I am excited to announce the new podcast “Wireless Future“, where Emil Björnson and Erik G. Larsson are discussing current and future wireless technologies, as well as their impact on society. Each episode will focus on a particular topic and be available in two formats: A video podcast on YouTube and an audio-only podcast that can be downloaded from the major podcast apps (there is a list below). We intend to release one episode every other week, starting from today. We hope you will enjoy it! Please send us feedback, questions, and suggestions on future topics to email@example.com.
Episode 1: Massive MIMO: Where do we stand?
In the first episode of “Wireless Future”, Erik G. Larsson and Emil Björnson talk about the brand new 5G networks and what role the technology component “Massive MIMO” is playing. They reflect upon whether the practical implementation of the technology became as they envisioned in their textbooks “Fundamentals of Massive MIMO” and “Massive MIMO Networks”.
You can listen to audio-only podcast at the following places:
When researchers study the basic properties of multi-antenna technologies, it is a common practice to model the channels using independent and identically distributed (i.i.d.) Rayleigh fading. This practice goes back many decades and is convenient since: 1) every antenna observes an independent realization of the channel; 2) each antenna is statistically equally good, so the ordering doesn’t matter; 3) the channel coefficients are complex Gaussian distributed, which leads to convenient mathematics.
The i.i.d. Rayleigh fading model has become the baseline that is considered unless the research is explicitly focused on a different model. When using the model to study spatial diversity, the diversity gain becomes proportional to the number of antennas. When characterizing the ergodic capacity of Massive MIMO, one can derive simple closed-form bounds where the SINR is proportional to the number of antennas. Both results are correct, but their generality is limited by the generality of the underlying fading model. Hence, it is important to know under what conditions i.i.d. Rayleigh fading can be observed.
When i.i.d. fading might occur
In isotropic scattering environments, where the multi-path components are uniformly distributed over all directions (in three dimensions), the fading realizations observed at two points have a correlation determined by the distance d between them. More precisely, the cross-correlation is sinc(2d/λ), where λ is the wavelength. The sinc function is zero when the argument is a non-zero integer, thus the fading realizations at two different points are uncorrelated if and only if they are separated by an integer multiple of λ/2. For example, d =λ/2, λ, 3λ/2, etc. Since the channel coefficients are Gaussian distributed in isotropic fading, uncorrelated fading results in independent fading.
The figure above illustrates a setup where 3 antennas are deployed on the dashed line with a separation of λ/2. The red circles around the “red antenna” show at which locations one can observe fading realizations that are independent of the observation made at the red antenna. The circles have radius λ/2, λ, 3λ/2, etc. The blue and green circles have the same meanings for the blue and green antennas, respectively. Since all the antennas are deployed on the circles of the other antennas, they will observe mutually uncorrelated (independent) fading. This will give rise to i.i.d. Rayleigh fading.
Suppose we want to deploy a fourth antenna. To retain an i.i.d. fading distribution, we must put it at a point where a red, a blue, and a green circle intersect. As indicated by the figure, such points are only be found along the dashed line. Hence, a uniform linear array (ULA) with λ/2-separation between the adjacent antennas will observe i.i.d. fading if deployed in an isotropic scattering environment.
The horizontal and vertical ULAs in the figure above can observe i.i.d. fading, while the planar array cannot; even if the horizontal and vertical antenna spacing is λ/2, the spacings along the diagonals are different.
Looking further into the future, two new array concepts are currently receiving attention from the research community:
Large intelligent surfaces (LIS);
Reconfigurable intelligent surfaces (RIS).
LIS are large active arrays, while RIS are large passive arrays with elements that scatter incident signals in a semi-controllable fashion. In both cases, the word “surface” signifies that at a planar array, or even a three-dimensional array, is considered. Hence, these arrays can never observe i.i.d. fading—it is physically impossible. Moreover, a key characteristic of LIS and RIS is that the element spacing is smaller than λ/2 (to approximate a continuously controllable surface), which is yet another reason for obtaining spatial channel correlation. It is therefore worrying that several early papers on these topics are making use of the i.i.d. fading model: the analysis might be beautiful but the results are insignificant since they cannot be observed in practice.
The way forward
Even if we have reached the end of the road for the i.i.d. Rayleigh fading model, we don’t have to wander into the darkness. We just need to switch to utilizing the more general spatially correlated Rayleigh fading model. There is already a rich literature on how to design communication systems for such channels. My book “Massive MIMO networks” is one possible starting point, but not the only one.
To make the transition to physically accurate models easier, I have co-authored the paper “Rayleigh Fading Modeling and Channel Hardening for Reconfigurable Intelligent Surfaces“, which derives a spatial correlation model for LIS and RIS in isotropic scattering environments. It can take the role as the new baseline channel model that is used when no other specific channel model is studied. We also elaborate on why the classical “Kronecker approximation” of spatial correlation matrices is inaccurate; for example, it results in i.i.d. fading also for planar arrays.
Cell-free massive MIMO might be one of the core 6G physical layer technologies. One of my students, Giovanni Interdonato, defended his Ph.D. thesis on this topic earlier this week. In this video, he speaks with me about his thesis work and his time as a doctoral student.
I have written several posts about Massive MIMO field trials during this year. A question that I often get in the comment field is: Have the industry built “real” reciprocity-based Massive MIMO systems, similar to what is described in my textbook, or is something different under the hood? My answer used to be “I don’t know” since the press releases are not providing such technical details.
The 5G standard supports many different modes of operation. When it comes to spatially multiplexing of users in the downlink, the way to configure the multi-user beamforming is of critical importance to control the inter-user interference. There are two main ways of doing that.
The first option is to let the users transmit pilot signals in the uplink and exploit the reciprocity between uplink and downlink to identify good downlink beams. This is the preferred operation from a theoretical perspective; if the base station has 64 transceivers, a single uplink pilot is enough to estimate the entire 64-dimensional channel. In 5G, the pilot signals that can be used for this purpose are called Sounding Reference Signals (SRS). The base station uses the uplink pilots from multiple users to select the downlink beamforming. This is the option that resembles what the textbooks on Massive MIMO are describing as the canonical form of the technology.
The second option is to let the base station transmit a set of downlink signals using different beams. The user device then reports back some measurement values describing how good the different downlink beams were. In 5G, the corresponding downlink signals are called Channel State Information Reference Signal(CSI-RS). The base station uses the feedback to select the downlink beamforming. The drawback of this approach is that 64 downlink signals must be transmitted to explore all 64 dimensions, so one might have to neglect many dimensions to limit the signaling overhead. Moreover, the resolution of the feedback from the users is limited.
In practice, the CSI-RS operation might be easier to implement, but the lower resolution in the beamforming selection will increase the interference between the users and ultimately limit how many users and layers per user that can be spatially multiplexed to increase the throughput.
New field trial based on SRS
The Signal Research Group has carried out a new field trial in Plano, Texas. The unique thing is that they confirm that the SRS operation was used. They utilized hardware and software from Ericsson, Accuver Americas, Rohde & Schwarz, and Gemtek. A 100 MHz channel bandwidth in the 3.5 GHz band was considered, the downlink power was 120 W, and a peak throughput of 5.45 Gbps was achieved. 8 user devices received two layers each, thus, the equipment performed spatial multiplexing of 16 layers. The setup was a suburban outdoor cell with inter-cell interference and a one-kilometer range. The average throughput per device was around 650 Mbps and was not much affected when the number of users increased from one to eight, which demonstrates that the beamforming could effectively deal with the interference.
It is great to see that “real” reciprocity-based Massive MIMO provides such great performance in practice. In the report that describes the measurements, the Signal Research Group states that not all 5G devices support the SRS-based mode. They had to look for the right equipment to carry out the experiments. Moreover, they point out that:
“Operators with mid-band 5G NR spectrum (2.5 GHz and higher) will start deploying MU-MIMO, based on CSI-RS, later this year to increase spectral efficiency as their networks become loaded. The SRS variant of MU-MIMO will follow in the next six to twelve months, depending on market requirements and vendor support.“
The following video describes the measurements in further detail:
If you are an academic physical-layer researcher, like me, you might be used to treating the base station as a single unit that takes a digital data signal as input and then outputs an electromagnetic radio wave (or the opposite in the uplink). The reality is quite different, or at least it used to be.
A traditional base station consists of three main components: a baseband unit (BBU) that takes care of digital signal processing, a radio unit that creates the analog radio-frequency (RF) signal, and a passive antenna that emits the RF signals with a constant radiation pattern. Due to the size and weight constraints of masts and towers, the radio and BBU are deployed underneath and there is a long RF feeder cable between the antenna and radio, resulting in substantial power losses. This is illustrated as “Step 1” in the figure below. A single BBU can support multiple radios that are deployed on the same site, which might cover different frequency bands or cell sectors (this is not illustrated).
Now when the radio hardware has reduced in size, it is common to use remote radio units that are deployed in the tower, close to the antenna instead of close to the BBU. This is denoted as “Step 2” in the figure above and became common in the 4G era. Only a short RF feeder cable is then needed, while an optical fiber can be drawn from the BBU to the radio. The next step in the development is active antennas that integrate the antenna and radio into a single unit. There are many types of active antennas, from single-antenna units with constant radiation patterns to Massive MIMO antennas that adapt the radiation patterns by beamforming. To distinguish these things, the term advanced antenna system (AAS) is being used in the industry to refer to active Massive MIMO antenna arrays. This setup is denoted as “Step 3” in the figure and is becoming the dominating approach in the 5G era. To limit the capacity of the optical fiber between the AAS and BBU, an AAS might perform a limited set of baseband processing to compress/decompress the signals.
In summary, the latest radio-integrated active antennas are quite similar to what physical-layer researchers have been imaging for a while: A single unit that takes digital signals as input and emits an RF signal. Small cells can even include the BBU in the active antenna, while macro cell deployments purposely keep the BBU separate so it can be shared between multiple active antennas (it can even be moved to a nearby “cloud” computer). The advent of AAS technology is a key enabling factor for Massive MIMO deployment; a single box with 64 antennas and 64 radios can be made rather compact, while a deployment with 64 separate antenna boxes, 64 separate radio units, and an equal number of cables wouldn’t make practical sense.
I received an email in late August 2019 from my former boss at KTH, Professor Peter Händel. He had been working for many years on the modeling of hardware imperfections in wireless transceivers. Our research journeys had recently crossed since he had written several papers on the modeling of imperfections in MIMO transmitters and their impact on communication performance. I have been working on similar things but using far less sophisticated models.
The essence of the email was that he wanted us to write a paper together, but the circumstances came as a chock. Peter had been sick for a while and it turned out to be a terminal illness. He asked me to finalize a manuscript that he had initiated. I agreed and we exchanged a few emails but just as I and my postdoc were about to begin the editing of Peter’s manuscript, he passed away on September 15, 2019.
Impact of Backward Crosstalk in MIMO Transmitters
The manuscript considers a type of hardware impairment called backward crosstalk. It can be a major issue in the design of multi-antenna transmitters, but is generally overlooked by communication engineers. The issue arises when you build an antenna-integrated radio, for example, a Massive MIMO array with many antenna elements, power amplifiers, and radio-signal generators in a compact box. In this case, the output signal from one power amplifier will leak into the inputs of the neighboring power amplifiers. Even if the leakage is small in relative terms, it can still have a non-negligible impact since the output power of an amplifier is much higher than the input power. A small fraction of a large power value can still be rather large. In addition to this kind of backward crosstalk between amplifiers, there is also forward crosstalk in practice but it can be neglected for the very same reason.
We managed to finalize the manuscript, thanks to the excellent work by my postdoc Özlem Tuğfe Demir. The paper is now available:
The paper considers a system model containing backward crosstalk, as well as, power amplifier non-linearities and transmitter noise. We characterize the performance both at the transmitter side (the normalized mean-squared error) and at the receiver side (the spectral efficiency). In turns out that optimization based on these two metrics can lead to very different transmission strategies; from a spectral efficiency perspective, one can transmit at higher power and accept a higher level of distortion since the desired signal power is also growing. In the paper, we also demonstrate how the precoding can be adapted to partially compensate for the crosstalk.
This paper is just a first step towards modeling real hardware imperfections that are normally ignored in academia or lumped together into a single additive term characterized by the error-vector magnitude. In the last emails I received from Peter, he expressed his view that there is a lot of open problems to solve at the interface between proper modeling of communication hardware and the design of signal processing schemes. I agree with him and encourage anyone who is looking for open problems on MIMO communications to have a closer look at his final papers on this topic:
There are basically two approaches to achieve high data rates in 5G: One can make use of huge bandwidths in mmWave bands or use Massive MIMO to spatially multiplex many users in the conventional sub-6 GHz bands.
As I wrote back in June, I am more impressed by the latter approach since it is more spectrally efficient and requires more technically advanced signal processing. I was comparing the 4.7 Gbps that Nokia had demonstrated over an 840 MHz mmWave band with the 3.7 Gbps that Huawei had demonstrated over 100 MHz of the sub-6 GHz spectrum. The former example achieves a spectral efficiency of 5.6 bps/Hz while the latter achieves 37 bps/Hz.
T-Mobile and Ericsson recently described a new field trial with even more impressive results. They made use of 100 MHz in the 2.5 GHz band and achieved 5.6 Gbps, corresponding to a spectral efficiency of 56 bps/Hz; an order-of-magnitude more than one can expect in mmWave bands!
The press release describes that the high data rate was achieved using a 64-antenna base station, similar to the product that I described earlier. Eight smartphones were served by spatially multiplexing and each received two parallel data streams (so-called layers). Hence, each user device obtained around 700 Mbps. On average, each of the 16 layers had a spectral efficiency of 3.5 bps/Hz, thus 16-QAM was probably utilized in the transmission.
I think these numbers are representative of what 5G can deliver in good coverage conditions. Hopefully, Massive MIMO based 5G networks will soon be commercially available in your country as well.