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Background 5: Estimation Theory

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Wireless Future

Wireless Future

Күн бұрын

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@umerashraf992
@umerashraf992 3 жыл бұрын
Lectures on other types of estimators will be appreciated
@huuducdo143
@huuducdo143 Жыл бұрын
Hello, thank you very much for your lectures. Can I have the prove of bayesian function of g given y (the one finally link to the gaussian distribution of g, at 9.50 of the video)? Thank you very much.
@WirelessFuture
@WirelessFuture Жыл бұрын
Hi! A short proof for the real valued case can be found in eceweb1.rutgers.edu/~csi/ECE541/Chapter6.pdf I have written a proof in Appendix B.4 of my book Massive MIMO networks: massivemimobook.com/wp/free-pdf/ But it looks more complicated since we consider vectors.
@huuducdo143
@huuducdo143 Жыл бұрын
Thank you very much! @@WirelessFuture
@alirezanavi405
@alirezanavi405 3 жыл бұрын
Hello, Thank you for the lecture, it was so useful. I just had a question. In this method, we need prior knowledge, the parameter beta, to be able to use MSE. In real-world scenarios, how is this information obtained? thank you
@WirelessFuture
@WirelessFuture 3 жыл бұрын
Yes, the MMSE estimator is a Bayesian estimator, which means that it makes use of the statistics of the random variable. To utilize the expression presented in the video, the variable must be complex Gaussian distributed with variance beta. In practice, one can estimate beta from a set of realizations using the sample variance formula (mathworld.wolfram.com/SampleVariance.html). This is what the function “var” in MATLAB is doing.
@WirelessFuture
@WirelessFuture 3 жыл бұрын
@@jdt12880 Yes, if we transmit a known symbol/signal to enable channel estimation, we call it a pilot symbol/signal.
@nithinbabu4962
@nithinbabu4962 2 жыл бұрын
@@WirelessFuture@ Wireless Future Hi Professor, I am confused by this reply. The MMSE estimation you explained is happening in the pilot phase of the transmission, right? The estimation formula depends on beta, which is the variance of the prior g. From the above reply, we need a few realizations of g in order to get beta. I suppose the realizations of g can only be obtained from the estimation, which depends on the beta. In short, how can we get beta using realizations of g, which needs beta for its estimation?
@WirelessFuture
@WirelessFuture 2 жыл бұрын
@@nithinbabu4962 There are other estimators than the MMSE estimator, some of which require no prior information. The sample variance is one such estimator that can be used to first obtain an estimate of beta. After that, you can use the MMSE estimator to estimate future realizations of g
@niravpatel3961
@niravpatel3961 4 ай бұрын
sir here mmse estimation is carried out for Gaussian distributed variables. however, if we are interested for rician distributed variables mmse estimation then what will be change in to the derivation provided in to the video or where I will find it . kindly provide link or details of it.
@WirelessFuture
@WirelessFuture 4 ай бұрын
The general formula for the MMSE estimator (Slide 4) holds regardless of the distribution, but it is considerably more complicated to compute the estimate. I'm not aware of a general closed-form expression of it, but there are two special cases that have been treated in the prior literature: "Phase-aware MMSE estimator" and "Phase-unaware linear MMSE estimator". We cover these things in the following paper: arxiv.org/pdf/1903.07335
@getsamik1019
@getsamik1019 3 жыл бұрын
How size of pilot bits are decided as to estimate we require sample size and depending on sample size, estimator's performance varies. Does it depends on frequency band.
@WirelessFuture
@WirelessFuture 3 жыл бұрын
Hi! When it comes to estimating a single variable, it is only the total pilot signal energy that determines the estimation quality (power*number of pilot symbols). Transmitting one pilot symbol at 1 W power or two pilot symbols at 0.5 W result in the same estimation quality (same MSE). The general principle is to transmit pilots at maximum power and compute what the MSE will be. If you need to reduce the MSE to get a sufficiently good estimate, then you transmit additional pilot symbols. These principles are the same for any frequency band, but the SNR per pilot symbol might differ. If you have a weaker channel in a higher frequency band, you will have to send multiple pilots to get the same estimation quality.
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