Capacity of Point-to-point SIMO and MISO Channels [Video 5]

[@mahshidnarimanikenari2378]

thank you so much for such a good explanation

[@wenqingli425]

Thank you for this wonderful video! I am still confused on 7:57~8:07. It is a mathematical question, we want to know which part of x can be projected onto g? I still did not understand the reply below, why we use g^* rather than g. The second question, (g^T x) is maximized only when x equals g^*, why this is related with our question? x is fixed and g is fixed, why we could maximize (g^T x)? We don't have variable here.

[@wenqingli425]

sorry, in 7:43, why we want to know which part of x (rather than received signal y) is pointing in the same direction with channel vector g*? In SIMO cases, we projected y onto channel vector.

[@celestials_being]

very good explanation like iits professor's

[@JayLikesLasers]

How do you know what all your gain factors, g_i are? Are they all a set quantity by the antenna designer?

[@WirelessFuture]

These parameters indeed depend on the antennas, but mostly on the propagation environment between the transmitter and receiver. The values vary rapidly in practical scenarios where the user device is mobile. To deal with this, known so-called pilot reference signals are transmitted every few milliseconds to measure their current values.

[@JayLikesLasers]

Do these concepts all apply to only one channel? E.g. is it fair to say if you have one transmitter and 3 receivers, each receiving a different message, is it still SIMO? Or is it 3x SISO?

[@WirelessFuture]

There are multiple accepted terminologies for this scenario. I would call it SIMO based on the number of antennas, and then distinguish between single-user SIMO (considered in the video) and multi-user SIMO if there is a single-antenna base station and three receiving single-antenna users.

[@sathviks7442]

Sir, I have one doubt, I have been trying this for several weeks, but kinda stuck here. How to apply MRC for MIMO system, because, unlike SIMO (where you have explained MRC), MIMO involves >1 Transmit and Receive antennas. Eg: (2 by 2 MIMO), Y1 = g11 x1 + g12 x2 + awgn. Y2 = g21 x1 + g22 x2 + awgn If we apply MRC here: Y_combined = V1 (Y1) + V2 (Y2). How exactly to calculate V1, V2 here, either I get stuck with matrix dimension mismatch, or which all g's to consider for V1 or V2. Any specifically, should the transmit data from multiple tx antennas should be same or different? 2. If data from different tx. Antennas are different again, here I get confused with channel estimation using Least Square equation. 3. Zero force receiver and MRC are different things right, they can be used together. As in, MRC to combine and ZF to estimate X from received signal Y at rx.

[@WirelessFuture]

MRC is used for SIMO channels and MRT is used for MISO channels. One shouldn’t use any of these methods in a MIMO channel. The next video in this series (Video 6) is describing the MIMO case. Least square estimation is not considered in this video. But if you want the estimate a MIMO channel, you can first send a pilot signal from the first antenna and then from the second antenna. You essentially divide the problem into estimation of SIMO channels.

[@sathviks7442]

Firstly, a big thank you for explaining concepts in terms of vector diagrammatic representation , I had never thought it in that way. All this time, I was trying to implement MIMO using MRC. 😅 Secondly, so basically MIMO revolves around SVD or Zero force receiver? Or are there any other methods? Also, for Single user MIMO, we can either choose different data or same data to be transmitted from multiple transmit antennas right? (Both the case sum of power is ensured to be equal to total power?)

[@bhupendrakumar7665]

Thanks for providing such thought-provoking videos. I like them because of their immaculate presentation. Will you please upload more of them or indicate the URL? Waiting.

[@WirelessFuture]

You can find the playlist here: kzbin.info/aero/PLTv48TzNRhaKz0C-dCAwimXSypV_5UTxg More videos will be added to it over time.

[@saikrishnacharan]

Thanks for great explanation! I have one doubt regarding MISO case. You said Vector(x) = Vector(w) * Information signal (x tilda). That means, are we sending same information signal through all the transmit antennas?

[@WirelessFuture]

Yes, the same signal from all antennas but with different phase shifts. The phase shifts create a beam in a particular direction using the phenomenon of constructive interference.

[@saikrishnacharan]

@@WirelessFuture Thanks for such quick reply!

[@user-bu7xm6of7x]

Thank you for this video. In the context of Satellites MIMO signal processing, I would like to ask what will be different if we have one mobile user connected to two satellites and we are considering both uplink and downlink channels. We want to compare the throughput with the case when the user is connected to only one satellite. Besides the capacity (throughput) analysis, I would also like to know what do you think the differences are compared to the terrestrial case?

[@WirelessFuture]

It is the same theory that can be applied to this case, but with a different channel model. One key question is whether the two satellites will be phase-synchronized (so they can do coherent beamforming, or if space-time codes will have to be used) and how they will exchange data between each other - do they have to send everything through a gateway on Earth?

[@user-bu7xm6of7x]

@@WirelessFuture I believe that Satellites could achieve synchronization by exchanging information through ISL (inter-satellite Links), regarding the data exchange it will be a direct communication between Satellites and the user mobile phone, no gateway is considered in this scenario.

[@VikramReddyAnapana]

wonderful

[@xiaotang5945]

Many thanks for the insightful video. I have one question, for the MISO case, why the signal is projected onto g-conjugate, g*, rather than onto the channel g? Thanks for the kind help.

[@WirelessFuture]

The inner product (g^T v) is maximized when v = g*. Since the vectors are complex, this is actually an inner product between g* and v. This optimal type of precoding is also known as "conjugate beamforming.

[@xiaotang5945]

@@WirelessFuture Thank you very much for the kind help.

[@foerfoer]

Could someone explain why is he multiplying the signal by the channel instead of making convolution?

[@WirelessFuture]

foerfoer It is the so-called discrete time complex baseband representation. If you have a one-tap channel and transmit using pulse-amplitude modulation, you can get the channel model considered in this video after sampling at the receiver. The continuous time channel response will then be g*delta(t).

[@jelenamladenovic4347]

Thank you very much for sharing such a good explanation. I have one question. Is it possible for the MISO case that the same signal is sent over each antenna? If that is possible, can this situation be treated as beamformig or transmit diversity? Thanks.

[@WirelessFuture]

If you send the same signal on all the antennas without any phase-shifts, then that corresponds to using a precoding/beamforming vector with only ones. So it is a type of beamforming.

[@mrjatt435]

why we do transpose of g w. r. to x at 7:33?

[@WirelessFuture]

It is a vector representation of the summation shown at 7:00. The vector description enables us to use linear algebra to identify the preferable precoding.

[@mrjatt435]

@@WirelessFuture ok, same with the case at 5.44 where we square signal power (g)^2 of the SNR value, if not what was the reason for that, why we do square of SNR values in some case like (single power)^2/(noise)^2 in the channel capacity ?

[@WirelessFuture]

@@mrjatt435 The SNR is a ratio of powers. The signal has amplitude sqrt(q)*g and power q*|g|^2. The system models are operating in the amplitude domain, while the SNR is computed in the power domain.

[@Yash-re3wi]

Is v^H the hermitian norm of v?

[@WirelessFuture]

It is the Hermitian transpose of v, also known as conjugate transpose.

[@xuesongcai2901]

I think MRC has beamforming gain, however not for MRT. As the total power of M transmitting antenna sums to one unit, while the M receivers can receive M copies.

[@WirelessFuture]

The beamforming gain is the same in both cases, but is achieved in different ways. As you say, in the SIMO case, we are collecting M times more power. MRC is then combining the M signal so that we extract M times more signal power without extracting M times more noise. In the MISO case, the transmission is focused towards the receiver so that M times more signal power is traveling in that direction. It is based on the concept of constructive interference.

[@xuesongcai2901]

@@WirelessFuture Thanks for the reply. ''''the transmission is focused towards the receiver so that M times more signal power is traveling in that direction.'' I think this means you need to transmit M times the original power - If you limit the power transmitted by all the M antennas also as one unit, then there is no beamforming gain, and only diversity gain can be achieved. I think the video also tells the same thing: In 8:34, there is a norm g on the denominator of w, so when you perform MRT in 9:17, there is a mistake - should not be a norm g there in the second line.

[@WirelessFuture]

No, the norm at 8:34 is making sure that the total transmit power is constant irrespective of the number of antennas. This norm is utilized at 9:17, where the computation between the first and second line is g^T w = g^T g^*/||g|| = ||g||^2/||g|| = ||g||. The beamforming gain when using MRT is achieved by creating a directional transmission where M times more power is traveling in the desired direction and less power in other directions.

[@xuesongcai2901]

@@WirelessFuture Yes, true. I made the mistake of thinking no CSI at the transmitter. Thank you.

[@engAhmedRaafathosny]

Thank you very much for the nice explanation for the capacity expressions for MISO and SIMO cases assuming MRT and MRC. I have one question, how these capacity expressions change if we assume no channel knowledge at BS for MISO or at the UT for SIMO ?

[@WirelessFuture]

Eng/Ahmed Ra'fat Note that MRT and MRC are not assumptions, but they are the capacity achieving methods. I have assumed static/deterministic channels in this video and then it would be weird not knowing the channels. But in time varying channels, we can have partial channel knowledge. The base station needs to know the channel to make use of MRT/MRC. There are capacity lower bounds for the case with imperfect channel knowledge. You find such things in my book Massive MIMO networks or in the paper arxiv.org/pdf/1705.03577.pdf (there are many other papers)

[@engAhmedRaafathosny]

Great, Thanks a lot

[@SaikSaketh]

@@WirelessFuture Helpful..!!!!!!

[@-gbogbo-]

Hi Emil and LIU folks, congrats, that's a neat series ! Do you plan to release the video about MIMO case ? Thanks

[@WirelessFuture]

Yes, we plan to continue the video series during the coming months.

[@-gbogbo-]

Excellent, thanks for the quick answer :-)@@WirelessFuture

[@WirelessFuture]

@@-gbogbo- The next video is finally available: kzbin.info/www/bejne/eYmno2Cdodatrpo

[@litebohorantso8053]

how is precoding different from beamforming vector?

[@WirelessFuture]

It is more or less the same thing. Precoding sometimes has a more general meaning, while beamforming is restricted to transmission in line-of-sight communications. You can find a further discussion here: ma-mimo.ellintech.se/2017/10/03/what-is-the-difference-between-beamforming-and-precoding/

[@mrjatt435]

what is precoding (w) ?

[@WirelessFuture]

When we want to transmit the same data from multiple transmit antenna, the radiated signal will become directive. We use precoding to control the directivity by varying the power and phase (delay) between the antennas.

[@mrjatt435]

@@WirelessFuture ok thanks

[@George-do8jc]

thanks :)