Math behind the pairing UEs in MU-MIMO

Hello Experts.

I am looking for a very detailed MU-MIMO resource (books, website etc), explaining in a simple way the math behind the pairing UEs and how gNB allocates same PRBs for several users per TTI.

Admin note: this post was updated with image below.

Sharetechnote is a good resource.

Simply put: UE are spatially separated they do not interfere each other.

Could you please show me where sharetechnote explains mumimo pairing mechanism?

I am asking how they spatially seperated.

I have read several times those pages, not enough info for me.

There are explanations of csi-rs type 1 type 2 but not the overal MU-MIMO pairing or spatial multiplexing in deep.

As the author @Jaeku_Ryu confessed even he also do not understand completely. :frowning:

Indeed, pairing is not explained on Sharetechnote

It is explained in vendor documentation however.

Huawei explained it well, do a search on HEDEX.


Will have a look Huawei doc.

Could you share doc name for Huawei?

Solution tech guideline or RAN feature doc…

The gNB uses a variety of algorithms to do this, but one common approach is to use a pairing algorithm.

This algorithm pairs UEs that have similar channel conditions and traffic demands.

This is done because UEs with similar channel conditions are more likely to be able to decode each other’s signals, and UEs with similar traffic demands are more likely to be able to share PRBs without causing interference.

Once the UEs have been paired, the gNB allocates PRBs to the pairs in a way that minimizes the interference between the pairs.

This is done by using a variety of techniques, such as assigning different PRBs to different pairs or assigning PRBs to pairs in a staggered manner.

The exact math behind the pairing algorithm and the PRB allocation algorithm is quite complex, but the basic idea is to maximize the overall system throughput by taking into account the channel conditions, traffic demands, and available PRBs of the UEs.

Yes, Thanks.

More or less I know those details but very rough explanation.

If 4 UEs are paired with rank2 or rank1 each all lets say all 100 PRBs to be allocated to those users with full buffer.

How same PRBs can be allocated to different UEs without interfering?

:point_up_2: how is that possible which technique?

You may consult these books:

  1. Thomas L. Marzetta, Erik G. Larsson, Hong Yang, Hien Quoc Ngo - Fundamentals of Massive MIMO-Cambridge University Press (2016)
  2. Shahid Mumtaz, Jonathan Rodriguez, Linglong Dai - mm_ Wave Massive MIMO. A Paradigm for 5G-Academic Press (2016)
  3. Emil Björnson - Massive MIMO Networks_ Spectral, Energy, and Hardware Efficiency-Now Publishers (2017)
  4. Rakhesh Singh Kshetrimayum - Fundamentals of MIMO Wireless Communications (2017)

Beam1 is with maximum gain for user A and null on user B.

Beam 2 is iwth maximum gain on user B and null on user A.

This is why beam 1 and beam 2 do not interfere each other and both user A and user B can use full 273 PRBs from N78.

Not exactly…

Imagine single user MIMO, 2 UEs are in beam 1 and beam 2, and they share 273 PRBs (143 / 130 PRBs for instance).

They do not interfere each other (or very low interference) and asking how exactly those 2 users share the same PRB (in subscarriers level).

Single user MIMO means they do not share same PRBs.

Single user MIMO usually refers to several users within same beam so they share the PRBs, they do not use all 273 PRBs each.

FDM of scheduled users in a slot is vendor dependent.

And all SU-MIMO users.

Usually when 2 UEs are paired they have low channel correlation, meaning that the channel of UE1 is different from the channel of UE2, so they don’t interfere with each other.

This is usually achieved using spatial separation, meaning if 2 UEs are very spatially close we can’t use MU-MIMO.

I believe that gNB will calculate the correlation matrix and decide whether to pair 2 UEs or not.


Means that those users are served by different antenna sub arrays?

I’m not 100% sure.

I think this depends on whether beamforming is implemented in Time domain (analog) or in the frequency domain (digital).

Basically MU-MIMO opens another dimension to separate the UEs which is the spatial domain.


I am asking this because N1 N2 O1 O2 doing things complicated when from logical to physical antenna mapping, which I try to figure out also.

In my understanding, those paired users must be seperated logically first with different DFT beams and signal is mapped to physical antenna ports.

This is the most complicated part.

Paired users must be in different O1 and O2.

You canot pair 2 UEs that are in same O1 and same O2 but in different N1 and N2.

Please check that…

Not so sure about that, as FDM features may allow that, as i said this is vendor specific feature.

FDM feature is Nokia concept.

I think you are correct, since N1 N2 O1 O2 values pair for single direction means a physical UE1 location.

And since we know that the UEs must be separated spatially the value sets of these parameters can’t be duplicate.

If they are duplicated this means that the 2 beams for 2 UEs are directed at the same location.