Category Archives: Education

Limited-Time Offer: New MIMO book for $50

If you want to develop a strong foundational knowledge of MIMO technology, I recommend you to read our new book Introduction to Multiple Antenna Communications and Reconfigurable Surfaces.

The PDF is available for free from the publisher’s website, and you can download the simulation code and answers to the exercises from GitHub.

I am amazed at how many people have already downloaded the PDF. However, books should ideally be read in physical format, so we have arranged a special offer for you. Until May 15, you can also buy color-printed copies of the book for only $50 (the list price is $145). To get that price, click on “Buy Book” at the publisher’s website, enter the discount code 919110, and unselect “Add Track & Trace Shipping” (the courier service costs extra).

Here is a video where I explain why we wrote the book and who it is for:

How Many Beams Can You Send from a MIMO Array?

I receive many questions from students and researchers on social media, including this blog, YouTube, and ResearchGate. I do my best to answer such questions while commuting to work or having few minutes between meetings. I receive some questions quite frequently, making it worth creating videos where I try to answer them once and for all.

Below, you can find the first video in that series, and it answers the question: How many beams can you send from a MIMO array? As you will notice when watching the video, we obtain a more appropriate question if “can you send” is replaced by “do you want to send”.

If you have remaining doubts or comments after watching it, please feel free to post a comment on YouTube.

New book: Introduction to Multiple Antenna Communications and Reconfigurable Surfaces

The way that mobile communication networks are designed changed dramatically with the advent of 5G. In the past, it was all about utilizing large bandwidths and deploying many base stations. Nowadays, we are instead equipping each base station and smartphone with multiple antennas, which enables us to use signal processing algorithms to improve signal strength, enhance reliability, and send more data of the same spectrum by controlling the spatial direction of each signal layer. In essence, we refine the hardware and algorithms instead of deploying more infrastructure and requiring more signal resources.

Further dramatic changes are envisioned in the 6G era, where the use of even larger antenna arrays uncovers near-field effects, conventional frequency bands will be complemented with millimeter and sub-terahertz spectrum, optimized reflections from reconfigurable surfaces might improve propagation conditions, and communication networks can provide new localization and sensing services.

These extraordinary changes will affect not only the wireless technology but also the required knowledge and skills among the engineers and researchers who will implement it. Hence, it is essential to revise the curriculum in basic wireless communication courses to shift focus onto these new aspects of the physical layer.

When I realized the need for a new basic textbook, I joined forces with Özlem Tuğfe Demir to write “Introduction to Multiple Antenna Communications and Reconfigurable Surfaces”, NowOpen (2024). The book provides a gentle introduction to multiple antenna communications with a focus on system modeling, channel capacity theory, algorithms, and practical implications. The reader is expected to be familiar with basic signals and systems, linear algebra, probability theory, and digital communications, but a comprehensive recap is provided in the book. Once the fundamental point-to-point and multi-user MIMO theory and its practical implications have been covered, we also demonstrate how similar methodologies are used for wireless localization, radar sensing, and optimization of reconfigurable intelligent surfaces.

The first draft of the book was written for the first-year Master course TSKS14 Multiple Antenna Communications at Linköping University. You might have seen the YouTube video series that I produced while teaching that course during the pandemic. The book covers the same things and much more, and it contains numerous new examples and exercises.

The writing process focused on pinpointing all the technical and practical know-how that we believe the next-generation wireless engineers must have within this topic. We then wrote the text as a story that leads to these points. The writing has taken a long time: four years of progressive course material development followed by two years of intense writing with the goal of completing a book.

Our ambition has not been to write the one-and-only textbook on the topic, but the book that one should read first to build a deep knowledge foundation. After that, one can continue reading books such as “Fundamentals of Massive MIMO,” “Massive MIMO Networks,” or “Foundations of User-Centric Cell-Free Massive MIMO,” depending on personal preference.

The book is published with open access and accompanying MATLAB code that reproduces all the simulation results. You can access the PDF from the publisher’s website, where you can also buy printed copies. We are extremely proud of the book and hope you will like it too!

The Golden Frequencies

The golden frequencies for wireless access are in the band below 6 GHz. Why are these frequencies so valuable? The reasons, of course, are rooted in the physics. First, the wavelength is short enough that a (numerically) large array has an attractive form factor, enabling spatial multiplexing even from a single antenna panel. At the same time, the wavelength is large enough that a sufficiently large aperture can be obtained with a reasonable number of antennas – which, in turn, directly translates into a favorable link budget and high coverage. Second, below 6 GHz, Doppler is low enough, even at high mobility, that reciprocity-based beamforming based on uplink pilots for channel estimation works without relying on prior assumptions on the propagation environment, let alone on the fading statistics. This directly translates into robustness, simplicity of implementation, and scalability with respect to the number of service antennas. Third, these frequencies are not hindered so much by blockage, and strong multipath components can guarantee connectivity even when there is no line-of-sight, while in contrast, for mmWave a human blocking the line-of-sight path can suffice to break the link. Finally, analog microelectronics for the golden bands is mature, and very energy-efficient.

Distributed MIMO (D-MIMO) with reciprocity-based beamforming is the natural way of best exploiting the golden frequencies. This technology naturally operates in the [geometric] near-field of the “super-array” collectively constituted by all antenna panels together. In fact, the actual antenna deployment hardly matters at all! With reciprocity-based beamforming, the physical shape of the actual beams, and grating lobe phenomena in particular, become irrelevant. If anything, given a set of antennas, it is advantageous to spread them out over as large aperture as possible. The only definite no-no is to place antennas closer than half a wavelength together: such dense packing of antennas is almost never meaningful, as sampling points lambda/2-spaced apart captures essentially all the degrees of freedom of the field; putting the antennas closer results in coupling effects that are usually of more harm than benefit.

REINDEER is the European project that develops and demonstrates D-MIMO for the golden frequencies. What are the most important technical challenges? One is, down-to-earth, to handle the vast amounts of baseband data, and process them in real time. Another is time and phase synchronization of distributed MIMO arrays: antenna panels driven by independent local oscillators must be re-calibrated for joint reciprocity every time the oscillators have drifted apart. Locking the clocks using cabling is possible in principle, but considered very expensive to deploy. A third is initial access, covering space uniformly with system information signals, and waking up sleeping devices. A fourth is energy-efficiency, at all levels in the network. A fifth is the integration of service of energy-neutral devices that communicate via backscattering. D-MIMO naturally offers the infrastructure for that, permitting simultaneous transmission and reception from different panels in a bistatic setup; however, these activities break the TDD flow and must be carefully integrated into the workings of the system.

If sub-6 GHz are gold, then what is silver? Perhaps right above: the 7-15 GHz band, that is intended in 6G to extend the “main capacity” layer. It appears that these bands can still be suitable mobile applications, and that higher carriers (28 GHz, 38 GHz) are appropriate for fixed wireless access mostly. But the sub-6 GHz bands will remain golden and the first choice for the most challenging situations: high mobility, area coverage, and outdoor-to-indoor.

Erik G. Larsson
Liesbet Van der Perre

Who is Who in Massive MIMO?

I taught a course on complex networks this fall, and one component of the course is a hands-on session where students use the SNAP C++ and Python libraries for graph analysis, and Gephi for visualization. One available dataset is DBLP, a large publication database in computer science, that actually includes a lot of electrical engineering as well.

In a small experiment I filtered DBLP for papers with both “massive” and “MIMO” in the title, and analyzed the resulting co-author graph. There are 17200 papers and some 6000 authors.  There is a large connected component, with over 400 additional much smaller connected components!

Then I looked more closely at authors who have written at least 20 papers. Each node is an author, its size is proportional to his/her number of “massive MIMO papers”, and its color represents identified communities. Edge thicknesses represent the number of co-authored papers.  Some long-standing collaborators, former students, and other friends stand out.  (Click on the figure to enlarge it.)

To remind readers of the obvious, prolificacy is not the same as impact, even though they are often correlated. Also, the study is not entirely rigorous. For one thing, it trusts that DBLP properly distinguishes authors with the same name (consider e.g., “Li Li”) and I do not know how well it really does that. Second, in a random inspection all papers I had filtered out dealt with “massive MIMO” as we know it. However, theoretically, the search criterion would also catch papers on, say, MIMO control theory for a massive power plant.  Also, the filtering does miss some papers written before the “massive MIMO” term was established, perhaps most importantly Thomas Marzetta’s seminal paper on “unlimited antennas”.  Third, the analysis is limited to publications covered by DBLP, which also means, conversely, that there is no specific quality threshold for the publication venues. Anyone interested in learning more, drop me a note. 

Cracking the Pilot Contamination Nut

When T. Marzetta introduced the Massive MIMO concept in his seminal article from 2010, he concluded that “the phenomenon of pilot contamination impose[s] fundamental limitations on what can be achieved with a noncooperative cellular multiuser MIMO system.”

More precisely, he showed that the channel capacity under i.i.d. Rayleigh fading converges to a finite limit as the number of base stations goes to infinity.  The value of this limit is determined by the interference level in the channel estimation phase. There are hundreds of papers on IEEEXplore that deals with the pilot contamination issue, trying to push the limit upwards or achieve higher performance for a given number of antennas. Various advanced mitigation methods have been developed to cure the symptoms of pilot contamination.

But was pilot contamination really a fundamental limitation to start with? In 2018, we published a paper called “Massive MIMO Has Unlimited Capacity” where we showed that there is an unexpectedly simple solution to the problem. You don’t need a sledgehammer to “crack the pilot contamination nut“, but the right combination of state-of-the-art tools will do. While I have written about this in previous blog posts and briefly mentioned it in videos, I have finally recorded a comprehensive lecture on the topic. It is 82 minutes long and was given online by invitation from Hacettepe University, Turkey. No previous knowledge on the topic is required. I hope you will enjoy it in small or big doses!