Dear Mr Moarad !

Theoretically! A lot of literature is available to reduce the interference in MIMO sytem . But actually! There is no method to calculate the number of users that may establish a optimum number of call s without interface at its busy hours. You can easily get the KPI report from telecom operators and see the deviation from theoretical model to its practicality .

Thank you Khalid for the answer but what is the exact or approximate value of this number according to M and N (according to the BER also )?

Dear Dr.Mourad

i think it is also the number of user it is also regarded with the type of user/service that utilized the channel for example in 5G networks there are three different types of application namely eMBB, URLLC and mMTC, and each type of this application demand different type of bit rate to each users.

i hope this could also help you

sciencerly

thank you Tarik for the answer, yes it is an answer if we see it on the application side, what I want is to suppose that we have K users (or UE: unit equipment), what is the maximum number of K can be transmitted or received by a URA in Mm waves?

Dear Mr. Mourad,

The number of users that can be simultaneously supported depends on the radio environment and the application type.

I hope the following paper could help you.

Article Massive MIMO in the UL/DL of cellular networks: How many ant...

thank you Imran for your response, I saw the abstract of the article. I think that the article is good but its written only in the case of a uniform and linear Array (ULA) with N antennas in Massive MIMO and moreover it dates from 2013.

I asked the question in the case of a URA with MXN antennas and in Massive MIMO in the Mm Waves and without interferences.

So I ask the question again: what is the maximum number K of users that can be transmitted or received under the conditions described above?

Dear Benyarou Mourad

If you have a MIMO wireless communication system with Nt antennas and Nr single antenna users. which is termed multi user Mimo then the number of independent users will be Nr that All users can be occupy the same frequency and the same time but differ only in the space. If Nr is smaller eqaul Nt the number of users that can be served will be equal to Nr which means that the maximum number of users that can be served with the whole band width at the same time will be Nt. This is irrespective of the shape of the array as it is assumed that the antennas are point sources.

Best wishes

Thank you Abdelhalim, i totally agree with you with the terms of multiuser MIMO.

Dear friend, I ask the same question again, if we have M uniform and linear array (ULA) with N antennas each, then we will have a rectangular and uniform array (URA) with MXN antennas.

In a simpler case, if a ULA with N antennas can send or receive K users, therefore normally a URA with MXN antennas can send or receive KX M users, this is not always true because we have to see what the type of multiplexing is used between users, the type of diversity used, the symbol rate and therefore the BER...

I am looking for the maximum number K of users in a most general case.

Thanks again

Hi Benyarou Mourad,

Do not confuse the number of antennas with the array configuration. For example, an N1xN2-element uniform planar array (UPA) has N=N1N2 elements in total. Now, in typical Massive MIMO, we have a fully-digital array architecture, that is one RF chain per antenna. Therefore, with N antennas/RF chains, we can serve up to N single-antenna users!! Last but not least, the transmission/reception technique can be zero-forcing, in case the channel matrix is well-conditioned. Alternatively, we can use simple maximum ratio combining/transmission since the user channels tend to become orthogonal to each other, as the number of BS antennas increase; in fact, this is the so-called favourable propagation property of Massive MIMO.

Hope this helps.

Regards,

Kostis

For mmWave/THz systems, we have a hybrid analog-digital array, where the number of RF chains is much smaller than the number of BS antennas. In this case, the BS can serve up to Nrf users, where Nrf is the number of RF chains.

Regards,

Kostis

Thak you Konstantinos, your explanation is remarkable and precise, your resonance assumes that upstream of the RF chains we have only a single user / RF chain, but this is not always the case because we can increase the number of users before the same RF chain in the spatial, frequency, temporal domain or even by orthogonal codes (for example in DS-CDMA).

In my question I wrote without interference so normally the beams directed or received from the users are orthogonal according to the angles theta and phi of each user. A beam may contain, depending on its opening, one or more users (depending on the access technique used in this small space).

So the total number K of users is the product of the number of users contained in each RF chain (by looking at the type of the access or the multiplexing technique and the diversity used) times the number of users that can transmit or receive the Uniform and Rectangular Array (URA) in the MmWives.

my regards and thank you once again.

Exactly. We can also consider an orthogonal multiple access scheme (OFDMA, CDMA, etc) to increase the number of served users per RF chain.

Thanks for the nice discussion!

Regards,

Kostis

Thank you Konstantinos for your intervention,

So we come back to our point of departure and the same question:

What is the maximum number of users can be tansmitted or received without interferences in Massive MIMO with a Uniform and Rectangular Array (URA) with the MXN antennas in MmWaves?

Thank you

The final answer depends on the rate requirements of each user. For instance, you can divide the frequency resource to multiple subcarriers to serve multiple users per RF chain. But then each user will get part of the bandwidth, i.e., W/M, where M is the number of subcarriers, which can give a user rate smaller than a prescribed minimum rate (to ensure QoS).

Regards,

Kostis

thanks again Konstantinos , yes it's an idea if we use spectrum sharing like in OFDMA or use some other type of sharing.

You see that there is a multitude of combinations to increase this number of users K, by choosing for example the type of multiple access, the type of diversity, the symbol rate, a resonable BER = f(SNR) (or SNIR) .....

Is it necessary to study each case separately and then we will take the one that has the greatest number of users? I think it is too cumbersome and its going to take a long time.

So the question that arises, is there not a simpler method to calculate this maximum number K without going through the study of each case?

I remind you the frequency band used in our case in MmWaves is in general 30GHz

Dear Benyarou Mourad , I agree with approach of Konstantinos Dovelos , Abdelhalim abdelnaby Zekry , Imran A. Khoso , and Tariq Kanaan As an additional comment, I'd like to say that by such calculation need to take into account the using of Double Polarization, Coding of Signals, NOMA , Time multiplexing.

In the general case for MxN antennas in MmWaves and if each user will get only the one subcarrier then we can get the total number users:

K=2xMxNxWxTxNOMAxCode, where W is a full number of subcarriers, T is a number of time slots, NOMA is the quantity of position of NOMA-levels, Code is the number of orthogonal codes of signals, and coefficient 2 subordinate to the quantity of polarizations of signals (Horizontal and Vertical polarizations).

If each user will get part of the bandwidth, i.e., W/D, where D is the number of subcarriers for one user (is the same for all users), W is is a full number of subcarriers then we have:

K=2xMxNxWxTxNOMAxCode/D.

Dear Benyarou Mourad ,

Thank you Vadym!

There are two functions for using MIMO. These are the space diversity and space multiplexing. It is sensible to determine which applications are targeted from using MIMO.

The most interesting application of the MIMO is the space multiplexing. In this MIMO operation one would like to set up independent wireless signal passes in the system. I termed these independent paths virtual wireless wires.

So your question is related to such virtual wireless wires.

In space multiplexing the signals distinguished by an an independent path rather than time or frequency.

Irrespective of the MIMO system with total number of transmit antenna Nt and total receive antennas Nr the maximum number of independent paths is Nr provided Nr

Yes, dear Abdelhalim abdelnaby Zekry , it is the significant aspect that need to take into account. Thank you!

Thank you Vadym Slyusar Abdelhalim abdelnaby Zekry Konstantinos Dovelos Imran A. Khoso Benyarou Mourad it is really a useful discussion

Thank you dear colleagues for your answers, I am truly honored, the answers are clear, crisp and precise.

I apologize for not being able to answer in time because I was traveling by car of more than 900km, I have just entered the house I will answer you in the evening or tomorrow.

My greetings

Dear Benyarou Mourad , welcome to Home!

Always keen on having discussions about massive MIMO!!

Best regards,

Kostis

thank you for your answer dear colleague Abdelhalim., i completely agree with you, space multiplexing is used to increase the capacity of our system and diversity has many forms and one of them is the use of polarization antennas (+ 45 degree or vertical and -45 degree or horizontal) as in GSM to once again increase the capicity (X2).

thank you dear colleague Vadym, so I think that's the answer, they simple and defined all the parameters of the system.

K=2xMxNxWxTxNOMAxCode/D.

well done

Do not forget to add that this number does not take into account the interferences (noises and jammers), we cannot have all the access in 5D (time, frequeny, space, diversity, code) so this report is for one case ideal communications.

So the real ratio is much lower than that indicated above.

my greetings

Dear researchers

IN addition to what you mentioned i would add some basic explain;

the number of users depends on the application. However, we can use another merit to measure Bandwidth efficiency such as channel capacity or throughput. in general we modeled wireless channel as complex envelope and in mimo channel case we modeled as matrix of complex envelope and you can find many stanards describe multipath propagation in mimo wire less channel in 3GPP and IEEE. However, the capacity of channel also depends on other factor like diversity, beamforming and spatial multiplexing. so that, if you want to make research in this field, you have to specify system parameters, application and and communication scenario in your experiments. However, i recommend you three papers that have a good explanation to what i mentioned.

P.S: in third paper researchers mention that capacity in N*M mimo channel is

C=sum(log2(1+(SNR/N)*di))

Best Regards Benyarou Mourad Konstantinos Dovelos Vadym Slyusar Abdelhalim abdelnaby Zekry Imran A. Khoso Khalid Ali Khan

[1] E. Bonek. The MIMO radio channel. http://publik.tuwien.ac.at/files/pub-et_11093.pdf.

[2] W. Warzanskyj Garcı´a, L. Miguel Campoy Cervera & J.M. Va´zquez Burgos. MIMO antenna arrays: a promise for increasing capacity in mobile communications (in Spanish). Comunicaciones de Telefo´nica IþD, 36, 2005,

21–34.

[3] D. Gesbert, M. Shafi, D. Shiu, P.J. Smith & A. Naguib. From theory to practice: an overview of MIMO space-time

coded wireless systems. IEEE J. Select. Areas Comm., 21(3), 2003, 281–302.

Thanks Dr tarique !

Your explaination as you per your considered parameters are technically strong.i agree with you.

Dear Benyarou Mourad , yes, if we have active jammer attacks from L jammers in space then the formula will be updated to:

К = 2x(MxN - L)xWxTxNOMAxCode / D.

By additional jammers in the frequency area, if we have Q suppressed sub-carriers from W then this formula can be changed to follow

К = 2x(MxN - L)x(W - Q)xTxNOMAxCode / D.

Yes, this report is for one case ideal communications and the "real ratio is lower than that indicated above".

I agree with Tariq Kanaan that needs to take into account the Bandwidth limitation. Thank you!

Thank you dear tarik for your intervention, i fully agree with you. I will read the documents you cited.

Thank you dear Vadym for your intervention, I prefer to put L jammers so as not to confuse with K users of more L

Dear Benyarou Mourad , thank you for your proposal. I'm sorry for this confusion, and I updated formulas regarding your suggestions (L jammers).

Dear colleagues, I thank you all for your interventions and I hope that this question has served us all.

Sincerely