Category Archives: Technical insights

The Role of Massive MIMO in Designing Energy Efficient Networks

The next generation of cellular networks need to be much more energy-efficient than the current generation, if we should deliver 100-1000 times more data in a cost-efficient and environmentally friendly manner. In this video, I explain the methodology that can be used to design energy efficient 5G networks, and also the key role that Massive MIMO will play.

Disadvantages with TDD

LTE was designed to work equally well in time-division duplex (TDD) and frequency division duplex (FDD) mode, so that operators could choose their mode of operation depending on their spectrum licenses. In contrast, Massive MIMO clearly works at its best in TDD, since the pilot overhead is prohibitive in FDD (even if there are some potential solutions that partially overcome this issue).

Clearly, we will see a larger focus on TDD in future networks, but there are some traditional disadvantages with TDD that we need to bear in mind when designing these networks. I describe the three main ones below.

Link budget

Even if we allocate the same amount of time-frequency resources to uplink and downlink in TDD and FDD operation, there is an important difference. We transmit over half the bandwidth all the time in FDD, while we transmit over the whole bandwidth half of the time in TDD.  Since the power amplifier is only active half of the time, if the peak power is the same, the average radiated power is effectively cut in half. This means that the SNR is 3 dB lower in TDD than in FDD, when transmitting at maximum peak power.

Massive MIMO systems are generally interference-limited and uses power control to assign a reduced transmit power to most users, thus the impact of the 3 dB SNR loss at maximum peak power is immaterial in many cases. However, there will always be some unfortunate low-SNR users (e.g., at the cell edge) that would like to communicate at maximum peak power in both uplink and downlink, and therefore suffer from the 3 dB SNR loss. If these users are still able to connect to the base station, the beamforming gain provided by Massive MIMO will probably more than compensate for the loss in link budget as compared single-antenna systems. One can discuss if it should be the peak power or average radiated power that is constrained in practice.

Guard period

Everyone in the cell should operate in uplink and downlink mode at the same time in TDD. Since the users are at different distances from the base station and have different delay spreads, they will receive the end of the downlink transmission block at different time instances. If a cell center user starts to transmit in the uplink immediately after receiving the full downlink block, then users at the cell edge will receive a combination of the delayed downlink transmission and the cell center users’ uplink transmissions. To avoid such uplink-downlink interference, there is a guard period in TDD so that all users wait with uplink transmission until the outmost users are done with the downlink.

In fact, the base station gives every user a timing bias to make sure that when the uplink commences, the users’ uplink signals are received in a time-synchronized fashion at the base station. Therefore, the outmost users will start transmitting in the uplink before the cell center users. Thanks to this feature, the largest guard period is needed when switching from downlink to uplink, while the uplink to downlink switching period can be short. This is positive for Massive MIMO operation since we want to use uplink CSI in the next downlink block, but not the other way around.

The guard period in TDD must become larger when the cell size increases, meaning that a larger fraction of the transmission resources disappears. Since no guard periods are needed in FDD, the largest benefits of TDD will be seen in urban scenarios where the macro cells have a radius of a few hundred meters and the delay spread is short.

Inter-cell synchronization

We want to avoid interference between uplink and downlink within a cell and the same thing applies for the inter-cell interference. The base stations in different cells should be fairly time-synchronized so that the uplink and downlink take place at the same time; otherwise, it might happen that a cell-edge user receives a downlink signal from its own base station and is interfered by the uplink transmission from a neighboring user that connects to another base station.

This can also be an issue between telecom operators that use neighboring frequency bands. There are strict regulations on the permitted out-of-band radiation, but the out-of-band interference can anyway be larger than the desired inband signal if the interferer is very close to the receiving inband user. Hence, it is preferred that the telecom operators are also synchronizing their switching between uplink and downlink.


Massive MIMO will bring great gains in spectral efficiency in future cellular networks, but we should not forget about the traditional disadvantages of TDD operation: 3 dB loss in SNR at peak power transmission, larger guard periods in larger cells, and time synchronization between neighboring base stations.

Are 1-bit ADCs Meaningful?

Contemporary base stations are equipped with analog-to-digital converters (ADCs) that take samples described by 12-16 bits. Since the communication bandwidth is up to 100 MHz in LTE Advanced, a sampling rate of a 500 Msample/s is quite sufficient for the ADC. The power consumption of such an ADC is at the order of 1 W. Hence, in a Massive MIMO base station with 100 antennas, the ADCs would consume around 100 W!

ADC SymbolFortunately, the 1600 bit/sample that are effectively produced by 100 16-bit ADCs are much more than what is needed to communicate at practical SINRs. For this reason, there is plenty of research on Massive MIMO base stations equipped with lower-resolution ADCs. The use of 1-bit ADCs has received particular attention. Some good paper references are provided in a previous blog post: Are 1-bit ADCs sufficient? While many early works considered narrowband channels, recent papers (e.g., Quantized massive MU-MIMO-OFDM uplink) have demonstrated that 1-bit ADCs can also be used in practical frequency-selective wideband channels. I’m impressed by the analytical depth of these papers, but I don’t think it is practically meaningful to use 1-bit ADCs.

Do we really need 1-bit ADCs?

I think the answer is no in most situations. The reason is that ADCs with a resolution of around 6 bits strike a much better balance between communication performance and power consumption. The state-of-the-art 6-bit ADCs are already very energy-efficient. For example, the paper “A 5.5mW 6b 5GS/S 4×-lnterleaved 3b/cycle SAR ADC in 65nm CMOS” from ISSCC 2015 describes a 6-bit ADC that consumes 5.5 mW and has a huge sampling rate of 5 Gsample/s, which is sufficient even for extreme mmWave applications with 1 GHz of bandwidth. In a base station equipped with 100 of these 6-bit ADCs, less than 1 W is consumed by the ADCs. That will likely be a negligible factor in the total power consumption of any base station, so what is the point in using a lower resolution than that?

The use of 1-bit ADCs comes with a substantial loss in communication rate. In contrast, there is a consensus that Massive MIMO with 3-5 bits per ADC performs very close to the unquantized case (see Paper 1Paper 2, Paper 3, Paper 4Paper 5). The same applies for 6-bit ADCs, which provide an additional margin that protects against strong interference. Note that there is nothing magical with 6-bit ADCs; maybe 5-bit or 7-bit ADCs will be even better, but I don’t think it is meaningful to use 1-bit ADCs.

Will 1-bit ADCs ever become useful?

To select a 1-bit ADC, instead of an ADC with higher resolution, the energy consumption of the receiving device must be extremely constrained. I don’t think that will ever be the case in base stations, because the power amplifiers are dominating their energy consumption. However, the case might be different for internet-of-things devices that are supposed to run for ten years on the same battery. To make 1-bit ADCs meaningful, we need to greatly simplify all the other hardware components as well. One potential approach is to make a dedicated spatial-temporal waveform design, as described in this paper.

Massive MIMO Hardware Distortion Measured in the Lab

I wrote this paper to make a single point: the hardware distortion (especially out-band radiation) stemming from transmitter nonlinearities in massive MIMO is a deterministic function of the transmitted signals. One consequence of this is that in most cases of practical relevance, the distortion is correlated among the antennas. Specifically, under line-of-sight propagation conditions this distortion is radiated in specific directions: in the single-user case the distortion is radiated into the same direction as the signal of interest, and in the two-user case the distortion is radiated into two other directions.

The derivation was based on a very simple third-order polynomial model. Questioning that model, or contesting the conclusions? Let’s run WebLab. WebLab is a web-server-based interface to a real power amplifier operating in the lab, developed and run by colleagues at Chalmers University of Technology in Sweden. Anyone can access the equipment in real time (though there might be a queue) by submitting a waveform and retrieving the amplified waveform using a special Matlab function, “weblab.m”, obtainable from their webpages. Since accurate characterization and modeling of amplifiers is a hard nonlinear identification problem, WebLab is a great tool to researchers who want to go beyond polynomial and truncated Volterra-type toy models.

A $\lambda/2$-spaced uniform linear array with 50 elements beamforms in free space line-of-sight to two terminals at (arbitrarily chosen) angles -9 respectively +34 degrees. A sinusoid with frequency $f_1=\pi/10$ is sent to the first terminal, and a sinusoid with frequency $f_2=2\pi/10$ is transmitted to the other terminal. (Frequencies are in discrete time, see the Weblab documentation for details.) The actual radiation diagram is computed numerically: line-of-sight in free space is fairly uncontroversial: superposition for wave propagation applies. However, importantly, the actual amplification all signals is run on actual hardware in the lab.

The computed radiation diagram is shown below. (Some lines overlap.) There are two large peaks at -9 and +34 degrees angle, corresponding to the two signals of interest with frequencies $f_1$ and $f_2$. There are also secondary peaks, at angles approximately -44 and -64 degrees, at frequencies different from $f_1$ respectively $f_2$. These peaks originate from intermodulation products, and represent the out-band radiation caused by the amplifier non-linearity. (Homework: read the paper and verify that these angles are equal to those predicted by the theory.)

The Matlab code for reproduction of this experiment can be downloaded here.

3D Beamforming, is that Massive MIMO?

No, these are two different but somewhat related concepts, as I will explain in detail below.

Contemporary multiantenna base stations for cellular communications are equipped with 2-8 antennas, which are deployed along a horizontal line. One example is a uniform linear array (ULA), as illustrated in Figure 1 below, where the antenna spacing is uniform. All the antennas in the ULA have the same physical down-tilt, with respect to the ground, and a fixed radiation pattern and directivity.

Figure 1: Azimuth 2D beamforming from a horizontal ULA.

By sending the same signal from all antennas, but with different phase-shifts, we can steer beams in different angular directions and thereby make the directivity of the radiated signal different from the directivity of the individual antennas. Since the antennas are deployed on a one-dimensional horizontal line in this example, the ULA can only steer beams in the two-dimensional (2D) azimuth plane as illustrated in Figure 1. The elevation angle is the same for all beams, which is why this is called 2D beamforming. The beamwidth in the azimuth domain shrinks the more antennas are deployed. If the array is used for multiuser MIMO, then multiple beams with different azimuth angles are created simultaneously, as illustrated by the colored beams in Figure 1.

Figure 2: Elevation 2D beamforming from a vertical ULA.

If we would rotate the ULA so that the antennas are instead deployed at different heights above the ground, then the array can instead steer beams in different elevation angles. This is illustrated in Figure 2. Note that this is still a form of 2D beamforming since every beam will have the same directivity with respect to the azimuth plane. This antenna array can be used to steer beams towards users at different floors of a building. It is also useful to serve flying objects, such as UAVs, jointly with ground users. The beamwidth in the elevation domain shrinks the more antennas are deployed.

Figure 3: 3D beamforming from a planar array.

If we instead deploy multiple ULAs on top of each other, it is possible to control both the azimuth and elevation angle of a beam. This is called 3D beamforming and is illustrated in Figure 3 using a planar array with a “massive” number of antennas. This gives the flexibility to not only steer beams towards different buildings but also towards different floors of these buildings, to provide a beamforming gain wherever the user is in the coverage area. It is not necessary to have many antennas to perform 3D beamforming – it is basically enough to have three antennas deployed in a triangle. However, as more antennas are added, the beams become narrower and easier to jointly steer in specific azimuth-elevation directions. This increases the array gain and reduces the interference between beams directed to different users, as illustrated by the colors in Figure 3.

The detailed answer to the question “3D Beamforming, is that Massive MIMO?” is as follows. Massive MIMO and 3D beamforming are two different concepts. 3D beamforming can be performed with few antennas and Massive MIMO can be deployed to only perform 2D beamforming. However, Massive MIMO and 3D beamforming is a great combination in many applications; for example, to spatially multiplex many users in a city with high-rise buildings. One should also bear in mind that, in general, only a fraction of the users are located in line-of-sight so the formation of angular beams (as shown above) might be of limited importance. The ability to control the array’s radiation pattern in 3D is nonetheless helpful to control the multipath environment such that the many signal components add constructively at the location of the intended receiver.

I was wrong: Two incorrect speculations

Our 2014 massive MIMO tutorial paper won the IEEE ComSoc best tutorial paper award this year. The idea when writing that paper was to summarize the state of the technology, and to point out research directions that were relevant (at that time). It is of course, reassuring to see that many of those research directions evolved into entire sub-fields themselves in our community. Naturally, in the envisioning of these directions I also made some speculations.

It looks to me now that two of these speculations were wrong:

  • First, “Massive MIMO increases the robustness against both unintended man-made interference and intentional jamming.” This is only true with some qualifiers, or possibly not true at all. (Actually I don’t really know, and I don’t think it is known for sure. It seems that this question remains a rather pertinent research direction for anyone interested in physical layer security and MIMO.) Subsequent research by others showed that Massive MIMO can be extraordinarily susceptible to attacks on the pilot channels, revealing an important, fundamental vulnerability at least if standard pilot-based channel estimation is used and no excess dimensions are “wasted” on interference suppression or detection. Basically this pilot channel attack exploits the so-called pilot contamination phenomenon, “hijacking” the reciprocity-based beamforming mechanism.
  • Second, “In a way, massive MIMO relies on the law of large numbers to make sure that noise, fading, and hardware imperfections average out when signals from a large number of antennas are combined in the air.” This is not generally true, except for in-band distortion and with many simultaneously multiplexed users and frequency selective Rayleigh fading. In general the distortion that results from hardware imperfections is correlated among the antennas. In the special case of line-of-sight with a single terminal, an important basic reference case, the distortion is identical (up to a phase shift) at all antennas, hence resulting in a rank-one transmission: the distortion is beamformed in the same direction as the signal of interest and hardware imperfections do not “average out” at all.
    This is particularly serious for out-band effects. Readers interested in a thorough mathematical treatment may consult my student’s recent Ph.D. dissertation.

Have you found any more? Let me know. The knowledge in the field continues to evolve.

What is a Transmit Antenna?

This is supposedly a simple question to answer; an antenna is a device that emits radio waves. However, it is easy to get confused when comparing wireless communication systems with different number of transmit antennas, because these systems might use antennas with different physical sizes and properties. In fact, you can seldom find fair comparisons between contemporary single-antenna systems and Massive MIMO in the research literature.

Each antenna type has a predefined radiation pattern, which describes its inherent directivity; that is, how the gain of the emitted signal differs in different angular directions. An ideal isotropic antenna has no directivity, but a practical antenna always has a certain directivity, measured in dBi. For example, a half-wavelength dipole antenna has 2.15 dBi, which means that there is one angular direction in which the emitted signal is 2.15 dB stronger than it would be with a corresponding isotropic antenna. On the other hand, there are other angular directions in which the emitted signal is weaker. This is not a problem as long as there will not be any receivers in those directions.

In cellular communications, we are used to deploying large vertical antenna panels that cover a 120 degree horizontal sector and have a strong directivity of 15 dBi or more. Such a panel is made up of many small radiating elements, each having a directivity of a few dBi. By feeding them with the same input signal, a higher dBi is achieved for the panel. For example, if the panel consists of 8 patch antenna elements, each having 7 dBi, then you get a 7+10·log10(8) = 16 dBi antenna.

Figure 1: Photo of an LTE site with three 8TX-sectors.

The picture above shows a real LTE site that I found in Nanjing, China, a couple of years ago. Looking at it from above, the site is structured as illustrated to the right. The site consists of three sectors, each containing a base station with four vertical panels. If you would look inside one of the panels, you will (probably) find 8 cross-polarized vertically stacked radiating elements, as illustrated in Figure 1. There are two RF input signals per panel, one per polarization, thus each panel acts as two antennas. This is how LTE with 8TX-sectors is deployed: 4 panels with dual polarization per base station.

At the exemplified LTE site, there is a total of 8·8·3 =192 radiating elements, but only 8·3 = 24 antennas. This disparity can lead to a lot of confusion. The Massive MIMO version of the exemplified LTE site may have the same form factor, but instead of 24 antennas with 16 dBi, you would have 192 antennas with 7 dBi. More precisely, you would connect each of the existing radiating elements to a separate RF input signal to create a larger number of antennas. Therefore, I suggest to use the following antenna definition from the book Massive MIMO Networks:

Definition: An antenna consists of one or more radiating elements (e.g., dipoles) which are fed by the same RF signal. An antenna array is composed of multiple antennas with individual RF chains.

Note that, with this definition, an array that uses analog beamforming (e.g., a phased array) only constitutes one antenna. It is usually called an adaptive antenna since the radiation pattern can be changed over time, but it is nevertheless a single antenna. Massive MIMO for sub-6 GHz frequencies is all about adding RF chains (also known as antenna ports), while not necessarily adding more radiating elements than in a contemporary system.

What is the purpose of having more RF chains?

With more RF chains, you have more degrees of freedom to modify the radiation pattern of the transmitted signal based on where the receiver is located. When transmitting a precoded signal to a single user, you adjust the phases of the RF input signals to make them all combine constructively at the intended receiver.

The maximum antenna/array gain is the same when using one 16 dBi antenna and when using 8 antennas with 7 dBi. In the first case, the radiation pattern is usually static and thus only a line-of-sight user located in the center of the cell sector will obtain this gain. However, if the antenna is adaptive (i.e., supports analog beamforming), the main lobe of the radiation pattern can be also steered towards line-of-sight users located in other angular directions. This feature might be sufficient for supporting the intended single-user use-cases of mm-wave technology (see Figure 4 in this paper).

In contrast, in the second case, we can adjust the radiation pattern by 8-antenna precoding to deliver the maximum gain to any user in the sector. This feature is particularly important for non-line-of-sight users (e.g., indoor use-cases), for which the signals from the different radiating elements will likely be received with “random” phase shifts and therefore add non-constructively, unless we compensate for the phases by digital precoding.

Note that most papers on Massive MIMO keep the antenna gain constant when comparing systems with different number of antennas. There is nothing wrong with doing that, but one cannot interpret the single-antenna case in such a study as a contemporary system.

Another, perhaps more important, feature of having multiple RF chains is that we can spatially multiplex several users when having multiple antennas. For this you need at least as many RF inputs as there are users. Each of them can get the full array gain and the digital precoding can be also used to avoid inter-user interference.