Category Archives: Education

New Massive MIMO Book

For the past two years, I’ve been writing on a book about Massive MIMO networks, together with my co-authors Jakob Hoydis and Luca Sanguinetti. It has been a lot of hard work, but also a wonderful experience since we’ve learned a lot in the writing process. We try to connect all dots and provide answers to many basic questions that were previously unanswered.

The book has now been published:

Emil Björnson, Jakob Hoydis and Luca Sanguinetti (2017), “Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency”, Foundations and Trends® in Signal Processing: Vol. 11, No. 3-4, pp 154–655. DOI: 10.1561/2000000093.

What is new with this book?

Marzetta et al. published Fundamentals of Massive MIMO last year. It provides an excellent, accessible introduction to the topic. By considering spatially uncorrelated channels and two particular processing schemes (MR and ZF), the authors derive closed-form capacity bounds, which convey many practical insights and also allow for closed-form power control.

In the new book, we consider spatially correlated channels and demonstrate how such correlation (which always appears in practice) affects Massive MIMO networks. This modeling uncovers new fundamental behaviors that are important for practical system design. We go deep into the signal processing aspects by covering several types of channel estimators and deriving advanced receive combining and transmit precoding schemes.

In later chapters of the book, we cover the basics of energy efficiency, transceiver hardware impairments, and various practical aspects; for example, spatial resource allocation, channel modeling, and antenna array deployment.

The book is self-contained and written for graduate students, PhD students, and senior researchers that would like to learn Massive MIMO, either in depth or at an overview level. All the analytical proofs, and the basic results on which they build, are provided in the appendices.

On the website, you will find Matlab code that reproduces all the simulation figures in the book. You can also download exercises and other supplementary material.

Limited-time offer: Get a free copy of the book

Next week, we are giving a tutorial at the Globecom conference. In support of this, the publisher is currently providing free digital copies of the book on their website. This offer is available until December 7.

If you like the book, you can also buy a printed copy from the publisher’s website for the special price of $40! Use the discount code 552568, which is valid until December 31, 2017.

Upcoming Massive MIMO Webinars

IEEE ComSoc is continuing to deliver webinars on 5G topics and Massive MIMO is a key part of several of them. The format is a 40 minute presentation followed by a 20 minuter Q/A session. Hence, if you attend the webinars “live”, you have the opportunity to ask questions to the presenters. Otherwise, you can also watch each webinar afterwards. For example, 5G Massive MIMO: Achieving Spectrum Efficiency, which was given in August by Liesbet Van der Perre (KU Leuven), can still be watched.

In November, the upcoming Massive MIMO webinars are:

Massive MIMO for 5G: How Big Can it Get? by Emil Björnson (Linköping University), Thursday, 9 November 2017, 3:00 PM EST, 12:00 PM PST, 20:00 GMT.

Real-time Prototyping of Massive MIMO: From Theory to Reality by Douglas Kim (NI) and Fredrik Tufvesson (Lund University), Wednesday, 15 November 2017, 12:00 PM EST, 9:00 AM PST, 17:00 GMT.

Some Impactful Rejected Papers

Yes, my group had its share of rejected papers as well. Here are some that I specially remember:

  1. Massive MIMO: 10 myths and one critical question. The first version was rejected by the IEEE Signal Processing Magazine. The main comment was that nobody would think that the points that we had phrased as myths were true. But in reality, each one of the myths was based on an actual misconception heard in public discussions! The paper was eventually published in the IEEE Communications Magazine instead in 2016, and has been cited more than 180 times.
  2. Massive MIMO with 1-bit ADCs. This paper was rejected by the IEEE Transactions on Wireless Communications. By no means a perfect paper… but the review comments were mostly nonsensical. The editor stated: “The concept as such is straightforward and the conceptual novelty of the manuscript is in that sense limited.” The other authors left my group shortly after the paper was written. I did not predict the hype on 1-bit ADCs for MIMO that would ensue (and this happened despite the fact that yes, the concept as such is straightforward and its conceptual novelty is rather limited!). Hence I didn’t prioritize a rewrite and resubmission. The paper was never published, but we put the rejected manuscript on arXiv in 2014, and it has been cited 80 times.
  3. Finally, a paper that was almost rejected upon its initial submission: Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems, eventually published in the IEEE Transactions on Communications in 2013. The review comments included obvious nonsense, such as “Overall, there is not much difference in theory compared to what was studied in the area of MIMO for the last ten years.” The paper subsequently won the IEEE ComSoc Stephen O. Rice Prize, and has more than 1300 citations.

There are several lessons to learn here. First, that peer review may be the best system we know, but it isn’t perfect: disturbingly, it is often affected by incompetence and bias. Second, notwithstanding the first, that many paper rejections are probably also grounded in genuine misunderstandings: writing well takes a lot of experience, and a lot of hard, dedicated work. Finally, and perhaps most significantly, that persistence is really an essential component of success.

What is the Difference Between Beamforming and Precoding?

I’ve got an email with this question last week. There is not one but many possible answers to this question, so I figured that I write a blog post about it.

One answer is that beamforming and precoding are two words for exactly the same thing, namely to use an antenna array to transmit one or multiple spatially directive signals.

Another answer is that beamforming can be divided into two categories: analog and digital beamforming. In the former category, the same signal is fed to each antenna and then analog phase-shifters are used to steer the signal emitted by the array. This is what a phased array would do. In the latter category, different signals are designed for each antenna in the digital domain. This allows for greater flexibility since one can assign different powers and phases to different antennas and also to different parts of the frequency bands (e.g., subcarriers). This makes digital beamforming particularly desirable for spatial multiplexing, where we want to transmit a superposition of signals, each with a separate directivity. It is also beneficial when having a wide bandwidth because with fixed phases the signal will get a different directivity in different parts of the band. The second answer to the question is that precoding is equivalent to digital beamforming. Some people only mean analog beamforming when they say beamforming, while others use the terminology for both categories.

Analog beamforming uses phase-shifters to send the same signal from multiple antennas but with different phases. Digital beamforming designs different signals for each antennas in the digital baseband. Precoding is sometimes said to be equivalent to digital beamforming.

A third answer is that beamforming refers to a single-user transmission with one data stream, such that the transmitted signal consists of one main-lobe and some undesired side-lobes. In contrast, precoding refers to the superposition of multiple beams for spatial multiplexing of several data streams.

A fourth answer is that beamforming refers to the formation of a beam in a particular angular direction, while precoding refers to any type of transmission from an antenna array. This definition essentially limits the use of beamforming to line-of-sight (LoS) communications, because when transmitting to a non-line-of-sight (NLoS) user, the transmitted signal might not have a clear angular directivity. The emitted signal is instead matched to the multipath propagation so that the multipath components that reach the user add constructively.

A fifth answer is that precoding consists of two parts: choosing the directivity (beamforming) and choosing the transmit power (power allocation).

I used to use the word beamforming in its widest meaning (i.e., the first answer), as can be seen in my first book on the topic. However, I have since noticed that some people have a more narrow or specific interpretation of beamforming. Therefore, I nowadays prefer only talking about precoding. In Massive MIMO, I think that precoding is the right word to use since what I advocate is a fully digital implementation, where the phases and powers can be jointly designed to achieve high capacity through spatial multiplexing of many users, in both NLoS and LOS scenarios.

5.5 Hours of Massive MIMO Tutorials

Video recordings from the 2017 Joint IEEE SPS and EURASIP Summer School on Signal Processing for 5G Wireless Access are available for IEEE members, as we wrote about in a previous post. Now two of the Massive MIMO tutorial talks are openly available on Youtube.

Prof. Erik. G. Larsson gave a 2.5 hour tutorial on the fundamentals of Massive MIMO, which is highly recommended for anyone learning this topic. You can then follow up by reading his book with the same topic.

When you have viewed Erik’s introduction, you can learn more about the state-of-the-art signal processing schemes for Massive MIMO from another talk at the summer school. Dr. Emil Björnson gave a 3 hour tutorial on this topic:


I am borrowing the title from a column written by my advisor two decades ago, in the array signal processing gold rush era.

Asymptotic analysis is a popular tool within statistical signal processing (infinite SNR or number of samples), information theory (infinitely long blocks) and more recently, [massive] MIMO wireless communications (infinitely many antennas).

Some caution is strongly advisable with respect to the latter. In fact, there are compelling reasons to avoid asymptotics in the number of antennas altogether:

  • First, elegant, rigorous and intuitively comprehensible capacity bound formulas are available in closed form.
    The proofs of these expressions use basic random matrix theory, but no asymptotics at all.
  • Second, the notion of “asymptotic limit” or “asymptotic behavior” helps propagate the myth that Massive MIMO somehow relies on asymptotics or “infinite” numbers (or even exorbitantly large numbers) of antennas.
  • Third, many approximate performance results for Massive MIMO (particularly “deterministic equivalents”) based on asymptotic analysis are complicated, require numerical evaluation, and offer little intuitive insight. (And, the verification of their accuracy is a formidable task.)

Finally, and perhaps most importantly, careless use of asymptotic arguments may yield erroneous conclusions. For example in the effective SINRs in multi-cell Massive MIMO, the coherent interference scales with M (number of antennas) – which yields the commonly held misconception that coherent interference is the main impairment caused by pilot contamination. But in fact, in many relevant circumstances it is not (see case studies here): the main impairment for “reasonable” values of M is the reduction in coherent beamforming gain due to reduced estimation quality, which in turn is independent of M.

In addition, the number of antennas beyond which the far-field assumption is violated is actually smaller than what one might first think (problem 3.14).