Lecture 9: Downlink Multiuser MIMO With Linear Processing

[@karsonchung9519]

Dear Sir We can beamform to each multi user using same frequency if channel information(G) is known. If G is not known, diversity or multiplexing is not possible for downlink multi user environment ? In case of uplink, it seems that multi user(or massive mimo) detection scheme is the same as V-BLAST(point to point) though the channel characteristics is different. Yes ?

[@pitmaler4439]

Thank you for your interessting videos. To be clear: we get a signal x which is the summation of the single signals from K users -> and we give that signal x to each antenna feed-point and the array generates our desired beams to the K users yes?

[@WirelessFuture]

Yes, and the summation of K signals is containing weights: it a weighted sum with different weight on different antennas. The weights are determine the beam direction of each signal.

[@pitmaler4439]

@@WirelessFuture Thank you - and this method is also called digital beamforming, isn't it?

[@WirelessFuture]

@@pitmaler4439 Yes! This is the technology used in 5G for Massive MIMO in the mid band.

[@krabbe3]

Hi Professor, why are the downlink precoding vectors getting a complex conjugate compared to the uplink precoding vectors?

[@WirelessFuture]

This is just a matter of notation. The combining vector is applied with a conjugate transpose, while the precoding vector is not so it must contain the conjugation from the beginning.

[@dihatzou]

check out 14:28. I think that the subtracting term in the denominator must be deleted. "Var(X-constant)=Var(X)". Great Work

[@WirelessFuture]

No, the expression is correct. You are right that Var(X-constant) = Var(X), but this is not applicable in the derivation on Slide 9. The subtracting terms comes from the term with the minus sign and it contains q_i, which is a random variable so it is not constant. (EDIT: I was wrong, Var(X-constant) ≠ Var(X)).

[@dihatzou]

Var[(gT*a-E{gT*a})*q] = Var(gT*a-E{gT*a}) * Var(q) because of indepandance and Var(gT*a-E{gT*a}) * Var(q) = Var(gT*a) * Var(q) because the expectation is deterministic, so the subtracting term is deleted. Is my assumption wrong? Otherwise something is missing from the denominator in the MR capacity.

[@WirelessFuture]

I'm sorry, I was thinking incorrectly this morning. Var(X-constant) ≠ Var(X). The variance is the mean-square of the deviations around the mean. If you subtract a constant from X, then you are changing the mean. In this case: Var[gT*a-E{gT*a}] = E[ |gT*a-E{gT*a}|^2] = E[ |gT*a|^2] - |E{gT*a}|^2. The first equality follows from that gT*a-E{gT*a} has zero mean. And the second equality follows from expanding the | |^2-term.

[@jasminnadic2103]

Thank you. With respect to slide 6, the precoding vector ak: this vector varies the amplitude and the phase - is that correct? So I assume it is a vector with complex entries, yes? Only a real value could only change the amplitude I think.

[@WirelessFuture]

Yes, all signal and channel variables are complex in this lecture series.

[@raencarve4]

Thanks very much for publish the content of the course here professor. I haven't got the chance to look to all the videos, but those that I've already seen are very good, thanks again. One of the main concerns that I'm struggling to understand is the granularity of beams, with for example a 64T64R antenna with only 2 cross-polarized elements connected to each TRX then the doubt that I have is that you can form (as much and simultaneously) like 64 lobes (more than actual beams) is this assumptions correct?

[@WirelessFuture]

You can create an infinitely large number of beams, but they will be partially overlapping. With 64T64R, you can select up to 64 different physical locations and beamform to each one of them using “zero-forcing” without causing interference in between the different transmissions. At most other locations, we would receive a mix of all the signals. Since we cannot do perfect zero-forcing in practice since the communication channels are only partially known, “massive MIMO” is often assumed to have “more antennas than beams”. We are basically adding some space in between the beams.

[@manutauer]

Thanks I am a bit confused by the equation on slide 6. There we have the vector x [Mx1] wich depends on a summation term. But every entry of x gets the same result then? Is that right? I doubt that . I am confused by the dimension. Thanks a lot.

[@WirelessFuture]

There are K information signals, q_1,...,q_K, which are transmitted simultaneously using the M antennas. The precoding vectors a_1,...,a_K determine the spatial directivity that each signal is transmitted with. Hence, all antennas transmit all signals, but in a way that directs them in different directions, focused on different receiving users. The vector x is the summation of all the transmitted signals, and the entries are different: they contain the same K information signals but with different amplitudes/phases to achieve different directivity through constructive/destructive interference.

[@manutauer]

@@WirelessFuture thanks for the quick answer. I got it now. The [Mx1] vectors do not mean that all M antenna elements are in the same dimension, do they? It could also be a 8x4 array and I get my vector x [32x1]. Is that right?

[@WirelessFuture]

Yes, the antenna array can have any shape. The only assumption is that it consists of M antennas (each connected to a separate transceiver chain). The geometry of the array only determines the values of the channel vector, which depend on the propagation environment around the array and its geometry.

[@mohanadahmed2819]

Thank you professor for these informative lecture series, How does the base station know the number of users, K, in its covarage area? K seems to be a random number. I think this is important because the length of the pilot signal depends on the maximum K, right?

[@WirelessFuture]

This is video focuses on data transmission to users that are connected to the network. Whenever a user wants to connect, it must go through a procedure called random access. It sends a connection request and if the base station can decode the request, it will tell the user which pilot sequence to use and which time-frequency resources to use.

[@James_Knott]

I have noticed you often square an absolute value. Isn't that exactly the same result as just the square the value, without the absolute?

[@WirelessFuture]

@@James_Knott We don’t need absolute values when squaring real numbers. However, all the numbers are complex in communications, which is why we need an absolute value as well.

[@artie5172]

Professor, could you put a video in simulation of wireless communication system..

[@WirelessFuture]

Thank you for the suggestion. What would you like such a video to contain, in case we would eventually produce it? By the way, there is a video in this series about Monte Carlo simulation that might be useful for you.

[@artie5172]

@@WirelessFuture it would be very useful if it contains communication system in MU-MIMO case and simulation of how a message signal transmit over it

[@WirelessFuture]

​@@artie5172 The capacity bounds presented in this video are everything needed to simulate a MU-MIMO system. The graph shown at 25:53 is generated by computing those expressions for the parameter values stated on the slide. It is ~10 lines of Matlab code. More general simulation examples can be found in relation to my book, Massive MIMO networks: github.com/emilbjornson/massivemimobook/tree/master/Code

[@murtazarasheed7189]

Thanks for the Lecture, Can you please share link to some literature from which I can learn precoding and digital precoding for hybrid beamforming from scratch. That will be so much helpful