How many beams can you send from a MIMO array? [Frequently Asked Questions]

Professor Emil Björnson (KTH, Sweden) answers the question "How many beams can you send from a MIMO array?", which he has received repeatedly in emails, on his blog, and in comments on this KZbin channel. The answer is not what you think it is, unless we reformulate the question. Emil illustrates and explains the basic concepts in an accessible manner.
Intro music: Quiet Calculation by Joseph McDade.

[@prateekbhadauria7004]

Thank you sir for your delivering excellent knowledge and clearing the basic concepts.

[@MehdiTaherkhani-r7z]

Thanks for sharing the valuable information. At 3:07, you mentioned that the array can send infinite number of beams at the same time (while, you mentioned earlier that only one beam can be steered with phase shifting along the antenna elements). So, how is it possible to send multiple beams at the same time with an array?

[@WirelessFuture]

What I meant to say earlier in the video is: If you send the same signal from all antennas but with different phase shifts, then you will steer the signal as a beam. If you want to send multiple beams, each beam must contain a different signal. You design each of them as if you were only sending one beam and then add the phase-shifted signals at the input to each antenna. This is an instance of the “superposition principle”

[@MehdiTaherkhani-r7z]

@@WirelessFuture If I am not mistaken, you meant that each of the antenna elements can be excited with multiple signals with different phase shifts (with respect to each other) at the same time to produce multiple beams. Is that correct?

[@WirelessFuture]

Yes, that is correct

[@miriamc9582]

@@WirelessFuture Does this require infinite number of RF chains?

[@WirelessFuture]

@@miriamc9582No, it is sufficient to have two antennas, each connected to an RF chain. You can then send arbitrarily many signals simultaneously with slightly different beam directions. However, we don’t want to send more than two beams when having two antennas (RF chains) to avoid interference between them.

[@kakhaval]

Many thanks, I was struggling on this before but now you made clear. One question please: I assume the beam management will start with regularly spaced beams but once handsets locations and channel responses are known it will refine the beams. How does it locate the handset? is it using GPS or the network uses its own algorithm?

[@WirelessFuture]

It is not necessary to know the GPS location because to utilize that information, we also need to know the precise orientation of the handset and base station, and the exact environment around it. There is a simpler way: By measuring the receive amplitudes and phase shifts for some different beams, we can calculate “channel coefficients” that represent the complete channel between the transmitter and receiver. It is basically the total amplitude and phase shift between on each subcarrier for each pair of antennas. Based on that, we can calculate the beams that maximize the received signal power. This is the kind of things that we cover in the open access book “Introduction to Multiple antenna communications and reconfigurable surfaces”

[@getsamik1019]

Hello Professor Emil Björnson, mimo channel is defined as Y=Hx + n. why H, channel coefficient matrix is decomposed with SVD.

[@WirelessFuture]

The SVD is utilized when communicating over point-to-point channel, with multiple antennas at both the transmitter and receiver. The decomposition identifies ways to transmit multiple signals with different spatial directivity such that the receiver will observe them from different directions without any interference in between. In this way, one can transmit multiple streams/layers of data without them affecting each other, thereby increasing the capacity. Here is a lecture video where this is explained in detail: kzbin.info/www/bejne/h2SlY6ipYqxrl7s

[@AlexAlex2-r7l]

@ Wireless Future , Thank you so much! How can I cite the rule of X/4 in my work? Is it mentioned in a certain book or specification, please?

[@WirelessFuture]

This rule-of-thumb can be derived by analyzing what ratio between the number of antennas and number of users that give the largest sum rate. The exact optimal ratio depends on the exact setup. One source for the value X/4 is Figure 4 in arxiv.org/pdf/1503.06854 (the best ratio is 4.5 in that figure). You can also read Section 7.2 in the book Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency, which elaborates more on these things.

[@千里之行-z5r]

thank you sir

[@Dplynch]

Do you think that superdirective antenna arrays can be a practical solution for this problem?

[@WirelessFuture]

Superdirectivity can increase the gain of beams sent in particular directions, but not increase the total number of distinguishable beams. It is rather the opposite because the gain in some other beam directions is instead attenuated. I think one might use superdirectivity in fixed point-to-point links where the transmitter and receiver are deployed to exploit the extra directivity, but not in mobile scenarios where the user devices can be rotated arbitrarily.

[@Dplynch]

Ok, thank you for your response, my line of thinking was related to more narrow beam widths.

[@kakhaval]

Thanks again but it seems another factor also defines number of simultaneous beams. For example 20MHz LTE ofdm symbol may potentially be allocated to 100 UEs (one PRB per UE) over same symbol time of 67 microseconds so the number of beams must be 100 over 67 microseconds simultaneously. Am I missing something?

[@WirelessFuture]

The main benefit with multi-user MIMO is that you can assign the same PRBs to multiple users, because you are separating the users by transmitting different beams to them. This differs from previous technologies where 20 MHz spectrum implied 100 PRBs, which could then be distributed among up to 100 UEs. This is not how 5G and future systems operate. The number of users that you can serve (i.e., the number of beams) _on the same PRB_ is fundamentally limited in the way described in this video. In a practical system, you will also be limited by how many reference/pilot signals exist in the standard, because this determines how many users you can estimate the channel coefficients to in each PRB.

[@kakhaval]

@@WirelessFuture Many thanks Professor. Really helpful tips.

[@PukarShakya-v5j]

Thanks and one curious question, Is it possible to create orthogonal beams and send to same user so that separate streams can be transmitted on those beams and increase the data rate for that user ?

[@WirelessFuture]

Yes, this is known as single-user MIMO or point-to-point MIMO. The number of beams that can be sent in this way is equal to the number of distinguishable paths between the transmitter and receiver. If you begin with sending one beam directly between them, then the next beam needs to be aimed toward a reflecting object that is located outside the first beam, from both the transmitter’s and receiver’s viewpoint.

[@PukarShakya-v5j]

@@WirelessFuture thanks for the answer, but what if there is no reflection path, it is simply LoS scenario

[@WirelessFuture]

In a far-field free-space LOS channel, one can only transmit one beam since there is only one path. In practical LOS scenarios on earth, there are usually some reflected paths as well but they can be so much weaker than the LOS path that they doesn’t help much in boosting the data rate. This is why multi-user MIMO is particularly important in current and future systems because one can always send beams to multiple users, even in LOS scenarios.

[@PukarShakya-v5j]

@@WirelessFuture thanks for your very good explanation :)

[@dmitrypolpudenko8669]

Is there a short video on how closed loop M-MIMO beam forming works, how delay/weight coefficients are derived from SRS measurement?

[@WirelessFuture]

We don’t have a video of this length on that topic, but here is a lecture video about it: Lecture 6: Uplink Multiuser MIMO and Channel Acquisition kzbin.info/www/bejne/mZjUf55jfLyknKs

[@dmitrypolpudenko8669]

@@WirelessFuture Thank you so much! Keep up your great work! Always enjoy your videos and lot. Is there a chance you might interview Mischa Dohler?

[@WirelessFuture]

Yes, that might happen. What would you like to hear him talking about?

[@LipingBai]

X/4 beams where X is the number of antennas. Another rule of thumb to go in my notes. Communication is really a field filled with rule of thumbs :).

[@LipingBai]

Other rule of thumbs so far: coherence time is approximate with 𝑎𝜆/𝑣 where 𝑎 ∈ [0.25,0.5], 𝑣 user speed; Roughly 5% of the time is devoted to the pilot signal (depending on the operator design); for the multi-path channel modelling, if |d − d_i|

[@WirelessFuture]

There are indeed many rule-of-thumbs and heuristics. Some of them determine when specific simplifications/approximations are valid (e.g., coherence time, narrowband, iid correlation), while others are more related to what is a good radio resource management strategy (e.g., how many beams to send, how to allocate power between the beams).

[@mxmzry]

Hi professor nice video about mimo array no of beams my question is what is the increase in support distance using beamforming mimo ie what distance can mimo support in fixed wireless application where radios are long distances does 4x4 mimo double the support distance as an example thanks

[@WirelessFuture]

If you compare against a SISO system with a system with 4 transmit and 4 receiver antennas, then the multi-antenna case will give you 4*4=16 times higher SNR. In a line-of-sight scenario with a propagation loss that grows as “distance^2”, this allows for 4 times the range. In a non-line-of-sight scenario with a propagation loss that grows as “distance^4”, this allows for doubling the range.

[@Julia-hu4xe]

Thanks, I am on some exercises from your new book. The exercise 8.4 a) is about minimizing the MMSE equation. Can you derive the solution from the MMSE equations in the book from chapter 2.5? Thank you. I am struggeling a bit with that. (I have the solutions.)

[@WirelessFuture]

Exercise 8.4a is not an MMSE problem since there is no mean. It is instead called a least square problem. You can solve it following such methods: en.wikipedia.org/wiki/Least_squares#Solving_the_least_squares_problem

[@pitmaler4439]

Many Thanks, when I have any scenario e.g. 10 antennas and 2 targets - nonetheless, I can focus the beams to both UEs and can count all beams e.g. higher than -20 dB - that is a finite number - is that right? Thanks.

[@WirelessFuture]

I don’t fully understand the scenario that you consider. Each “beam” is a data signal transmitted with a particular directivity. In principle, multiple UEs can receive the same data from that beam, if the data is encoded to allow that. Normally, each beam is only meant for one UE. With 10 antennas, you don’t want to send more than 10 beams since these won’t be sufficiently distinguishable at the UEs.

[@pitmaler4439]

@@WirelessFuture yes, I meant all these additional beams that don't transmit any data but they are there, I suggest - we cannot cancel all these small beams. So I think we have to these 2 data transmitting beams additional perhaps 15 very small beams - I think it is known as side lobes.

[@WirelessFuture]

@@pitmaler4439 ok, now understand your point. A beam isn’t like a laser or flashlight that is entirely confined in a small area, but it contains a main lobe in the intended direction and side lobes that appear as small ripples in other directions. They all contain the same signal. When people illustrate beams, they usually only show the main lobes but the side-lobes are always there too. So if you send two beams, you will have two main lobes and a two collections of side-lobes.

[@jasminnadic2103]

Thanks, where can you find the solutions to the exercises in your new book?

[@WirelessFuture]

You can find detailed answers here: github.com/emilbjornson/mimobook/blob/main/intro-MIMO-with-answers.pdf

[@hassanrabbani3221]

what is the best course to understand MIMO ?

[@trinity832]

KZbin

[@WirelessFuture]

I would recommend my book, which you can download here: www.nowpublishers.com/article/BookDetails/9781638283140 We also have a video series called Introduction to Multiple Antenna Communications on our channel.

[@dhimanchoudhury4001]

Does this apply to RIS

[@WirelessFuture]

It doesn’t directly apply to an RIS since it isn’t generating signals but reflect them. An RIS has only a limited ability to modify the reflection directions of the incident signals. If signals arrive from widely different angles, a large RIS (width/height greater than the number of beams times the wavelength/2) will also reflect them in widely different directions but can shift them all by the same amount (in the wave number domain). The width of the reflected beams is determined by the size of the RIS, but since we must shift all beams similarly, we can in general not focus each signal at its desired location. Hence, an RIS can usually only control one beam reflection at the time, even if there are some exceptions.