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 hᴴg = 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 hᴴg/(‖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.

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.

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.

A series of recent papers,

• Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems
• One-bit massive MIMO: Channel estimation and high-order modulations,
• Performance of the Wideband Massive Uplink MIMO with One-Bit ADCs,

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.

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.