Quick Introduction to MIMO Channel Estimation

[@SaeEDKh313]

Wish i'd found your channel sooner well explained videos high quality presentation watching these saves a lot of time instead of looking in textbooks and stuff...gives an idea of just what you need

[@iain_explains]

Glad you like them!

[@hrachya_khachatryan]

Thank you Iain, I am learning a lot from your channel !

[@iain_explains]

Happy to hear that!

[@susceptibility_]

Just found your channel, I really like and appreciate the content, well explained! Thanks!

[@iain_explains]

Glad you found the channel, and it's great to know that you've found the videos helpful!

[@pitmaler4439]

Thanks. I have a short understanding question about the narrow band assumption in antenna arrays. I read the symbol duration Ts is way way greater than the transit time Tt (time to pass the array). So Ts = 1/B. Therefore, we can state that that depends on the signal bandwidth rather than on the carrier frequency? Seem a bit odd to me that the carrier frequency doesn't determine it.

[@iain_explains]

Sorry, I don't know what you mean by the phrase "time to pass the array". Perhaps you mean propagation time? The narrow band assumption is due to the fact that the gains of the different antenna elements depends on their spacing relative to the frequency. Half-wavelength spaced elements are only "half wavelength" for a single frequency. This beamforming video might give more insights: kzbin.info/www/bejne/d2LRZnuerNmtbZo

[@abdullahqayyum4917]

For the estimation of h_2, x vector will be x= [0 x 0 0]^T, will be the entries of X matrix be at positions x12, x23 and x34?

[@Kevin-m5v]

I'm a computer engineering student preparing a seminar on CGAN models for channel estimation. Could you explain why channel estimation is important? What values are typically found in the channel matrix (like h12, h11, h22, h21)? Also, is channel estimation used in everyday phone calls to obtain the channel matrix for equalization? I would appreciate your insights!

[@iain_explains]

Hopefully this video will help: "Channel Estimation for Mobile Communications" kzbin.info/www/bejne/kKSvmWNno9GFsLs

[@Kevin-m5v]

@@iain_explains Sir, I've watched the video you mentioned in the link, but there's no explanation about the channel coefficients inside the channel matrix. It would be easier for me to understand if you could reply with answers to the 3 questions I asked as a reply comment (explanation is only required on a surface level and in simple words)

[@someguy1507]

For OFDM MIMO, can we represent our test signals as DFT vectors, so that all the elements (x1, x2, y1, y2) are frequency samples rather than time samples, and still perform least squares channel estimation successfully? Some code I've been handed does this, and I want to make sure it's valid.

[@iain_explains]

I'm not exactly sure what you mean by "test signals as DFT vectors", but in general, yes, least squares can be used in whichever domain you can represent the parameters in, in a linear equation. Here's a video on least squares that might help: "What is Least Squares Estimation?" kzbin.info/www/bejne/eIuch5-jotqiqq8

[@someguy1507]

@@iain_explains Ah, by "test signals as DFT vectors", I mean that the signal is an array of samples in the time domain, that then gets converted into an array in frequency space using the Discrete Fourier Transform. That is, in MATLAB, the code I've received performs fft() on the signal, and does least squares estimation on the result. I find it kind of interesting that least squares works in frequency space as well. Does that imply that signals that are "close" to each other in frequency space are also "close" in the time domain? Is the least squares estimation the same result no matter the domain?

[@iain_explains]

The Fourier transform is a 1-to-1 transform. So if two signals are 'similar' to each other in one domain (eg. time), they will be 'similar' to each other in the other domain too (eg. frequency). Of course, it depends on your definition of 'similar'.

[@jimmyji8339]

Is there anyway to do this multiple channel estimate simultaneously? If I have a 64 channel then I would need 64x times longer time to finish the process?

[@iain_explains]

In many cases, parallel channels are correlated (for example, when they are neighbouring frequency domain sub-channels in OFDM). In this case it is only necessary to estimate a subset, and then interpolate to estimate the others.

[@ronghuali5]

Hi Professor, thanks for the great video. I have a question about channel estimation in practice: for instance in 802.11, does the receiver needs to know the transmitter antenna numbers (or know the size of the channel matrix) in advance?

[@iain_explains]

Yes, you make a good point. The channel estimation process for MIMO can only be done once a few other functions have been performed first, such as frequency locking, timing acquisition, frame/packet acquisition, etc. plus other information (such as numbers of antennas, etc) that has been shared either via a seperate control channel on a different (often lower) frequency channel, or is contained in the header of the frame using low order modulation formats that can be detected/decoded without the need for accurate channel estimates.

[@ronghuali5]

@@iain_explains Thank you Prof. Iain. A very detailed explanation

[@rafishaaya1658]

I appreciate all the effort that you give in your lectures. I need to ask you a favour, can you do a few videos about the AMP and its corresponding version LAMP algorithms as well as GM-LAMP algorithm in mmWave massive MIMO

[@mukulsharma2294]

Plese help to create video on angle of arrival estimation algo using bartlett alog

[@iain_explains]

Thanks for the suggestion. I've added it to my "to do" list.

[@nanjiang4158]

Appreciate your video. Let us see y_1=X_1h_1+n_1 in the upper right corner of the video. If I understand correctly, the matrix X_1 only represents what you are using when deriving the channel matrix. During training data transmission, x_1 has only been transmitted once by the first antenna. However, the matrix X_1 does not have an exact physical meaning, which is quite confusing (I mistakenly thought it means an antenna-temporal domain matrix when seeing the video at the first time). Also, the matrix of X_2, which means another training symbol for antenna 1 at slot 2, can be confusing because people think it may relate to h_2 (may be using X_b for slot b?). Furthermore, I think if you explained the matrix for the derivation of antenna 2, the video would be more understandable.

[@iain_explains]

Sorry, it's difficult to explain in this comments section. Perhaps try watching the video again, and try writing out the terms for yourself. It sometimes helps to write it out term-by-term.

[@abdulrahmanalayidh5752]

Could you please explain Time Divsion Duplexing in massive MIMO

[@iain_explains]

Thanks for the suggestion, I'll put it on my "to do" list.

[@muhammadahmedtariq2357]

How is mobile time varying channel estimated ?

[@iain_explains]

Have you seen this video? "Channel Estimation for Mobile Communications" kzbin.info/www/bejne/kKSvmWNno9GFsLs

[@bk_space]

Hello, Professor Thank you for the great explanation. I have some questions about this theme and theme of this (kzbin.info/www/bejne/kKSvmWNno9GFsLs) video. (I am try to understand how varying mimo channels estimation works) 1) The method of estimation channel you have explained needs to send almost-zero vectors of data (exception of x_k data on n-th antenna of tx). If a number of tx antennas is big, it will take an enormous time to do the estimation, isn't it? 2) The final formulae of channel matrix H included an inversion of matrix X. As I know, operation of invesion also takes much cpu time. The methods of computational math could give some improvment, based on specific matrix form. Is our matrix good for this operations? 3) I think, there should be more complex methods of channel matrix estimation, for example, based on some interpolators, methods of computational linear algebra, neural networks and so on. Do you know any of them? If yes, can please write a simple classification of them? English is not my mother tongue, I am sorry for any spelling and grammatical mistakes(

[@iain_explains]

Thanks for your interest in the videos. Short answers to your questions: 1) yes. Fundamentally, the more parameters you have to estimate, the more resources you need to devote to doing that task (either more time, or more power, or both). 2) Yes matrix inverses take time to perform. If the channel does not change quickly, then you can spend a bit of time to do a matrix inverse, and then use the estimate for many symbols before needing to re-estimate. But if the channel changes quickly, then you do need to think about estimating in other ways (probably not as accurate). 3) all the other methods you mention require waiting for longer periods of time to collect the necessary data (eg. interpolation is done over many training periods - not just within a single training period). They all have applications in particular circumstances.