What is MIMO SVD Communications?

Explains MIMO communications with a singular value decomposition (SVD) precoding and receiver. Discusses the design tradeoffs in terms of bit loading and power allocation.
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[@ahmetberkekaraca4578]

Hello Iain, this was a brilliant video. Thank you for your effort!

[@iain_explains]

Thanks for your nice comment. I'm glad you like the video.

[@Couldyanot]

Banger video, as always. I was stuck on a MIMO project, now I'm not, thank you!

[@iain_explains]

I'm glad it helped.

[@naveenpanakanapalli9585]

Excellent video on how SVD math concept is used in MIMO communications

[@iain_explains]

Glad it was helpful!

[@manutauer]

Thank you

[@iain_explains]

You're welcome

[@serrafayaz]

Thanks for all your videos. There are so helpful. ❤

[@iain_explains]

Glad you like them!

[@user-dh9qf4eu7i]

Thank you for the good explanation. Is this also a multi-channel beamforming?

[@iain_explains]

Yes, it can be described that way.

[@abdullahqayyum4917]

Hello Ian, For the downlink communication scenario with two users. In this setup, the base station is equipped with m antennas, and the users each have a single antenna. My question is about designing the precoding matrix at the base station. Since the channels for both users are different, should I: 1. Add the two channel matrices and then perform singular value decomposition (SVD) on the combined matrix? Afterward, multiply the resulting V matrix with both user channels? 2. Alternatively, should I compute the SVD of each user’s channel matrix separately and then multiply the respective V matrices? 3. Also, how different power can be allocated to different beams? I am interested in understanding the impact of these approaches on capacity vs SNR calculations.

[@iain_explains]

This video should help: "How are Beamforming and Precoding Related?" kzbin.info/www/bejne/n36sonimr92Bb7s

[@lucidasser7153]

Interesting, thanks a lot. So we in that example we can just use 2 data streams, but we use all 4 receiver antennas. They form kind of 2 stronger and narrower beams compared to a 2-antenna system. Is that about right? Thanks.

[@iain_explains]

Yes, that’s correct.

[@jasminnadic2103]

Many Thanks. Is the noise just caused by the reiceiver amplifier? No other causes?

[@henrikhellstrom1241]

Additive noise can be caused by different sources, and the dominant source will depend on the reality that your model is describing. Usually, noise is divided into internal and external noise, where internal noise refers to unwanted signals generated by electronics inside the receiver hardware (as you are suggesting in your comment). External noise refers to unwanted signals that arrive from outside sources, such as background radiation from the sun or other transmitting devices that interfere with the desired signal. The mathematics that Iain is describing here is general and could model other sources than just amplifier noise.

[@iain_explains]

Yes, as @henrikhellstrom1241 says, there can be other sources of noise. Although, if those sources have structure to them (spatially or temporally) then we tend to call it "interference" rather than "noise", and we try to exploit that structure, in order to cancel it. There is also "noise" in the transmitter amplifier (that then goes into the channel, and doesn't just appear as additive noise), however, in general, the transmit power is much higher than the transmitter noise from the transmit amplifiers, so it is ignored.

[@ste3191]

How do we compute the precoding matrix? And how the receiver know which u* to use? Thank you for your brilliant videos!

[@iain_explains]

Training data is used to estimate the channel at the receiver. Then any standard SVD computation approach is used to find the decomposed matrices, and then the precoding matrix needs to be sent back to the transmitter (usually over a control channel).

[@abdul-wadood-khan]

Hi Iain, How we know the values of unitary matrices i.e., V and U in advance? Or put it other way around how we calculate the values of V and U? Lastly, your approach to explain is simply beautiful and it reflects your knowledge. Thanks.

[@iain_explains]

The channel matrix needs to be estimated/measured first, and then decomposed into the SVD matrices. For more details on channel estimation, see: "Quick Introduction to MIMO Channel Estimation" kzbin.info/www/bejne/i4HKdWh9o9SUb5I

[@abdul-wadood-khan]

@@iain_explainsThank you.

[@John-pp2jr]

Normally the signal flow is from left to right on diagrams. Why are the receivers on the left and transmitters on the right?

[@iain_explains]

I drew them that way to match the order that the matrices appear in the transmission equation.

[@nelebauer7864]

With regard to the lower left sketch, the singular values are a kind of power regulation - do we really need this additional power regulation with the matrix P? Thanks.

[@iain_explains]

The singular values are a property of the channel. If you want to exploit them, then you need to do things at the transmitter (eg. with the P matrix). This video should help: "What is Water Filling for Communications Channels?" kzbin.info/www/bejne/g4GudHeggL6KqbM

[@hesami_nzh]

Thanks for your explanation on this topic, I wanted to know that here in this scenario, \alpha (9:15) is the rank of the channel matrix, right? and will this also explain why a channel matrix being full-rank is important in wireless communication?

[@iain_explains]

Yes.

[@pitmaler4439]

Can we do the SVD also with a quadratic matrix? (mxm) thanks

[@idrissmerah1907]

Yes