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:

http://www.bristol.ac.uk/news/2016/may/5g-wireless-spectrum-efficiency.html

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 τ_{c}, 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.

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.

I note that optimum, sometimes, is to serve up to K = 70 users with M = 200 base station antennas. It is thus not necessarily true that M ≫ K, i.e. there is not always an order of magnitude more antennas than users in massive MIMO.

You are absolutely right! To maximize the sum spectral efficiency it is often preferable to serve relatively many users, with M/K<10. Even if the spectral efficiency per user is not extraordinary, the sum spectral efficiency can be huge.

However, if we want to achieve high spectral efficiency per user, at the cost of lower sum spectral efficiency, we might want to have M/K>10.

Correct: Myth 6…

https://arxiv.org/pdf/1503.06854.pdf

I guess, all mentioned numbers correspond to quasi-static channel conditions (or instant ideal CSI), right? Because channel dynamics brings more and more degradation of SE if many layers are used.

Actually, it could be interesting to discuss the same issues for moving users with Doppler spread 10-20 Hz at least.

In the numerical analysis, we consider Rayleigh fading channels that are static within a coherence block, and independent between blocks. The channel variability is thus captured by the size of the coherence blocks. As you say, more channel dynamics lead to smaller blocks, which in turn give smaller SE.

For any given scenario (carrier frequency, Doppler spread, etc.), you can compute an approximate coherence time and coherence bandwidth, multiply them together and then you have the number of channel uses per coherence block.

Importantly: The Massive MIMO analysis does *not* rely on “ideal CSI” assumptions. Channels are estimated, once per coherence interval, from uplink pilots – and the resulting channel estimation errors (and the pilot overhead) are accounted for in the performance bounds.

Most of the research works consider linear techniques such as ZF, P-ZF, MRC and MMSE to improve the spectral efficiency, where SE is mostly related to SINR and rate. Is there any other techniques to increase SE? Next question is whether DL achievable SE is higher or UL achievable SE?

I would say that there is little need to develop new uplink receive combining or downlink precoding schemes. The schemes that you mention are the ones of main interest. Another way to improve the SE is power control. It can have a substantial impact on the SE:

https://arxiv.org/pdf/1505.03682.pdf

https://arxiv.org/pdf/1509.02633.pdf

https://www.metis2020.com/wp-content/uploads/publications/IEEE_ICC2014_Guo_etal_UplinkPowerControl.pdf

Regarding uplink versus downlink, there is not absolute answer to that question, because there can be substantial transmit power difference between the uplink and downlink. Traditionally, the downlink uses higher power and thereby achieves higher SE. If the total transmit power is the same, then the uplink SE can be larger since the base station has direct access to the channel estimates and can thus decode the signals more accurately.

Thank you Emil Björnson for your sparing your valuable time. I also wonder how to optimize SE and EE in massive MIMO, what is the trade-off between them? Most papers considered the impact of interference when evaluating the SE.

Interference plays an important role, both when evaluating the SE and the EE (energy efficiency). There are several papers that analyzes this tradeoff:

https://arxiv.org/pdf/1112.3810.pdf

https://arxiv.org/pdf/1403.6150.pdf

http://dx.doi.org/10.1109/TVT.2015.2436896

https://arxiv.org/pdf/1505.01181

https://arxiv.org/pdf/1401.4907v4.pdf

The good news is that Massive MIMO can achieve both high SE and EE, since both of these goals are achieved by multiplexing of many UEs, which share the energy costs and achieve a high sum SE. I believe that this is a topic we will return to on the blog.

Sir, can we have the expression for spectral efficiency of massive MIMO?

There are many different expressions for the computing spectral efficiency in Massive MIMO, depending on if it is uplink or downlink, or which processing scheme that is used.

You can find many of these things in Section 4 of my book Massive MIMO Networks, which you can download here: https://massivemimobook.com/wp/