There are thousands of papers that analyze different aspects of Massive MIMO. Although many different algorithms and models have been considered, I would say that the most common ones are:

- Independent Rayleigh fading channels;
- Signal processing based on maximum ratio (MR) or zero-forcing (ZF).

These are, for example, the assumptions made in the textbook Fundamentals of Massive MIMO. The beautiful analysis and insightful closed-form expressions developed under these assumptions have had a profound impact on the adoption of Massive MIMO in 5G. I would, therefore, like to refer to this *canonical form* of the technology as **Massive MIMO 1.0**.

*Taking the technology to the next level*

It is possible to squeeze out even higher spectral efficiency out of multi-antenna systems if we design the systems differently. For example, the paper “Massive MIMO has unlimited capacity” showed that the upper limit on the capacity that appears in Massive MIMO 1.0, due to pilot contamination, can be alleviated by replacing the two above-mentioned assumptions by:

- Spatially correlated Rayleigh fading;
- Signal processing that cancels interference between the pilot-sharing users.

Spatial correlation is something that appears naturally in all communication systems, thus the main difference is to embrace this fact in the signal processing design instead of neglecting it. I believe that this can make such as a huge difference that it is appropriate to introduce the term **Massive MIMO 2.0** to describe this development.

This is done in a recent review paper called “*Towards Massive MIMO 2.0: Understanding spatial correlation, interference suppression, and pilot contamination“*. The paper’s main conclusion is that the acquisition and utilization of spatial correlation information will be key in beyond-5G systems, to take the spectral efficiency to the next level. Since the largest gains appear when having even larger antenna arrays than in 5G, new antenna deployments concepts are bound to arise. Three promising examples are described in the paper: **large intelligent surfaces**, distributed **post-cellular architectures**, and the use of carrier frequencies **beyond 100 GHz**.

As a complement to the review paper, the basics of Massive MIMO 2.0 are also described in the following video:

Can You please provide a chart or some sort of pictorial representation of different ideas and their inter-relationship for a massive MIMO system along with some references. This might be helpful for researchers to gain a quick look on important engineering issues?

I don’t have a chart and I’m not sure what you had in mind for that chart either, but if you want to learn about new research directions for Massive MIMO in a less technical way, I recommend you to read this paper:

Emil Björnson, Luca Sanguinetti, Henk Wymeersch, Jakob Hoydis, Thomas L. Marzetta, “Massive MIMO is a Reality – What is Next? Five Promising Research Directions for Antenna Arrays,” Digital Signal Processing, Submitted for review. https://arxiv.org/pdf/1902.07678

Can I get a Matlab code for zero-forcing for a 10 by 10 antenna.

Zero-forcing is one of the many processing schemes that are considered in the book Massive MIMO Networks. You can download the simulation code at https://massivemimobook.com

Sir, in your video smart signal processing for 5G and beyond,

1 antenna, 8 radiation elements (7 dBi each), 1 transceiver chain, will give 16 dBi gain.

How? Kindly explain sir.

7 dBi + 10*log10(8) = 16 dBi

This is the beamforming gain that you can get if the signals from all 8 radiating elements are received in phase (constructive interference). This only happens if you are lucky and stand on the right place in the cell. By turning each radiating element into an antenna, you can control the phase of the transmitted signal and achieve the beamforming gain wherever the user is!

Sir, please elaborate more on 7 dBi + 10*log10(8) = 16 dBi

7dBi is gain of one antenna so for 8 antenna why it is not 7dBi *8=56 dBi

why we are adding 10*log10(8), what it indicate?

Addition in decibel scale corresponds to multiplication in the power domain.

7 dBi means that you get a ~5 times stronger signal transmitted in the main direction from the antennas, as compared to an isotropic antenna that radiates the signal equally strongly in all directions. When using 8 such antennas, you get 5*8 = 40 times stronger signal than with one isotropic antenna. If you covert 40 to dB-scale, you get 10*log10(40) = 16.

Sir, I got it!!! Thank you.

Dear Professor Emil, in your paper “Massive MIMO Has Unlimited Capacity” you used three different channel models and I was wondering which one is the closest one to the real world case and which one, if not the same, is the hardest to massive MIMO systems in the sense of capacity.

Thanks and kind regards,

Felipe

We didn’t select the spatial correlation models in that paper based on real-world modeling, but in order to cover different properties:

1. Spatially uncorrelated

2. Spatially correlated but all eigenvalues are non-zero

3. Spatially correlated and some eigenvalues are zero or close to zero (spatial sparsity).

The reason was to demonstrate that category 2 is sufficient to prove the unlimited capacity (i.e., linearly independent correlation matrices), while some previous works have required category 3 to show somewhat similar results (i.e., spatially orthogonal matrices). Our main claim is that our result turns the unlimited capacity result from being a special case, to actually being the normal case.

Since you ask about real-world models, let me say that 3GPP is normally considering models that resemble the “local scattering model” from Chapter 2 of my book Massive MIMO networks, but with six clusters instead of one. We use such a model in the paper “Massive MIMO with Spatially Correlated Rician Fading Channels” (https://arxiv.org/pdf/1805.07972.pdf)

Please kindly help me with the Matlab code for correlated upper bound downlink capacity performance in massive mimo using GBSM?

Thank you

I am not aware of any Matlab code that is carrying out this, but I recommend you to have a look at the Quadriga model: https://quadriga-channel-model.de

We use it in Section 7.7 of the book “Massive MIMO networks” http://massivemimobook.com to carry out simulations.

I am confused why many papers use the transmit power as SNR for spectral efficiency plots while their system model includes a noise variance different from unity and the received SNR is different for each user. Could you expain me this please if i missed some concept?

I’m not sure what paper you are referring to but I agree that the transmit power is not equivalent to the SNR in those cases. What I probably have done in some papers is to plot how the spectral efficiency varies when the transmit power varies. Every value of the transmit power will then lead to a different SNR for every user, but all of them will increase as we increase the transmit power and this can be used to show basic behaviors.

Thank you!!

The points you mentioned are right that’s why I am confused with those papers considerations. I will use transmit power for spectral efficiency plots since the received SNR depends on the user. But it is good if I have your works that you used Tx power for spectral efficiency plots. Could you help me how can I access the papers?

No particular paper comes to my mind, but here is a related solution for the case when the users have different SNRs:

https://arxiv.org/pdf/1709.07722.pdf

In some of the plots, we are showing the average SNR on the horizontal axis. When we are changing this SNR we are really just changing the power.

Tnx sir!! I found it useful.