Never heard such a great explanation related to that complex topic! This is so much for youtube platform, its like private company consulration with specialist. Apriciate a lot
Great explanation. However, you have not considered the precoding element in your argument. For example, in LTE 2x2 MIMO, the two symbols transmitted will already by multiplied by a DFT weight vector to sufficiently spread the signal across the phase dimension. Secondly, there is an element of polarisation diversity that becomes important in LOS scenarios. In those conditions, the cross polarisation between the antenna elements provides sufficient decorrelation to allow MIMO to work. Thoughts??
Thank you, Professor. Very great tutorial. I have a question. you did not assume the far-field condition in channel modeling. I think that by modeling the channel in the far-field mode, the channel matrix will be the outer product of 2 steering vectors. So, the real H will be rank 1 and consequently non-singular. So, the MIMO does not work even in far-field LOS scenarios. Is my deduction true? And how the LOS challenge is addressed? Thanks again for your consideration.
@@iain_explains For the cases when BS-BS or BS-MS distance is more than 2D^2/lambda, far-field assumption does not make scenes? I mean it may be approximate, but makes the signal processing easier.
You're right! I made the mistake of approximating a linear relationship between the antenna spacing and the angle between antennas. Either way, the main point I was trying to make still holds - namely, that the channel matrix can be inverted. ... but it's annoying that I made that assumption. Thanks for pointing it out.
wonderfully explained...however I beleive that φ is actually Δφ...it is the phase difference....Besides, for very novice audience, you may want to consider using 2nd law of motion to explain: t=Δsinθ/λ and f=c/λ when put in the expression Δφ=2πft to get the final form of Δφ=2πΔsinθ/λ My question is then how to increase channel capacity in a LoS link for example a UAV air to ground link....the Δ will always be
Dear Professor, At @8.28.How did you confirm that H estimation ( i.e estimation of pi )n will have 3-10 amount of values of pi. ? Do we have this LOS issue in case of beam forming too ? or just spatial multiplexing ? Please clear this to me
In beam forming you don't invert the channel, so you don't have a problem. In fact it is an advantage for beam forming. More details here: "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
Great video! I have a question, isn't Rayleigh fading used in urban scenarios where we have multipath? So considering Rayleigh fading in LOS isn't it a bit contradictory? Many thanks!
It's not about the receiver. It's about the transmitter. If you have LoS you won't be able to transmit seperate data streams on each antenna (spatial multiplexing). Instead, you can send a single data stream and use beam forming (spatial diversity). See "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
LoS matrix is of rank one (Columns are dependants), so any subdetermin should be zero, take the first four elements (left top corner 2x2 matrix), the determinant is not zero? so the element 2,2 should be exp(2theta) instead of one. This is for far field communications. (Please correct my undertsanding).
The thing is, I don't agree with your first statement - which is the point of my video. The LoS matrix is _not_ of rank one. Far field assumptions are OK for single transmit antennas, but when it comes to MIMO, the phase difference between every antenna pair is important. The waves from each transmit antenna might be arriving as a plane wave, according to the far field assumption, but each transmit antenna launches them from a different location, which means their phases are different. Techniques such as beamforming rely on this. Yes, there is one eigen vector that dominates all others in the LoS case, but the other eigen values are not actually zero (just very small and hard to estimate in noisy measurement conditions).
@@iain_explains This is really a nice different view for MIMO LoS channel, I want to refer to your example in one of my research paper that I am working in. Is this example mentioned in any paper published by you so I can cite it as a refernce
I don't have a paper where I discuss this point specifically, however in the following paper we assume the mean matrix (M) is arbitrary rank (in Section III) and we give references to other papers that support this, including an experimental measurement paper. The matrix M corresponds to the LoS component. M.R. McKay and I.B. Collings, "General Capacity Bounds for Spatially Correlated Rician MIMO Channels'', IEEE Trans. Information Theory, Vol. 51, No. 9, pp. 3121-3145, September 2005.
Hell Prof, sorry for the Off-Topic question, but a comment on a recent video of yours has a higher chance of a reply from you. My question is about Information Theory, The thing is How Does Channel Capacity's relation to Mutual Information makes sense Intuitively? as in iam confused about how mutual information intuitively relates to channel capacity. Take an example ,Let us have three random bits, X, Y, Z. X and Y are independent and unbiased, while Z is the exclusive or of X and Y. Then H(X,Y)=2, while H(X,Y|Z=z)=1 for any z∈{0,1} because knowing Z and the value of X determines Y. Then I(X,Y;Z)=H(X,Y)−H(X,Y|Z)=1. In words, if you know Z you only really need to encode X rather than both X and Y. So basically instead of sending complete information about the system (X,Y) , if i know Z i should only encode H(X,Y|Z) and that's enough! So I save he trouble in encoding 1 bit or I(X;Y) bits to represent the entire (X,Y) system. Now how does Channel capacity come into the picture? This mutual information is something that we don't need to encode because the receiver already knows it, they say the channel capacity is mutual information, how ? This is the part of information that the receiver already knows , how has it got to do anything with the channel?
Capacity is the maximum that can be achieved of the mutual information between the input to a channel, and the output from that channel. In other words it is the most "shared information" that you can achieve between the transmitter and receiver (in a probabilistic sense). Have you seen my video on Capacity? I didn't refer to MI in that video, but I've put the suggestion on my "to do" list for a future video. "What are Channel Capacity and Code Rate?" ua-cam.com/video/P0WY96WBUyA/v-deo.html
@@iain_explains Did watch the video Professor! , there you had quoted that Channel capacity is the rate at which i can send bits at nearly 0 probability of error, but mutual information is something that we dont need to send through the channel coz both the sender and reciever knows that information. How does Mutual Information (Or "Savings" as people call it or "Shared Information" as you call it) relate to "rate" or channel capacity? anyways in order to send the remnant information (entropy-mutual information) , i need to send it through the channel anyways! So i need to add redundancies to those bits, by knowing mutual information, the number of data bits certainly gets reduced, but to pass the remnant data bits with 0 probability of error, you anyways need to add infinite redundancy isn't it Professor? How is Mutual Information having the backing there? Also, i am waiting for your video on this!
Dear Professor, what is the relationship between accuracy and the SNR? let's say I have a paramter to estimate with true value of 1.123456789. in 30dB SNR, at which digit can I reach in my estimation?
To answer your question, you'd need to know how the noise affects the measurement (additive, multiplicative, ...), and you'd need to know the noise model (distribution, correlation, ...), and you'd need to know what type of estimator you're using (linear, nonlinear, optimal, ...), and you'd need to know if there were any other parameters in the system, or interfering signals, etc. Perhaps this video might give some insights: "What is Least Squares Estimation?" ua-cam.com/video/BZ9VlmmuotM/v-deo.html
You can click on the link in the description below the video. It links to a pdf file that shows the code. You can copy-and-paste the text from the pdf directly into Matlab.
Thanks，Professor. I have a question about MIMO：If LOS can not work for MIMO，then we need an environment full of scattering to creat more paths from transmitter to receiver and then I think now the flating channel （in LOS case），now will be changed to frequency selective channel，because same signal come to the receiver with different delay, so is it that mean MIMO can only work in frequency selective channel？
No, that's not necessarily the case. There can be lots of reflectors that are all roughly the same distance away, but in different directions. All of these reflected paths can arrive within the same symbol period - especially if the symbol period is long. Perhaps you might like to watch: "What are Flat Fading and Frequency Selective Fading?" ua-cam.com/video/KiKPFT4rtHg/v-deo.html
Yes Sir, This video same as others is very useful, and shame on me if I didn't support it with a like and a small comment 😅😅, The idea of using the variation on phase different is the key to finding the DOA on radar estimation techniques, I hope that you can make a video for this topic, Thank you very much.
@@iain_explains that would be great, perhaps with the calculation how you get to the noise expression sigma_n^2/M (M = number of antennas) using the expectation - I'm struggeling with that.
Hi professor, I have tested your code. If consider LOS, we cannot get an identity matrix by inv(Hest)*H. If I added a rayleigh fading to the channel, the identity matrix would be obtained close-perfectly. I suppose the mean of the exact and estimated channel Hest-H should be remarkably different between these two scenarios. However, I found that the means (Hest-H) are almost the same in those two scenarios. Would you please let me know why this happens?
This is great content, thanks a lot! But maybe it should be mentioned that there are use cases for LOS MIMO (spatial multiplexing). For example in microwave backhaul where antennas can be separated enough to make the streams orthogonal
If you’re talking about having directional antennas spaced so far apart that the beams do not overlap, then the propagation paths are parallel and independent. That’s not a MIMO channel.
@@iain_explains No, I'm talking about real MIMO. For example, Ericsson and Deutsche Telekom has demonstrated 4x4 LOS MIMO over a 1.5 km hop at E-band. The antenna separation is approximately 1.5-2.0 m. (for some reason youtube do not allow me to post links to the source material, but google 'Ericsson microwave mimo' if you want to read more)
OK, I see. That actually aligns with the point I make in my video. Namely that LoS-MIMO is possible, since it's not true that the H matrix can't be inverted (which is the commonly held belief). In the E-band example you're talking about, where L=1500m and Delta=2m, the value of psi would be 15.63 (for a 70GHz carrier), which is 10000 times higher than the value for the example I showed in the video for standard mobile signals at 1GHz carrier. And this value at E-band is clearly big enough to be estimated in the noisy conditions, which means H will be estimated accurately, and can be inverted. ... By the way, this is _not_ the reason that is given in the document you referred to - which is misleading, since that document talks about 90deg phase shifts, and claims that 90deg is what's needed to seperate the signals. That's only true for two antennas sending BPSK. That argument/logic doesn't scale to quadrature modulation, and higher numbers of antennas.
Tried it in Matlab, cool model thanks. How is line of sight combatted in the real world to achieve mimo? Thinking of a cell tower pointing at someone standing in an empty field. Is fading enough to enable mimo in this situation? Or just simply the NW chooses a pre-coder to fix this?
In line-of-sight conditions it is best to use the multiple antennas in a beamforming mode (spatial diversity), rather than the "standard MIMO" spatial multiplexing mode. See: "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
@Iain Explains Signals, Systems, and Digital Comms Hi professor, thank you for the video. One technique to obtain higher ranks on MIMO channels under LOS is by applying dual orthogonal polarization (like -45° / +45° per antenna element).
Hi Sir! Excellent video! Question. In you're example how did you arrive at 3-10 times the amount of noise with yields that much for the error in the phase? Thanks.
That's the topic of next week's video. But you can already find the answer in the Matlab code I posted for this video, which includes channel training and estimation.
Thank you Prof. This is very useful. I was working on the subject and jumped to this video and it helped a lot. I wanted to practice with the Matlab code but I couldn't find it. Can you append the link to this comment?
![Line-of-sight Channels [Video 7]](/img/n.gif)
Never heard such a great explanation related to that complex topic! This is so much for youtube platform, its like private company consulration with specialist. Apriciate a lot
Glad it was helpful! And I'm glad you liked the format of the video.
Great explanation. However, you have not considered the precoding element in your argument. For example, in LTE 2x2 MIMO, the two symbols transmitted will already by multiplied by a DFT weight vector to sufficiently spread the signal across the phase dimension. Secondly, there is an element of polarisation diversity that becomes important in LOS scenarios. In those conditions, the cross polarisation between the antenna elements provides sufficient decorrelation to allow MIMO to work. Thoughts??
Yes, if you have more dimensions (bandwidth, polarisation, etc) then you can always send more data.
Thank you, Professor. Very great tutorial. I have a question. you did not assume the far-field condition in channel modeling. I think that by modeling the channel in the far-field mode, the channel matrix will be the outer product of 2 steering vectors. So, the real H will be rank 1 and consequently non-singular. So, the MIMO does not work even in far-field LOS scenarios. Is my deduction true? And how the LOS challenge is addressed?
Thanks again for your consideration.
But why would you use a "far field" channel model, when it gives incorrect answers that don'y match reality?
@@iain_explains For the cases when BS-BS or BS-MS distance is more than 2D^2/lambda, far-field assumption does not make scenes? I mean it may be approximate, but makes the signal processing easier.
Dear Professor, @8:30 how is it estimated that the noise is 3-10 times for 20dB SNR?
Thank you professor Iain followed your videos got A grade in my Advanced digital communications course 😀 👍 😊
I'm so glad to hear it. Congratulations. I'm glad my videos have been a help.
I think you have a mistake in H definition.
The phase does not linearly advanced: 0, x, 2x, 3x,
but: 0, x, 4x, 9x …
You're right! I made the mistake of approximating a linear relationship between the antenna spacing and the angle between antennas. Either way, the main point I was trying to make still holds - namely, that the channel matrix can be inverted. ... but it's annoying that I made that assumption. Thanks for pointing it out.
wonderfully explained...however I beleive that φ is actually Δφ...it is the phase difference....Besides, for very novice audience, you may want to consider using 2nd law of motion to explain: t=Δsinθ/λ and f=c/λ when put in the expression Δφ=2πft to get the final form of Δφ=2πΔsinθ/λ
My question is then how to increase channel capacity in a LoS link for example a UAV air to ground link....the Δ will always be
The phase difference depends on the frequency too. The higher the frequency, the bigger the phase difference.
Dear Professor,
At @8.28.How did you confirm that H estimation ( i.e estimation of pi )n will have 3-10 amount of values of pi. ?
Do we have this LOS issue in case of beam forming too ? or just spatial multiplexing ? Please clear this to me
In beam forming you don't invert the channel, so you don't have a problem. In fact it is an advantage for beam forming. More details here: "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
Hey Ian! In the real world, even if you have line of sight, there are reflections from buildings, the land, etc, right?
Yes, that's right.
Excellent video Sir!
Glad you liked it!
Great video!
I have a question, isn't Rayleigh fading used in urban scenarios where we have multipath? So considering Rayleigh fading in LOS isn't it a bit contradictory?
Many thanks!
For a similar setup with WIFI, for example at 5.5 GHz and the devices are separated by 2 meters, it should not be a problem, right?
What if we apply some other receiver (not the ZF), then would it be helpful to use MIMO with LOS.
It's not about the receiver. It's about the transmitter. If you have LoS you won't be able to transmit seperate data streams on each antenna (spatial multiplexing). Instead, you can send a single data stream and use beam forming (spatial diversity). See "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
LoS matrix is of rank one (Columns are dependants), so any subdetermin should be zero, take the first four elements (left top corner 2x2 matrix), the determinant is not zero? so the element 2,2 should be exp(2theta) instead of one. This is for far field communications. (Please correct my undertsanding).
The thing is, I don't agree with your first statement - which is the point of my video. The LoS matrix is _not_ of rank one. Far field assumptions are OK for single transmit antennas, but when it comes to MIMO, the phase difference between every antenna pair is important. The waves from each transmit antenna might be arriving as a plane wave, according to the far field assumption, but each transmit antenna launches them from a different location, which means their phases are different. Techniques such as beamforming rely on this. Yes, there is one eigen vector that dominates all others in the LoS case, but the other eigen values are not actually zero (just very small and hard to estimate in noisy measurement conditions).
@@iain_explains This is really a nice different view for MIMO LoS channel, I want to refer to your example in one of my research paper that I am working in. Is this example mentioned in any paper published by you so I can cite it as a refernce
I don't have a paper where I discuss this point specifically, however in the following paper we assume the mean matrix (M) is arbitrary rank (in Section III) and we give references to other papers that support this, including an experimental measurement paper. The matrix M corresponds to the LoS component.
M.R. McKay and I.B. Collings, "General Capacity Bounds for Spatially Correlated Rician MIMO Channels'', IEEE Trans. Information Theory, Vol. 51, No. 9, pp. 3121-3145, September 2005.
Hell Prof, sorry for the Off-Topic question, but a comment on a recent video of yours has a higher chance of a reply from you. My question is about Information Theory, The thing is How Does Channel Capacity's relation to Mutual Information makes sense Intuitively?
as in iam confused about how mutual information intuitively relates to channel capacity. Take an example ,Let us have three random bits, X, Y, Z. X and Y are independent and unbiased, while Z is the exclusive or of X and Y. Then H(X,Y)=2, while H(X,Y|Z=z)=1 for any z∈{0,1} because knowing Z and the value of X determines Y. Then I(X,Y;Z)=H(X,Y)−H(X,Y|Z)=1. In words, if you know Z you only really need to encode X rather than both X and Y. So basically instead of sending complete information about the system (X,Y) , if i know Z i should only encode H(X,Y|Z) and that's enough! So I save he trouble in encoding 1 bit or I(X;Y) bits to represent the entire (X,Y) system. Now how does Channel capacity come into the picture? This mutual information is something that we don't need to encode because the receiver already knows it, they say the channel capacity is mutual information, how ? This is the part of information that the receiver already knows , how has it got to do anything with the channel?
Capacity is the maximum that can be achieved of the mutual information between the input to a channel, and the output from that channel. In other words it is the most "shared information" that you can achieve between the transmitter and receiver (in a probabilistic sense). Have you seen my video on Capacity? I didn't refer to MI in that video, but I've put the suggestion on my "to do" list for a future video. "What are Channel Capacity and Code Rate?" ua-cam.com/video/P0WY96WBUyA/v-deo.html
@@iain_explains Did watch the video Professor! , there you had quoted that Channel capacity is the rate at which i can send bits at nearly 0 probability of error, but mutual information is something that we dont need to send through the channel coz both the sender and reciever knows that information. How does Mutual Information (Or "Savings" as people call it or "Shared Information" as you call it) relate to "rate" or channel capacity? anyways in order to send the remnant information (entropy-mutual information) , i need to send it through the channel anyways! So i need to add redundancies to those bits, by knowing mutual information, the number of data bits certainly gets reduced, but to pass the remnant data bits with 0 probability of error, you anyways need to add infinite redundancy isn't it Professor? How is Mutual Information having the backing there? Also, i am waiting for your video on this!
Dear Professor, what is the relationship between accuracy and the SNR? let's say I have a paramter to estimate with true value of 1.123456789. in 30dB SNR, at which digit can I reach in my estimation?
To answer your question, you'd need to know how the noise affects the measurement (additive, multiplicative, ...), and you'd need to know the noise model (distribution, correlation, ...), and you'd need to know what type of estimator you're using (linear, nonlinear, optimal, ...), and you'd need to know if there were any other parameters in the system, or interfering signals, etc. Perhaps this video might give some insights: "What is Least Squares Estimation?" ua-cam.com/video/BZ9VlmmuotM/v-deo.html
Thank you for excellent video!
Glad you liked it!
Thx. Where can I find the matlab code you posted?
You can click on the link in the description below the video. It links to a pdf file that shows the code. You can copy-and-paste the text from the pdf directly into Matlab.
Thanks，Professor. I have a question about MIMO：If LOS can not work for MIMO，then we need an environment full of scattering to creat more paths from transmitter to receiver and then I think now the flating channel （in LOS case），now will be changed to frequency selective channel，because same signal come to the receiver with different delay, so is it that mean MIMO can only work in frequency selective channel？
No, that's not necessarily the case. There can be lots of reflectors that are all roughly the same distance away, but in different directions. All of these reflected paths can arrive within the same symbol period - especially if the symbol period is long. Perhaps you might like to watch: "What are Flat Fading and Frequency Selective Fading?" ua-cam.com/video/KiKPFT4rtHg/v-deo.html
Thank you！
@@iain_explains
Yes Sir, This video same as others is very useful, and shame on me if I didn't support it with a like and a small comment 😅😅, The idea of using the variation on phase different is the key to finding the DOA on radar estimation techniques, I hope that you can make a video for this topic, Thank you very much.
Thanks for the suggestion. I've got the radar topic on my "to do" list.
Thanks a lot. Have you already done a video how averaging the noise can improve the SNR?
Keep an eye out for next week's video. 😉
@@iain_explains that would be great, perhaps with the calculation how you get to the noise expression sigma_n^2/M (M = number of antennas) using the expectation - I'm struggeling with that.
OK, well that's not in the video that's going to be posted on Monday, but I'll add it to my "to do" list.
Hi professor, I have tested your code. If consider LOS, we cannot get an identity matrix by inv(Hest)*H. If I added a rayleigh fading to the channel, the identity matrix would be obtained close-perfectly. I suppose the mean of the exact and estimated channel Hest-H should be remarkably different between these two scenarios. However, I found that the means (Hest-H) are almost the same in those two scenarios. Would you please let me know why this happens?
Sorry, I'm not sure exactly what you mean when you say that you added Rayleigh fading to the channel.
This is great content, thanks a lot! But maybe it should be mentioned that there are use cases for LOS MIMO (spatial multiplexing). For example in microwave backhaul where antennas can be separated enough to make the streams orthogonal
If you’re talking about having directional antennas spaced so far apart that the beams do not overlap, then the propagation paths are parallel and independent. That’s not a MIMO channel.
@@iain_explains No, I'm talking about real MIMO. For example, Ericsson and Deutsche Telekom has demonstrated 4x4 LOS MIMO over a 1.5 km hop at E-band. The antenna separation is approximately 1.5-2.0 m. (for some reason youtube do not allow me to post links to the source material, but google 'Ericsson microwave mimo' if you want to read more)
OK, I see. That actually aligns with the point I make in my video. Namely that LoS-MIMO is possible, since it's not true that the H matrix can't be inverted (which is the commonly held belief). In the E-band example you're talking about, where L=1500m and Delta=2m, the value of psi would be 15.63 (for a 70GHz carrier), which is 10000 times higher than the value for the example I showed in the video for standard mobile signals at 1GHz carrier. And this value at E-band is clearly big enough to be estimated in the noisy conditions, which means H will be estimated accurately, and can be inverted. ... By the way, this is _not_ the reason that is given in the document you referred to - which is misleading, since that document talks about 90deg phase shifts, and claims that 90deg is what's needed to seperate the signals. That's only true for two antennas sending BPSK. That argument/logic doesn't scale to quadrature modulation, and higher numbers of antennas.
@@iain_explainsThank you for the feedback. And again, your videos are great and very educational
Tried it in Matlab, cool model thanks. How is line of sight combatted in the real world to achieve mimo? Thinking of a cell tower pointing at someone standing in an empty field. Is fading enough to enable mimo in this situation? Or just simply the NW chooses a pre-coder to fix this?
In line-of-sight conditions it is best to use the multiple antennas in a beamforming mode (spatial diversity), rather than the "standard MIMO" spatial multiplexing mode. See: "What are Spatial Diversity and Spatial Multiplexing in MIMO?" ua-cam.com/video/MNA0xn7EeyY/v-deo.html
@Iain Explains Signals, Systems, and Digital Comms Hi professor, thank you for the video. One technique to obtain higher ranks on MIMO channels under LOS is by applying dual orthogonal polarization (like -45° / +45° per antenna element).
Very helpful...
Hi Sir! Excellent video! Question. In you're example how did you arrive at 3-10 times the amount of noise with yields that much for the error in the phase? Thanks.
That's the topic of next week's video. But you can already find the answer in the Matlab code I posted for this video, which includes channel training and estimation.
Thank you Prof. This is very useful. I was working on the subject and jumped to this video and it helped a lot. I wanted to practice with the Matlab code but I couldn't find it. Can you append the link to this comment?
I found the code link and other resources. Thank you Prof. Iain Collings
Glad you found it. Hope it was helpful.