Statistical Modelling of MIMO Communication Channels

Discusses a statistical channel model for multiple input multiple output (MIMO) digital communications (see references below).
Related videos: (see: iaincollings.com)
• MIMO Communications • MIMO Communications
• Quick Introduction to MIMO Channel Estimation • Quick Introduction to ...
• Why doesn't MIMO work in Line-of-Sight (LoS) Channel Conditions? • Why doesn't MIMO work ...
• What is Massive MIMO? • What is Massive MIMO?
• What is Multi-User MIMO Communications (MU MIMO)? • What is Multi-User MIM...
• What is Beamforming? • What is Beamforming? (...
• What is Multi Channel Beamforming? • What is Multi Channel ...
• How does Antenna Spacing affect Beamforming? • How does Antenna Spaci...
• What is Rayleigh Fading? • What is Rayleigh Fading?
• What is Rician Fading? • What is Rician Fading?
• What are Fast Fading and Slow Fading? • What are Fast Fading a...
• What are Flat Fading and Frequency Selective Fading? • What are Flat Fading a...
Full categorised list of videos and PDF Summary Sheets: iaincollings.com
References:
[1] 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.
[2] D. Asztély, “On Antenna Arrays in Mobile Communication Systems:
Fast Fading and GSM Base Station Receiver Algorithms,” Royal Inst.
Techonol., Stockholm, Sweden, Tech. Rep. IR-S3-SB-9611, 1996.
[3] H. Bölcskei and A. J. Paulraj, “Performance of space-time codes in the
presence of spatial fading correlation,” in Proc. Asilomar Conf. Signals,
Systems, and Computers, Pacific Grove, CA, Sep. 2000, pp. 687-693.
[4] H. Bölcskei, M. Borgmann, and A. J. Paulraj, “Impact of the propagation
environment on the performance of space-frequency coded MIMO-OFDM,”
IEEE J. Select. Areas Commun., vol. 21, no. 3, pp. 427-439,
Apr. 2003.
[5] D. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading correlation
and its effect on the capacity of multi element antenna systems,” IEEE
Trans. Commun., vol. 48, no. 3, pp. 502-513, Mar. 2000.
[6] C. Chuah, D. N. C. Tse, J. M. Kahn, and R. A. Valenzuela, “Capacity
scaling in MIMO wireless systems under correlated fading,” IEEE
Trans. Inf. Theory, vol. 48, no. 3, pp. 637-650, Mar. 2002.
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[@davebordenkircher8131]

This is of great help to me in my research project. Thank you for the excellent video. I have been an avid watcher since I was a second year.

[@iain_explains]

I'm so glad you're finding the videos useful. It's great to hear.

[@saitejabhushanam4232]

sir, while watching your video on cosine with some phase I got a doubt In the magnitude spectrum of cos(wot), how can it have magnitudes at 2 frequencies as Sinusoidal signals should have only one frequency right?

[@iain_explains]

I think you must be referring to the delta at w_o and the other one at -w_o. It would be a good idea to watch my video "What is Negative Frequency?" kzbin.info/www/bejne/nauZcn6NYrdpb9U

[@mohamedessam4704]

Hello sir, I found out that the spatial correlation matrix for 2 transmitting antennas and 2 receiving antennas (2x2 case), is a 4x4 Matrix I thought for the (2x2) case, I would have a spatial matrix of size (2x2) I need to know how to get the H matrix(impulse response) given the spatial correlation matrix and say for example H11 only how to calculate the rest H12 and H22 etc.. if you have an explanation for that I would be very thankful

[@iain_explains]

The spatial correlation matrix is shown in the video (bottom centre of the page). It is the Kronecker product of R and S. So yes, in the 2x2 antenna case, the spatial correlation matrix is 4x4. To generate channel values, use the formula in the middle of the page. Generate H_w by filling it with zero mean unit variance Gaussian values, and then multiply by R^(1/2) and S^(1/2), as shown.

[@amitbora6336]

Hi professor, I have a doubt. We know that due to the diversity, a 4x4 MIMO system has better BER performance than a 2x2 MIMO system. But how about in a spatially correlated channel? Will the BER of a 4x4 spatially correlated MIMO system be worse than a similarly spatially correlated 2x2 MIMO system? Thanks a lot, and wish you merry Christmas and a very happy new year!

[@iain_explains]

It all depends on the spatial correlation. However, in general, having more antennas is better.

[@tianyuez]

Dear Professor, thanks for your great lectures! I've been watching your videos for 5 hours and they taught much more than my professors taught me in 4 years! And by the way, is it possible for you to give some lectures on OTFS, which is a very hot topic today? And do you think it is good research idea to integrate radar with communication? Many thanks!

[@iain_explains]

Thanks for your comments. I'm so glad you have found the videos useful. And yes, thanks for the suggestion, OTFS is up near the top of my "to do" list. Hopefully I'll have a video on it in the next few weeks.

[@tianyuez]

@@iain_explains Thanks you very much professor. Looking forward to your videos on OTFS.

[@mopol4400]

hello Mr first thank you for all these information. what is spatially correlation channel in a short answer please ?

[@iain_explains]

Spatial correlation at a receiver is when transmission paths (that are random and depend on the location of the user, the base station and the scatterers) are more likely to come in (for receivers), or go out (for transmitters), from certain directions, compared to other directions. In other words, the communication paths are random, but there is correlation in the angle parameter between different paths. An example is explained at the 4min mark of the video.

[@someguy1507]

Hello professor, First, thank you for all the help you give us with your videos! I have a small question though: You mentioned at the start of the video that the elements of the H vector can be modeled as i.i.d. samples of a normal distribution with a mean of 0. My understanding of H is that each value is a gain value, where the magnitude is how much the signal is amplified/attenuated, and the phase is how much the signal is delayed/out-of-phase. With this assumption, then: why is the mean of this sample zero? Isn't perfect reception, where an antenna receives the waveform with no gain or phase offset, the value "1"? This makes me feel that this should be the "average" value, as a mean of 0 implies that the "average" antenna does not get a signal at all, or gets a very highly suppressed signal, which doesn't sound right. If we assume that even a slight change in the environment can completely change the phase of the signal, then shouldn't the random number be formed with a normally distributed magnitude of mean 1, and a uniformly distributed phase? Am I just overthinking this?

[@iain_explains]

Hopefully this video helps: "What is Rayleigh Fading?" kzbin.info/www/bejne/Y3eyn4x4j5yNnLM

[@someguy1507]

@@iain_explains That explained literally everything I had on my mind. Thank you so much!