Category Archives: 5G

5G, News

Massive MIMO is Supporting the Super Bowl in Atlanta

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When I went to high school in Sweden, some of my friends stayed up very late at night (due to the time difference) to watch the Super Bowl; the annual championship in the American football league. This game is generally not a big thing in Sweden, but it is huge in America.

This Sunday, the Super Bowl takes place in Atlanta and one million people are expected to come to downtown Atlanta, to either watch the game at the stadium or root for their teams in other ways. Hence, massive flows of images and videos will be posted on social media from people located in a fairly limited area. To prepare for the game, the telecom operators have upgraded their cellular networks and taken the opportunity to market their 5G efforts.

Massive MIMO in the sub-6 GHz band with 64 antennas (and 128 radiating elements) is a key technology to handle the given situation, where huge capacity can be achieved by spatially multiplexing a large number of users in the downtown. Massive MIMO is a “small box with a massive impact” Cyril Mazloum, Network Manager for Sprint in Atlanta, told Hypepotamus. This refers to the fact that the Massive MIMO equipment is, despite the naming, physically smaller than the legacy equipment it replaces. In the following video, Heather Campbell of the Sprint Network Team explains how a ten times higher capacity is achieved in the 2.5 GHz band by their Massive MIMO deployment, which I have also reported about before.

All the major cellular operators have upgraded their networks in preparation for the big game. AT&T has reportedly spent $43 million to deploy 1,500 new antennas. Verizon has installed 30 new macro sites, 300 new small cells, and upgraded the capacity of 150 existing sites. T-Mobile has reportedly boosted its network capacity by eight times. Massive MIMO and 5G are clearly one of the key technologies in all these cases.

5G, Beyond 5G, Education, Technical insights

Beamforming From Distributed Arrays

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When an antenna array is used to focus a transmitted signal on a receiver, we call this beamforming (or precoding) and we usually illustrate it as shown to the right. This cartoonish illustration is only applicable when the antennas are gathered in a compact array and there is a line-of-sight channel to the receiver.

If we want to deploy very many antennas, as in Massive MIMO, it might be preferable to distribute the antennas over a larger area. One such deployment concept is called Cell-free Massive MIMO. The basic idea is to have many distributed antennas that are transmitting phase-coherently to the receiving user. In other words, the antennas’ signal components add constructively at the location of the user, just as when using a compact array for beamforming. It is therefore convenient to call it beamforming in both cases—algorithmically it is the same thing!

The question is: How can we illustrate the beamforming effect when using a distributed array?

The figure below shows how to do it. I consider a toy example with 80 star-marked antennas deployed along the sides of a square and these antennas are transmitting sinusoids with equal power, but different phases. The phases are selected to make the 80 sine-components phase-aligned at one particular point in space (where the receiving user is supposed to be):

Clearly, the “beamforming” from a distributed array does not give rise to a concentrated signal beam, but the signal amplification is confined to a small spatial region (where the color is blue and the values on the vertical axis are close to one). This is where the signal components from all the antennas are coherently combined. There are minor fluctuations in channel gain at other places, but the general trend is that the components are non-coherently combined everywhere except at the receiving user. (Roughly the same will happen in a rich multipath channel, even if a compact array is used for transmission.)

By looking at a two-dimensional version of the figure (see below), we can see that the coherent combination occurs in a circular region that is roughly half a wavelength in diameter. At the carrier frequencies used for cellular networks, this region will only be a few centimeters or millimeters wide. It is almost magical how this distributed array can amplify the signal at such a tiny spatial region! This spatial region is probably what the company Artemis is calling a personal cell (pCell) when marketing their distributed MIMO solution.

If you are into the details, you might wonder why I simulated a square region that is only a few wavelengths wide, and why the antenna spacing is only a quarter of a wavelength. This assumption was only made for illustrative purposes. If the physical antenna locations are fixed but we would reduce the wavelength, the size of the circular region will reduce and the ripples will be more frequent. Hence, we would need to compute the channel gain at many more spatial sample points to produce a smooth plot.

Reproduce the results: The code that was used to produce the plots can be downloaded from my GitHub.

5G, Beyond 5G, Commentary, News

Dataset with Channel Measurements for Distributed and Co-located Massive MIMO

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Although there are nowadays many Massive MIMO testbeds around the world, there are very few open datasets with channel measurement results. This will likely change over the next few years, spurred by the need for having common datasets when applying and evaluating machine learning methods in wireless communications.

The Networked Systems group at KU Leuven has recently made the results from one of their measurement campaigns openly available. It includes 36 user positions and two base station configurations: one 64-antenna co-located array and one distributed deployment with two 32-antenna arrays.

The following video showcases the measurement setup:

5G, Commentary, News

Can Every Company Be First With 5G?

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If you are following the 5G news, you might have noticed the many claims from various operators and telecom manufactures of being first with 5G. How can more than one company be first?

One telling example from this week is that on Thursday, Sprint/Nokia/Qualcomm reported about the “First 5G Data Call Using 2.5 GHz” and on Friday, Ericsson/Qualcomm reported about a “5G data call on 2.6 GHz band (…) adding a new frequency band to those successfully tested for commercial deployment.” The difference in carrier frequency is so small that I suppose the same hardware could have been used in both bands; for example, the LTE Massive MIMO product that I wrote about last August is designed for the frequency range 2496-2690 MHz. Yet, there is no contradiction between the two press releases; there are many different frequency bands and 5G features that one can be the first to demonstrate the use of, so we will likely see many more reports like these ones.

SOURCE Sprint

The multitude of press releases of this kind is an indicator of: 1) The many tests of soon-to-be-released hardware that are ongoing; 2) The importance for the companies to push out a steady stream of 5G related news.

When it comes to Massive MIMO, Sprint has previously showcased their use of fully digital 64-antenna panels at sub-6 GHz frequencies. In the new press release, they mention that hundreds of such panels were deployed in their network in 2018. Dr. Wen Tong, Head of Wireless Research at Huawei, made a similar claim about China in his keynote at GLOBECOM 2018. These are of course very small numbers compared to the millions of LTE base stations that exist in the world, but it indicates how important Massive MIMO will be in 5G. In fact, there are good reasons to believe that some kind of Massive MIMO technology will be used in almost every 5G base station.

5G, Commentary, News

Massive MIMO Deployments in the UK

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2018 was the year when the deployment of Massive MIMO capable base stations began in many countries, such as Russia and USA. Nevertheless, I still see people claiming that Massive MIMO is “too expensive to implement“. In fact, this particular quote is from a review of one of my papers that I received in November 2018. It might have been an accurate (but pessimistic) claim a few years ago, but nowadays it is plainly wrong.

This photo is from the Bristol Temple Meads railway station. The Massive MIMO panel is at the bottom. (Photo: Vodafone UK Media Centre.)

I recently came across a website about telecommunication infrastructure by Peter Clarke. He has gathered photos of Massive MIMO antenna panels that have been deployed by Vodafone and by O2 in the United Kingdom. These deployments are using hardware from Huawei and Nokia, respectively. Their panels have similar form factors and are rather easy to recognize in the pictures since they are almost square-shaped, as compared to conventional rectangular antenna panels. You can see the difference in the image to the right. The technology used in these panels are probably similar to the Ericsson panel that I have previously written about. I hope that as many wireless communication researchers as possible will see these images and understand that Massive MIMO is not too expensive to implement but has in fact already been deployed in commercial networks.

5G, Commentary, Technical insights

Adaptive Beamforming and Antenna Arrays

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Adaptive beamforming for wireless communications has a long history, with the modern research dating back to the 70s and 80s. There is even a paper from 1919 that describes the development of directive transatlantic communication practices that were developed during the First World War. Many of the beamforming methods that are considered today can be found already in the magazine paper Beamforming: A Versatile Approach to Spatial Filtering from 1988. Plenty of further work was carried out in the 90s and 00s, before the Massive MIMO paradigm.

I think it is fair to say that no fundamentally new beamforming methods have been developed in the Massive MIMO literature, but we have rather taken known methods and generalized them to take imperfect channel state information and other practical aspects into account. And then we have developed rigorous ways to quantify the achievable rates that these beamforming methods achieve and studied the asymptotic behaviors when having many antennas. Closed-form expressions are available in some special cases, while Monte Carlo simulations can be used to compute these expressions in other cases.

As beamforming has evolved from an analog phased-array concept, where angular beams are studied, to a digital concept where the beamforming is represented in multi-dimensional vector spaces, it easy to forget the basic properties of array processing. That is why we dedicated Section 7.4 in Massive MIMO Networks to describe how the physical beam width and spatial resolution depend on the array geometry.

In particular, I’ve observed a lot of confusion about the dimensionality of MIMO arrays, which are probably rooted in the confusion around the difference between an antenna (which is something connected to an RF chain) and a radiating element. I explained this in detail in a previous blog post and then exemplified it based on a recent press release. I have also recorded the following video to visually explain these basic properties:

A recent white paper from Ericsson is also providing a good description of these concepts, particularly focused on how an array with a given geometry can be implemented with different numbers of RF chains (i.e., different numbers of antennas) depending on the deployment scenario. While having as many antennas as radiating element is preferable from a performance perspective, but the Ericsson researchers are arguing that one can get away with fewer antennas in the vertical direction in deployments where it is anyway very hard to resolve users in the elevation dimension.

5G, Beyond 5G, Commentary, Education, Technical insights

Downlink Massive MIMO Analysis

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The tedious, time-consuming, and buggy nature of system-level simulations is exacerbated with massive MIMO. This post offers some relieve in the form of analytical expressions for downlink conjugate beamforming [1]. These expressions enable the testing and calibration of simulators—say to determine how many cells are needed to represent an infinitely large network with some desired accuracy. The trick that makes the analysis feasible is to let the shadowing grow strong, yet the ensuing expressions capture very well the behaviors with practical shadowings.

The setting is an infinitely large cellular network where each N-antenna base station (BS) serves K single-antenna users. The large-scale channel gains include pathloss with exponent $\eta$ and shadowing having log-scale standard deviation \sigma_{\scriptscriptstyle \rm dB}, with the gain between the \ellth BS and the kth user served by a BS of interest denoted by G_{\ell;k}.  With conjugate beamforming and receivers reliant on channel hardening, the signal-to-interference ratio (SIR) at such user is [2]

    $$\mathsf{SIR}_k = \frac{N p_k\,G_{k}}{\sum_{\ell} G_{\ell:k} } . $$

where G_{k} is the gain from the serving BS and p_k is the share of that BS’s power allocated to user k. Two power allocations can be analyzed:

  1. Uniform: p_k = 1/K.
  2. SIR-equalizing [3]: p_{k} \propto \frac{\sum_{\ell} G_{\ell;k}}{G_{k}}, with the proportionality constant ensuring that \sum_k p_k = 1. This makes \mathsf{SIR}_k = \mathsf{SIR} \, \forall k. Moreover, as N and K grow large, \mathsf{SIR} \rightarrow \frac{N}{K} \, (1- 2 / \eta) .

The analysis is conducted for \sigma_{\scriptscriptstyle \rm dB} \to \infty, which makes it valid for arbitrary BS locations.

SIR

For notational compactness, let \delta = 2/\eta. Define s<0 as the solution to {s}^\delta \,\gamma(-\delta,s)=0, where \gamma(\cdot) is the lower incomplete gamma function. For \eta=4, in particular, s = -0.85. Under a uniform power allocation, the CDF of \mathsf{SIR}_k is available in an explicit form involving the Gauss hypergeometric function {}_2 F_1 (available in MATLAB and Mathematica):

$\!\!\!\!\!\!\begin{cases} F_{\mathsf{SIR}_k}(\theta) \simeq e^{s \left(\frac{N}{\theta \,K}-1\right)} & 0 \leq \theta < \frac{N/K}{3 + \epsilon} \\ F_{\mathsf{SIR}_k}(\theta) = 1 - \left(\frac{N}{\theta \,K}-1\right)^{\delta} \mathrm{sinc} \, \delta + B \! \left(\frac{\theta \,K}{N-2\,\theta \,K}\right) & \frac{N/K}{3} \leq \theta < \frac{N / K}{2 } \\ F_{\mathsf{SIR}_k}(\theta) = 1 - \left(\frac{N}{\theta \,K}-1\right)^{\delta} \mathrm{sinc} \, \delta \quad\qquad & \frac{N / K}{2} \leq \theta<\frac{N}{K}\end{cases}$

where “\simeq” indicates asymptotic (\theta \to 0) equality, \epsilon is such that the CDF is continuous, and

    $$B(x) = \frac{ {}_2 F_1 \big(1, \delta+1; 2 \, \delta + 2; -1/x \big) \, \delta }{x^{1+2\,\delta}\;\Gamma (2\,\delta + 2)\,{\Gamma^2 (1-\delta)}} .$$

Alternatively, the CDF can be obtained by solving (e.g., with Mathematica) a single integral involving the Kummer function {}_1 F_1:

$\!\!\!\!\!\! F_{\mathsf{SIR}_k}(\theta)=\frac{1}{2}-\frac{1}{\pi}\int_{0}^{\infty}\Im\!\left\{\frac{e^{\frac{i\omega}{1-\theta K/N}}}{{}_1 F_1\left(1,1-\delta,\frac{i\theta\omega}{N/K-\theta}\right)}\right\}\frac{d\omega}{\omega}\,\,\,0<\theta<\frac{N}{K}.$

This latter solution can be modified for the SIR-equalizing power allocation as

$\!\!\!\!\!\!\!\!F_{\mathsf{SIR}}(\theta) = \frac{1}{2} - \frac{1}{\pi} \int_{0}^{\infty} \Im \! \left\{\frac{e^{i\,\omega}}{\left\{{}_1 F_1\!\left(1,1-\delta,i \,\theta\,\omega/N\right)\right\}^K}\right\} \frac{d\omega}{\omega} \,\,\, 0<\theta<\frac{N}{K}.$

Spectral Efficiency

The spectral efficiency of user k is C_k=\log_2(1+\mathsf{SIR}_k), with CDF F_{C_k}(\zeta) = F_{\mathsf{SIR}_k}(2^\zeta-1) readily characterizable from the expressions given earlier. From C_k, the sum spectral efficiency at the BS of interest can be found as C_{\Sigma} = \sum_{k} C_k . Expressions for the averages \bar{C} = \mathbb{E} \big[ C_k \big] and \bar{C}_{\scriptscriptstyle \Sigma} = \mathbb{E} \! \left[ C_{\scriptscriptstyle \Sigma} \right] are further available in the form of single integrals.

With a uniform power allocation,

(1)   \begin{equation*}\bar{C} = \log_2(e) \,\int_{0}^{\infty} \frac{ 1-e^{-z N/K}}{ {}_1 F_1 \big( 1,1-\delta,z \big)} \, \frac{{d}z}{z}\end{equation*}

and \bar{C}_{\scriptscriptstyle \Sigma} = K \bar{C}. For the special case of \eta=4, the Kummer function simplifies giving

(2)   \begin{equation*}\bar{C}=\log_2(e) \,\int_{0}^{\infty} \frac{ 1-e^{-z N/K}}{1 + e^z \sqrt{\pi z} \, \erf\sqrt{z}} \, \frac{{d}z}{z} .\end{equation*}

With an equal-SIR power allocation

(3)   \begin{equation*}\bar{C}=\log_2(e)\,\int_{0}^{\infty} \frac{ 1-e^{-z}}{{}_1 F_1\left(1,1-\delta,z/N \right)^K} \, \frac{{d}z}{z}\end{equation*}

and \bar{C}_{\scriptscriptstyle \Sigma} = K \bar{C}.

Application to Relevant Networks

Let us now contrast the analytical expressions (computable instantaneously and exactly, and valid for arbitrary topologies, but asymptotic in the shadowing strength) with some Monte-Carlo simulations (lengthy, noisy, and bug-prone, but for precise shadowing strengths and topologies).

First, we simulate a 500-cell hexagonal lattice with N=100, K=10 and \eta=4. Figs. 1a-1b compare the simulations for \sigma_{\scriptscriptstyle \rm dB}= 10–14 dB with the analysis. The behaviors with these typical outdoor values of \sigma_{\scriptscriptstyle \rm dB} are well represented by the analysis and, as it turns out, in rigidly homogeneous networks such as this one is where the gap is largest.

Figure 1: Analysis vs hexagonal network simulations with lognormal shadowing

For a more irregular deployment, let us next consider a network whose BSs are uniformly distributed. BSs (500 on average) are dropped around a central one of interest. For each network snapshot, users are then uniformly dropped until K of them are served by the central BS. As before, N=100, K = 10 and \eta =4. Figs. 2a-2b compare the simulations for \sigma_{\scriptscriptstyle \rm dB} = 10 dB with the analysis, and the agreement is now complete. The simulated average spectral efficiency with a uniform power allocation is \bar{C}=2.77 b/s/Hz/user while (2) gives \bar{C}=2.76 b/s/Hz/user.

Figure 2: Analysis vs Poisson network simulations with lognornmal shadowing.

The analysis presented in this post is not without limitations, chiefly the absence of noise and pilot contamination. However, as argued in [1], there is a broad operating range (N \lesssim 150–200 with very conservative premises) where these effects are rather minor, and the analysis is hence applicable.

[1] G. George, A. Lozano, M. Haenggi, “Massive MIMO forward link analysis for cellular networks,” arXiv:1811.00110, 2018.

[2] T. Marzetta, E. Larsson, H. Yang, and H. Ngo, Fundamentals of Massive MIMO. Cambridge University Press, 2016.

[3] H. Yang and T. L. Marzetta, “A macro cellular wireless network with uniformly high user throughputs,” IEEE Veh. Techn. Conf. (VTC’14), Sep. 2014.