How “Massive” are the Current Massive MIMO Base Stations?

I have written earlier that the Massive MIMO base stations that have been deployed by Sprint, and other operators, are very capable from a hardware perspective. They are equipped with 64 fully digital antennas, have a rather compact form factor, and can handle wide bandwidths in the 2-3 GHz bands. These facts are supported by documentation that can be accessed in the FCC databases.

However, we can only guess what is going on under the hood – what kind of signal processing algorithms have been implemented and how they perform compared to ideal cases described in the academic literature. Erik G. Larsson recently wrote about how Nokia improved its base station equipment via a software upgrade. Are the latest base stations now as “Massive MIMO”-like as they can become?

My guess is that there is still room for substantial improvements. The following joint video from Sprint and Nokia explains how their latest base stations are running 4G and 5G simultaneously on the same 64-antenna base station and are able to multiplex 16 layers.

This is the highest number of multiuser MIMO layers achieved in the US” according to the speaker. But if you listen carefully, they are actually sending 8 layers on 4G and 8 layers 5G. That doesn’t sum up to 16 layers! The things called layers in 3GPP are signals that are transmitted simultaneously in the same band, but with different spatial directivity. In every part of the spectrum, there are only 8 spatially multiplexed layers in the setup considered in the video.

It is indeed impressive that Sprint can simultaneously deliver around 670 Mbit/s per user to 4 users in the cell, according to the video. However, the spectral efficiency per cell is “only” 22.5 bit/s/Hz, which can be compared to the 33 bit/s/Hz that was achieved in real-world trials by Optus and Huawei in 2017.

Both numbers are far from the world record in spectral efficiency of 145.6 bit/s/Hz that was achieved in a lab environment in Bristol, in a collaboration between the universities in Bristol and Lund. Although we cannot expect to reach those numbers in real-world urban deployments, I believe we can reach higher numbers by building 64-antenna arrays with a different form factor: long linear arrays instead of compact square panels. Since most users are separable in terms of having different azimuth angles to the base station, it will be easier to separate them by sending “narrower” beams in the horizontal domain.

Record 5G capacity via software upgrade!

In the news: Nokia delivers record 5G capacity gains through a software upgrade.   No surprise!  We expected, years ago, this would happen.

What does this software upgrade consist of?  I can only speculate.  It is, in all likelihood, more than the usual (and endless) operating system bugfixes we habitually think of as “software upgrades”.   Could it be even something that goes to the core of what massive MIMO is?  Replacing eigen-beamforming with true reciprocity-based beamforming?! Who knows. Replacing maximum-ratio processing with zero-forcing combining?!  Or even more mind-boggling, implementing more sophisticated processing of the sort that has been stuffing the academic journals in the last years? We don’t know!  But it will certainly be interesting to find out at some point, and it seems safe to assume that this race will continue.  

A lot of improvement could be achieved over the baseline canonical massive MIMO processing. One could, for example, exploit fading correlation, develop improved power control algorithms or implement algorithms that learn the propagation environment, autonomously adapt, and predict the channels.  

It might seem that research already squeezed every drop out of the physical layer, but I do not think so.  Huge gains likely remain to be harvested when resources are tight, and especially we are limited by coherence: high carriers means short coherence, and high mobility might mean almost no coherence at all.  When the system is starved of coherence, then even winning a couple of samples on the pilot channel means a lot.  Room for new elegant theory in “closed form”?  Good question. Could sound heartbreaking, but maybe we have to give up on that.  Room for useful algorithms and innovation? Certainly yes.  A lot.  The race will continue.

Towards 6G: Massive MIMO is a Reality—What is Next?

The good side of the social distancing that is currently taking place is that I have spent more time recording video material than usual. For example, I was supposed to give a tutorial entitled “Signal Processing for MIMO Communications Beyond 5G” at ICASSP 2020 in Barcelona in the beginning of May. This conference has now turned into an online event with free registration. Hence, anyone can attend the tutorial that I am giving together with Jiayi Zhang from Beijing Jiaotong University. We have prerecorded the presentations, which will be broadcasted to the conference attendees on May 4, but will be available for live discussions in between each video segment.

As a teaser for this tutorial, I have uploaded the 30 minute introduction to YouTube:

In this video, I explain what Massive MIMO is, what role it plays in 5G, why there will be a large gap between the theoretical performance and what is achieved in practice, and what might come next. In particular, I explain my philosophy regarding 6G research.

The remaining 2.5 hours of the tutorial will only be available from ICASSP. I hope to meet you online on May 4!

Beyond the Cellular Paradigm: Cell-Free Architectures with Radio Stripes

I just finished giving an IEEE Future Networks Webinar on the topic of Cell-free Massive MIMO and radio stripes. The webinar is more technical than my previous popular-science video on the topic, but it can anyway be considered an overview on the basics and the implementation of the technology using radio stripes.

If you missed the chance to view the webinar live, you can access the recording and slides afterwards by following this link. The recording contains 42 minutes of presentation and 18 minutes of Q/A session. If your question was not answered during the session, please feel to ask it here on the blog instead.

Update: The recording from the webinar has been delayed (due to the virus crisis), so I have recorded an alternative video:

Rician Fading – a Channel Model Often Misunderstood

Line-of-sight channels normally contain many propagation paths, whereof one is the direct path and the others are paths were the signals are scattered on different objects. The interaction between these paths lead to fading phenomena, which is often modeled statistically using Rician fading (sometimes written as Ricean fading). The main assumption is that the complex-valued channel coefficient h \in \mathbb{C} in the complex baseband can be divided into two parts:

h = m e^{j\theta}+ s,

where m \geq 0 is the magnitude of the direct path between the transmitter and receiver and \theta \in [0,2\pi] is the corresponding phase shift. The second part, s, represents all the scattered paths. This part is separated from the direct path since it consists of many paths, each being of roughly the same strength but substantially weaker than the direct path. It is modeled by Rayleigh fading, which implies s\sim \mathcal{CN}(0,\sigma^2). The complex Gaussian distribution is motivated by the central limit theorem, which says that the sum of many independent and identically distributed random variables is approximately Gaussian.

Under these assumptions, the magnitude |h|=|m e^{j\theta} +s| of the channel coefficient is Rice/Rician distributed, which is why it is called Rician fading. More precisely, |h| \sim \mathrm{Rice}(m,\sqrt{\sigma^2/2}), which depends on the magnitude m and the variance \sigma^2 of the scattering.

Interestingly, the distribution does not depend on the phase \theta, because the magnitude removes phases and s and s e^{j\theta} are equally distributed. Hence, it is common to omit \theta in the performance analysis of Rician fading channels. As long as the channel is perfectly known at the receiver, it will not make any difference when quantifying the SNR or capacity.

The common misunderstanding

We cannot neglect the phase \theta when analyzing practical systems where the receiver needs to estimate the channel. The value of \theta varies at the same pace as s, and for exactly the same reason: The transmitter or receiver moves, which induces small phase shifts in every path. Since s contains a large number of paths with approximately the same magnitude but random phases, the sum of the many terms with random phases give rise to the Gaussian distribution. The phase-shift of the direct path must be treated separately since this path is substantially stronger.

Unfortunately, my experience is that the vast majority of paper on Rician fading channels ignores this fact by simply treating m e^{j\theta} as a deterministic constant that is perfectly known at the receiver. I have done this myself in several papers, including this one from 2010 that has received 200+ citations. Unfortunately, the results obtained with that simplified model are practically questionable. If we don’t know s in advance, how can we know \theta? At best, the results obtained with a perfectly known \theta can be interpreted as an upper bound on what is practically achievable.

We analyzed the importance of correctly modeled random phases in a recent paper on cell-free massive MIMO. We compared the performance when using an ideal phase-aware MMSE estimator and a phase-unaware LMMSE estimator. The spectral efficiency loss due to a lack of knowing \theta ranges from 2% to 50% in different simulations, depending on the pilot length and interference situation. Hence, there are cases where it is very important to know the phase correctly.

Infinitely Large Arrays?

A defining factor for the early Massive MIMO literature is the study of communication systems where the number of base station antennas M goes to infinity. Marzetta’s original paper considered this asymptotic regime from the outset. Many other papers derived rate expressions for a finite M value, and then studied their behavior as M\to \infty . In these papers, the signal-to-noise ratio (SNR) grows linearly with M, and the rate grows towards infinity as \log_2(M) (except when pilot contamination is a limiting factor).

I have carried out such asymptotic analysis myself, but there is one issue that has been disturbing me for a while: The SNR cannot grow without bound in practice because we can never receive more power than what was transmitted from the base station. It doesn’t matter how many transmit antennas that are used or how razor-sharp the beams become, the law of conservation of energy must be respected. So where is the error in the analysis?

The problem is not that M\to \infty implies the use of infinitely large arrays. If we accept that the universe is infinite, it is plausible to create an M-antenna planar array for any value of M, for example, using a \sqrt{M} \times \sqrt{M} grid. Such an array is illustrated in Figure 1.

Figure 1: A planar array with 9 x 9 antennas are used to communicate with a user device.

The actual issue is how the channel gains (pathlosses) between the antennas and the user are modeled. We are used to considering channel models based on far-field approximations, where the channel gain is the same for all antennas (when averaging over small-scale fading). However, as the size of the array grows, the approximate far-field models become inaccurate. Instead, one needs to model the following phenomena that appear in the near-field:

  1. The propagation distance is different between each base station antenna and the user.
  2. The effective antenna areas vary in the array, even if the physical areas are equal, since the antennas are observed from different angles.
  3. The polarization losses vary between the antennas, because of the different angles from the antennas to the user.

It might seem complicated to take these phenomena into account, but the following paper shows how to compute the channel gain exactly when the user is centered in front of the array. I generalized this formula to non-centered users in a new paper. We utilized the new result to study the asymptotic behaviors of Massive MIMO and also intelligent reflecting surfaces. It turned out that all the three aforementioned phenomena are important to get accurate asymptotic results. When transmitting from an isotropic antenna to a planar Massive MIMO array, the total channel gain converges to 1/3 and instead of going to infinity. The remaining 2/3 of the transmit power is lost due to polarization mismatch or radiation into the opposite direction of the array. If any of the first two phenomena are ignored, the channel gain will grow unboundedly as M\to \infty , which is physically impossible. If the last one is ignored, the asymptotic channel gain is overestimated by 50%, so this is the least critical factor.

Although the exact channel model can be used to accurately predict the asymptotic SNR behavior, my experience from studying this topic is that the far-field approximations are accurate in most cases of practical interest. It is first when the propagation distance is shorter than the side length of the array that the near-field phenomena are critically important. In other words, the scaling laws that have been obtained in the Massive MIMO literature are usually applicable in practice, even if they break down asymptotically.

Two Roles of Deep Learning in Massive MIMO

The hype around machine learning, particularly deep learning, has spread over the world. It is not only affecting engineers but also philosophers and government agencies, which try to predict what implications machine learning will have on our society.

When the initial excitement has subsided, I think machine learning will be an important tool that many engineers will find useful, alongside more classical tools such as optimization theory and Fourier analysis. I have spent the last two years thinking about what role deep learning can have in the field of communications. This field is rather different from other areas where deep learning has been successful: We deal with man-made systems that have designed based on rigorous theory to operate close to the fundamental performance limits, for example, the Shannon capacity. Hence, at first sight, there seems to be little room for improvement.

I have nevertheless identified two main applications of supervised deep learning in the physical layer of communication systems: 1) algorithmic approximation and 2) function inversion.

You can read about them in my recent survey paper “Two Applications of Deep Learning in the Physical Layer of Communication Systems” or watch the following video:

In the video, I’m exemplifying the applications through two recent papers where we applied deep learning to improve Massive MIMO systems. Here are links to those papers:

Trinh Van Chien, Emil Björnson, Erik G. Larsson, “Sum Spectral Efficiency Maximization in Massive MIMO Systems: Benefits from Deep Learning,” IEEE International Conference on Communications (ICC), 2019.

Özlem Tugfe Demir, Emil Björnson, “Channel Estimation in Massive MIMO under Hardware Non-Linearities: Bayesian Methods versus Deep Learning,” IEEE Open Journal of the Communications Society, 2020.

News – commentary – mythbusting