see this paper.

Thank you Mr. Aamir for the paper , but I still can not figure out the answer, my question was in the downlink,  some reference signal need to be broadcasted to the user  terminals before assigning any resource to this users, and this need to be sent to all users,  does that mean these signals are sent without any beamforming?

and when beamforming is activated to benefit from the array gain, how is the interference from other cell is modeled?

You are right! To reach a user that has not sent a pilot, the transmission needs to be performed without directive precoding/beamforming. Here is a paper that describes how to do this:

M. Karlsson and E. G. Larsson, “On the operation of massive MIMO with and without transmitter CSI,” in Proc. IEEE SPAWC, 2014.

As you can see from this paper, the broadcasting of reference signal is still doable using conventional techniques. You can also read more about this in my paper "Massive MIMO: 10 Myths and One Grand Question" where one of myths is that reference signals cannot be broadcasted in massive MIMO.

when beamforming is activated to benefit from the array gain, how is the interference from other cell is modeled?

In massive MIMO the inter-cell interference can be unusually high, since there can be tens of users per cell. Hence, you should model and compute this interference in the same way as the intra-cell interference. For example as a Rayleigh fading vector with a variance that depends on distant-dependent pathloss and shadowing.

Thank you Dr. Emil, in order to do system level simulation of massive MIMO, where each user is served by Nt antennas, the user will benefit from the beamforming gain which equal theoretically to 10log10(Nt), so the user received power is

Pr=Pt+Ant Gain + Beamforming Gain+User ant Gain - Pathloss(distance+shadowing).

the user may receive also interference from other cell base station.

how we calculate the user SINR?  do we need to check  if he lies in the beam of other cells in system level simulation?

Omid m.kandelusy: If we want to improve the spectral efficiency of future cellular networks (i.e., the bit/s/Hz/cell), then spatial multiplexing of many users is the way to go. Massive MIMO is a method to achieve this. A good and recent tutorial on this topic is:

T. L. Marzetta, “Massive MIMO: An Introduction,” Bell Labs Technical Journal, 2015

You can also check out my slides from the tutorial I gave at the VTC-Spring conference earlier this week: http://www.commsys.isy.liu.se/~ebjornson/presentation_5wireless.pdf

Abdelrahman Arbi: You can compute the strength of the interfering signals from other base stations in the same way as the desired signal that you gave a formula for. Then you use them all to compute the SINR:

Signal Power / (Interference Power + Noise Power).

Note that the power needs to be measured in linear scale when computing the SINR and not in dB (as in your computations). Moreover, the SINR expression above is only an approximation. There is much more behind this. See for example:

H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, “Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems,” IEEE Trans. Commun., 2013.

When calculating the interfering signals from other base station, how we model the beamforming gain? I know precoding is used to beamform the signals from the base station to the user terminal, but no beamforming from interfering base station , i.e beamforming gain is good from the serving cell and we like to have zero beamforming gain from interfering cell. However, there is still some probability to have the user terminal lie on the same line connecting the interfering base station with one of its users, which means high inter cell interference. Do you know how this can be taken into account in the analysis? 

Abdelrahman Arbi: It depends a lot on the propagation environment. In line-of-sight cases, the downlink precoding is a classical beamforming where a signal beam is steered towards the user. Hence, there is a chance that another user stands "behind" the intended users and also receives an amplified interfering signal.

In non-line-of-sight cases, downlink precoding means to shape the multi path propagation so that as much as many paths as possible add coherently at the intended user. In this case, it is rather unlikely that it will add up coherently at other places - it might do it from time to time, but not on average.

I would say that you can safely model the beamforming gain as zero from interfering cells in most practical cases. However, there is also an effect called pilot contamination where the same uplink pilot sequences are reused in different cells. The users that are allocated the same pilot sequence will cause interference with beamforming gains toward each other, since the base station cannot separate their channels and amplifies both.

Thanks Dr. Emil for the clarification, forgive me for asking more, I read your paper of Massive MIMO: 10 Myths and One Grand Question, and it was really very informative. you highlighted in myth 10 that resource scheduling became simpler in massive MIMO, do you mean the scheduler will decide only how many  and which antennas will be allocated to the user  during the coherent block, and no need to the conventional time-frequency resource allocation in OFDMA systems? for example if 100 antenna massive MIMO base station serves 20 users, the scheduler can allocate full bandwidth all the time 5 antennas for each user  during the coherent time? and all the signals from other antennas treated as intracell interference if they are from the serving cell , intercell interference from other cells? 

There is no one-to-one correspondence between users and antennas in Massive MIMO. All the antennas at a base station are used to serve a user, by precoding.

Conventional systems divide the time/frequency space into resource blocks. Each block can be given to one user in an OFDMA fashion, and you would like to make the allocation based on channel knowledge.

In Massive MIMO you can give all resource blocks to everyone - if they have data buffers to transmit. The separation between users is done spatially by the downlink precoding and uplink detection, instead of making them orthogonal in the time/frequency space.

One example: The base station has 100 antennas and decides on that it will serve up to Kmax users. If there KKmax, you can divide the resources in some simple way between them - there is no need to use current channel knowledge since the small-scale fading averages.

Thank you Dr. Emil

Q1. Network reference signals (NRS) are an important aspect of massive MIMO systems as they help the user equipment (UE) to detect the network and estimate the channel. NRS are typically transmitted in all directions from the base station, and the UE uses these signals to estimate the channel and its characteristics, such as the delay and angle of arrival. In massive MIMO systems, beamforming is used to focus the transmitted signal in the direction of the UE, which can increase the signal-to-noise ratio (SNR) and improve the quality of the channel estimation. However, NRS still need to be sent in all directions to ensure that the UE can detect the network and estimate the channel even if it is not directly in the beamforming direction. In fact, some beamforming techniques, such as beam sweeping, require the transmission of NRS in multiple directions to enable channel estimation.

Q2. In massive MIMO systems, the received power at the UE depends on the beamforming gain, which is a function of the antenna array configuration and the direction of arrival of the signal. The beamforming gain is the ratio of the power received in the direction of the beamforming to the power received in the other directions. Therefore, the received power at the UE can be calculated as the product of the transmitted power and the beamforming gain in the direction of the UE. The beamforming gain depends on the antenna array configuration, the signal propagation environment, and the location of the UE. In practice, the UE can estimate the channel and use the estimated beamforming vector to compute the received power.