Category Archives: Technical insights

Pilot Contamination in a Nutshell

One word that is tightly connected with Massive MIMO is pilot contamination. This is a phenomenon that can appear in any communication system that operates under interference, but in this post, I will describe its basic properties in Massive MIMO.

The base station wants to know the channel responses of its user terminals and these are estimated in the uplink by sending pilot signals. Each pilot signal is corrupted by inter-cell interference and noise when received at the base station. For example, consider the scenario illustrated below where two terminals are transmitting simultaneously, so that the base station receives a superposition of their signals—that is, the desired pilot signal is contaminated.

When estimating the channel from the desired terminal, the base station cannot easily separate the signals from the two terminals. This has two key implications:

First, the interfering signal acts as colored noise that reduces the channel estimation accuracy.

Second, the base station unintentionally estimates a superposition of the channel from the desired terminal and from the interferer. Later, the desired terminal sends payload data and the base station wishes to coherently combine the received signal, using the channel estimate. It will then unintentionally and coherently combine part of the interfering signal as well. This is particularly poisonous when the base station has M antennas, since the array gain from the receive combining increases both the signal power and the interference power proportionally to M. Similarly, when the base station transmits a beamformed downlink signal towards its terminal, it will unintentionally direct some of the signal towards to interferer. This is illustrated below.

In the academic literature, pilot contamination is often studied under the assumption that the interfering terminal sends the same pilot signal as the desired terminal, but in practice any non-orthogonal interfering signal will cause the two effects described above.

Cell-Free Massive MIMO: New Concept

Conventional mobile networks (a.k.a. cellular wireless networks) are based on cellular topologies. With cellular topologies, a land area is divided into cells. Each cell is served by one base station. An interesting question is: shall the future mobile networks continue to have cells? My quick answer is no, cell-free networks should be the way to do in the future!

Future wireless networks have to manage at the same time billions of devices; each needs a high throughput to support many applications such as voice, real-time video, high quality movies, etc. Cellular networks could not handle such huge connections since user terminals at the cell boundary suffer from very high interference, and hence, perform badly. Furthermore, conventional cellular systems are designed mainly for human users. In future wireless networks, machine-type communications such as the Internet of Things, Internet of Everything, Smart X, etc. are expected to play an important role. The main challenge of machine-type communications is scalable and efficient connectivity for billions of devices. Centralized technology with cellular topologies does not seem to be working for such scenarios since each cell can cover a limited number of user terminals. So why not cell-free structures with decentralized technology? Of course, to serve many user terminals and to simplify the signal processing in a distributed manner, massive MIMO technology should be included. The combination between cell-free structure and massive MIMO technology yields the new concept: Cell-Free Massive MIMO.

What is Cell-Free Massive MIMO? Cell-Free Massive MIMO is a system where a massive number access points distributed over a large area coherently serve a massive number of user terminals in the same time/frequency band. Cell-Free Massive MIMO focuses on cellular frequencies. However, millimeter wave bands can be used as a combination with the cellular frequency bands. There are no concepts of cells or cell boundaries here. Of course, specific signal processing is used, see [1] for more details. Cell-Free Massive MIMO is a new concept. It is a new practical, useful, and scalable version of network MIMO (or cooperative multipoint joint processing) [2, 3]. To some extent, Massive MIMO technology based on the favorable propagation and channel hardening properties is used in Cell-Free Massive MIMO.

Cell-Free Massive MIMO is different from distributed Massive MIMO [4]. Both systems use many service antennas in a distributed way to serve many user terminals, but they are not entirely the same. With distributed Massive MIMO, the base station antennas are distributed within each cell, and these antennas only serve user terminals within that cell. By contrast, in Cell-Free Massive MIMO there are no cells. All service antennas coherently serve all user terminals. The figure below compares the structures of Cell-Free Massive MIMO and distributed Massive MIMO.

comami cellfree
Distributed Massive MIMO Cell-Free Massive MIMO

[1] H. Q. Ngo, A. Ashikhmin, H. Yang, E. G. Larsson, and T. L. Marzetta, “Cell-Free Massive MIMO versus Small Cells,” IEEE Trans. Wireless Commun., 2016 submitted for publication. Available:

[2] G. Foschini, K. Karakayali, and R. A. Valenzuela, “Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency,” IEE Proc. Commun. , vol. 152, pp. 548–555, Aug. 2006.

[3] E. Björnson, R. Zakhour, D. Gesbert, B. Ottersten, “Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies with Instantaneous and Statistical CSI,” IEEE Trans. Signal Process., vol. 58, no. 8, pp. 4298-4310, Aug. 2010.

[4] K. T. Truong and R.W. Heath Jr., “The viability of distributed antennas for massive MIMO systems,” in Proc. Asilomar CSSC, 2013, pp. 1318–1323.

Definition of Massive MIMO

What is Massive MIMO?  The term has been used for many different systems and the only common denominator seems to be a multi-user MIMO system with everything between 10 to infinitely many antennas.  In the book [1], the authors give the following definition:

“Massive MIMO is a useful and scalable version of Multiuser MIMO.  There are three fundamental distinctions between Massive MIMO and conventional Multiuser MIMO. First, only the base station learns G. Second, M is typically much larger than K, although this does not have to be the case. Third, simple linear signal processing is used both on the uplink and on the downlink. These features render Massive MIMO scalable with respect to the number of base station antennas, M.”

(Note: M is the number of antennas, K is the number of users, and G denotes the channel matrix).

In [2], we find another definition:

“Massive MIMO is a multi-user MIMO system with M antennas and K users per BS. The system is characterized by M ≫ K and operates in TDD mode using linear uplink and downlink processing.”

Both are nice general definitions that cover most systems that commonly are called “Massive MIMO”.  However, their generality also makes them vague and they fail to pinpoint the essence of Massive MIMO.  Here, is my take on a slightly more precise definition:

“Massive MIMO is a multi-user MIMO system that (1) serves multiple users through spatial multiplexing over a channel with favorable propagation in time-division duplex and (2) relies on channel reciprocity and uplink pilots to obtain channel state information.”

Now, you might ask: So what is then “favorable propagation”?  We need a second definition:

“The propagation is said to be favorable when users are mutually orthogonal in some practical sense.”

Again you ask: in what practical sense?  If h∈ℂᴹ is the channel vector to one user and g∈ℂᴹ the channel vector to another, the users are said to be orthogonal if hg = 0.  Unfortunately, this is never true in a real system.  It can be practically true, however, if we say that users are practically orthogonal when hg/(‖h‖‖g‖) has mean zero and a variance that is much smaller than one.

There we go: a more-or-less rigorous definition of Massive MIMO.  Note that this definition does not require the number of users to be small in any sense.  So, to the big question: How many antennas does a base station need to be “massive”? The answer is given for the i.i.d. Rayleigh fading channel in the following curve that shows how the users’ channels become practically orthogonal as the number of antennas is increased.

Massive MIMO base stations have more than 100 antennas


  1. [1] T. L. Marzetta, E. G. Larsson, H. Yang, N. Q. Ngo. Fundamentals of Massive MIMO. Cambridge University Press, 2016.
  2. [2] T. V. Chien, E. Björnson, “Massive MIMO Communications,” in 5G Mobile Communications, W. Xiang et al. (eds.), pp. 77-116, Springer, 2017.

How Many Antennas are Useful?

One question tends to reoccur: How many antennas can a Massive MIMO base station usefully deploy? Current thinking for macro-cellular is that 100-200 antennas would be suitable. Will we in the future see a lot more, thousands or so?

In that application, I don’t think so. Here is why.

What ultimately limits Massive MIMO is mobility: no more than half of the coherence time-bandwidth product should be occupied by pilot transmission activities. (This is the “half and half rule”.) In macro-cellular at 3 GHz, with highway mobility we may have on the order of 200 kHz x 1 millisecond coherence; that is 200 samples. With pilot reuse of 3 (that practically does away with pilot contamination), we could, then ultimately learn the channel to some 30 simultaneously served terminals – assuming mutually orthogonal pilots. Once the number of base station antennas M reaches beyond twice this number, with some margin – say M=100, the spectral efficiency grows logarithmically with M. That means, even doubling M yields only a 3dB effective SINR increase, that is a single extra bit per second/Hz per terminal. Beyond M=100 or M=200, it may not be worth it. Multiple antennas are only truly useful if they are used to multiplex, and mobility limits the amount of multiplexing we can perform.

So why not quadruple the number of antennas for additional coverage? May not be worth it either. Going from M=200 to M=2000 gives 10 dB – that pays for a 75% range extension, or, alternatively, a tenth of the losses incurred by an energy-saving coated window glass.

In stationary environments, the story is different – a topic that we will be returning to.

How distant into the future?
How distant into the future?

How Much does Massive MIMO Improve the Spectral Efficiency?

It is often claimed in the academic literature that Massive MIMO can greatly improve the spectral efficiency. What does it mean, qualitatively and quantitatively? This is what I will try to explain.

With spectral efficiency, we usually mean the sum spectral efficiency of the transmissions in a cell of a cellular network. It is measured in bit/s/Hz. If you multiply it with the bandwidth, you will get the cell throughput measured in bit/s. Since the bandwidth is a scarce resource, particularly at the frequencies below 5 GHz that are suitable for network coverage, it is highly desirable to improve the cell throughput by increasing the spectral efficiency rather than increasing the bandwidth.

A great way to improve the spectral efficiency is to simultaneously serve many user terminals in the cell, over the same bandwidth, by means of space division multiple access. This is where Massive MIMO is king. There is no doubt that this technology can improve the spectral efficiency. The question is rather “how much?”

Earlier this year, the joint experimental effort by the universities in Bristol and Lund demonstrated an impressive spectral efficiency of 145.6 bit/s/Hz, over a 20 MHz bandwidth in the 3.5 GHz band. The experiment was carried out in a single-cell indoor environment. Their huge spectral efficiency can be compared with 3 bit/s/Hz, which is the IMT Advanced requirement for 4G. The remarkable Massive MIMO gain was achieved by spatial multiplexing of data signals to 22 users using 256-QAM. The raw spectral efficiency is 176 bit/s/Hz, but 17% was lost for practical reasons. You can read more about this measurement campaign here:

256-QAM is generally not an option in cellular networks, due to the inter-cell interference and unfavorable cell edge conditions. Numerical simulations can, however, predict the practically achievable spectral efficiency. The figure below shows the uplink spectral efficiency for a base station with 200 antennas that serves a varying number of users. Interference from many tiers of neighboring cells is considered. Zero-forcing detection, pilot-based channel estimation, and power control that gives every user 0 dB SNR are assumed. Different curves are shown for different values of τc, which is the number of symbols per channel coherence interval. The curves have several peaks, since the results are optimized over different pilot reuse factors.

Spectral efficiency
Uplink spectral efficiency in a cellular network with 200 base station antennas.

From this simulation figure we observe that the spectral efficiency grows linearly with the number of users, for the first 30-40 users. For larger user numbers, the spectral efficiency saturates due to interference and limited channel coherence. The top value of each curve is in the range from 60 to 110 bit/s/Hz, which are remarkable improvements over the 3 bit/s/Hz of IMT Advanced.

In conclusion, 20x-40x improvements in spectral efficiency over IMT Advanced are what to expect from Massive MIMO.

Are 1-bit ADCs Sufficient?

A series of recent papers,

suggest the use of 1-bit ADCs in Massive MIMO base station receivers. Important studies of a concept, that offers great potential for cost saving and simplification of transceiver hardware.

One-bit ADCs
One-bit ADCs quantize the sign of the real and imaginary part of the complex baseband signal.


Granted, much lower resolution will be sufficient in Massive MIMO than in conventional MIMO, but will one bit be sufficient? These papers indicate that the price to pay is not insignificant: the number of antennas may have to be doubled in some cases. Also, while the use of symbol-sampled models as in these studies may give correct order-of-magnitude estimates of capacity, much future work appears to remain to understand the effects of digital channelization/prefiltering and sampling rate conversion if 1-bit frontends are going to be used.