . . . . 500
7.5 Millimeter Wavelength Communications . . . . . . . . . . 522
7.6 Heterogeneous Networks . . . . . . . . . . . . . . . . . . 527
7.7 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . 537
7.8 Summary of Key Points in Section 7 . . . . . . . . . . . . 546
Acknowledgements 548
Appendices 549
A Notation and Abbreviations 550
B Standard Results 558
B.1 Matrix Analysis . . . . . . . . . . . . . . . . . . . . . . . 558
B.2 Random Vectors and Matrices . . . . . . . . . . . . . . . 563
B.3 Properties of the Lambert W Function . . . . . . . . . . . 567
B.4 Basic Estimation Theory . . . . . . . . . . . . . . . . . . 567
B.5 Basic Information Theory . . . . . . . . . . . . . . . . . . 572
B.6 Basic Optimization Theory . . . . . . . . . . . . . . . . . 575
C Collection of Proofs 579
C.1 Proofs in Section 1 . . . . . . . . . . . . . . . . . . . . . 579
C.2 Proofs in Section 3 . . . . . . . . . . . . . . . . . . . . . 591
C.3 Proofs in Section 4 . . . . . . . . . . . . . . . . . . . . . 593
C.4 Proofs in Section 5 . . . . . . . . . . . . . . . . . . . . . 609
C.5 Proofs in Section 6 . . . . . . . . . . . . . . . . . . . . . 612
References 621