Category Archives: Education

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).

IEEE ComSoc Focuses on Massive MIMO

IEEE ComSoc provides new online material every month and in August the focus is on Massive MIMO.

First, four carefully selected articles are offered free of charge, see the screenshot below and click here for details.

More precisely, IEEE offers free access to the published versions of these articles, while the accepted versions were already openly available: Paper 1, Paper 2, Paper 3, and Paper 4.

Second, a live webinar entitled “5G Massive MIMO: Achieving Spectrum Efficiency” is organized by IEEE ComSoc on August 24. The speaker is Professor Liesbet Van der Perre from KU Leuven. She was the scientific leader of the MAMMOET project, which is famous for demonstrating that Massive MIMO works in practice. You can expect a unique mix of theoretical concepts and practical implementation insights from this webinar.

Reproducible Massive MIMO Research

Reproducibility is fundamental to scientific research. If you develop a new algorithm and use simulations/experiments to claim its superiority over prior algorithms, your claims are only credible if other researchers can reproduce and confirm them.

The first step towards reproducibility is to describe the simulation procedure in such detail that another researcher can repeat the simulation, but a major effort is typically needed to reimplement everything. The second step is to make the simulation code publicly available, so that any scientist can review it and easily reproduce the results. While the first step is mandatory for publishing a scientific study, there is a movement towards open science that would make also the second step a common practice.

I understand that some researchers are skeptical towards sharing their simulation code, in fear of losing their competitive advantage towards other research groups. My personal principle is to not share any code until the research study is finished and the results have been accepted for publication in a full-length journal. After that, I think that the society benefits the most if other researcher can focus on improving my and others’ research, instead of spending excessive amount of time on reimplementing known algorithms. I also believe that the primary competitive advantage in research is the know-how and technical insights, while the simulation code is of secondary importance.

On my GitHub page, I have published Matlab code packages that reproduces the simulation results in one book, one book chapter, and more than 15 peer-reviewed articles. Most of these publications are related to MIMO or Massive MIMO. I see many benefits from doing this:

1) It increases the credibility of my research group’s work;

2) I write better code when I know that other people will read it;

3) Other researchers can dedicate their time into developing new improved algorithms and compare them with my baseline implementations;

4) Young scientists may learn how to implement a basic simulation environment by reading the code.

I hope that other Massive MIMO researchers will also make their simulation code publicly available. Maybe you have already done that? In that case, please feel free to write a comment to this post with a link to your code.