I am trying to understand and visualize the usage of covariance in channel estimation in OFDM systems. For example in MMSE estimator, we use covariance in formulating the estimated h channel. I have a couple of questions below and I would appreciate if you could please help me in understanding covariance and correlation here. 1-As far as I know, covariance tells us how two variables are moving together at the same time, going up together, going down together or moving in opposite direction. What is the difference between the correlation and the covariance here in estimating the channel? 2-Could you please explain why we use covariance in channel estimation ? 3-Is there a reference or doc which explains step by step how to get estimated h formula in MMSE model estimator using covariance? I have made a search for this on Google but not found yet a useful one. Thanks in advance! _____________________________ Posted through www.DSPRelated.com
Covariance and Correlation in OFDM System Estimation
Started by ●May 30, 2014
Reply by ●May 30, 20142014-05-30
On Friday, May 30, 2014 3:04:52 PM UTC-4, runinrainy wrote:> I am trying to understand and visualize the usage of covariance in channel > > estimation in OFDM systems. For example in MMSE estimator, we use > > covariance in formulating the estimated h channel. I have a couple of > > questions below and I would appreciate if you could please help me in > > understanding covariance and correlation here. > > > > 1-As far as I know, covariance tells us how two variables are moving > > together at the same time, going up together, going down together or moving > > in opposite direction. What is the difference between the correlation and > > the covariance here in estimating the channel? > > > > 2-Could you please explain why we use covariance in channel estimation ? > > > > 3-Is there a reference or doc which explains step by step how to get > > estimated h formula in MMSE model estimator using covariance? I have made a > > search for this on Google but not found yet a useful one. > > > > Thanks in advance! > > > > > > _____________________________ > > Posted through www.DSPRelated.comIf two random variables are independent, their covariance is zero. However the reverse is not necessarilty true. I.e., you can define two variables to have a non-zero correlation and have thier covariance be zero. Clay
Reply by ●May 30, 20142014-05-30
clay@claysturner.com wrote: (snip on covariance)> If two random variables are independent, their covariance is zero. > However the reverse is not necessarilty true. I.e., you can define > two variables to have a non-zero correlation and have thier > covariance be zero.Reminds me of a story about someone doing a linear least squares fit to the flow velocity in a pipe, and finding the slope of zero. Note that the average slope of a symmetric region of a parabola is zero. (Yes, he did both sides.) Similar to covariance, if you include both positive and negative sides, it is easy to get a result of zero. Don't do that. -- glen
Reply by ●May 30, 20142014-05-30
On 2014-05-30 21:08:15 +0000, clay@claysturner.com said:> On Friday, May 30, 2014 3:04:52 PM UTC-4, runinrainy wrote: >> I am trying to understand and visualize the usage of covariance in channel >> >> estimation in OFDM systems. For example in MMSE estimator, we use >> >> covariance in formulating the estimated h channel. I have a couple of >> >> questions below and I would appreciate if you could please help me in >> >> understanding covariance and correlation here. >> >> >> >> 1-As far as I know, covariance tells us how two variables are moving >> >> together at the same time, going up together, going down together or moving >> >> in opposite direction. What is the difference between the correlation and >> >> the covariance here in estimating the channel? >> >> >> >> 2-Could you please explain why we use covariance in channel estimation ? >> >> >> >> 3-Is there a reference or doc which explains step by step how to get >> >> estimated h formula in MMSE model estimator using covariance? I have made a >> >> search for this on Google but not found yet a useful one. >> >> >> >> Thanks in advance! >> >> >> >> >> >> _____________________________ >> >> Posted through www.DSPRelated.com > > If two random variables are independent, their covariance is zero. > However the reverse is not necessarilty true. I.e., you can define two > variables to have a non-zero correlation and have thier covariance be > zero. > > ClayCorrelation is just covariance scaled so its maximum value is one in absolute value. The scaling is the reciprocal of the square root of the product of the separate variances. Or at least if one is using technical definitions. More loosely correlation means having some relation but without the ability to specify numerical values or functional forms. A common example is a collection of points around the circle which will have a zero covariance or correlation but the values are clearly functionally related.
Reply by ●May 31, 20142014-05-31
>On 2014-05-30 21:08:15 +0000, clay@claysturner.com said: > >> On Friday, May 30, 2014 3:04:52 PM UTC-4, runinrainy wrote: >>> I am trying to understand and visualize the usage of covariance inchannel>>> >>> estimation in OFDM systems. For example in MMSE estimator, we use >>> >>> covariance in formulating the estimated h channel. I have a couple of >>> >>> questions below and I would appreciate if you could please help me in >>> >>> understanding covariance and correlation here. >>> >>> >>> >>> 1-As far as I know, covariance tells us how two variables are moving >>> >>> together at the same time, going up together, going down together ormoving>>> >>> in opposite direction. What is the difference between the correlationand>>> >>> the covariance here in estimating the channel? >>> >>> >>> >>> 2-Could you please explain why we use covariance in channel estimation?>>> >>> >>> >>> 3-Is there a reference or doc which explains step by step how to get >>> >>> estimated h formula in MMSE model estimator using covariance? I havemade a>>> >>> search for this on Google but not found yet a useful one. >>> >>> >>> >>> Thanks in advance! >>> >>> >>> >>> >>> >>> _____________________________ >>> >>> Posted through www.DSPRelated.com >> >> If two random variables are independent, their covariance is zero. >> However the reverse is not necessarilty true. I.e., you can define two >> variables to have a non-zero correlation and have thier covariance be >> zero. >> >> Clay > >Correlation is just covariance scaled so its maximum value is one in >absolute value. >The scaling is the reciprocal of the square root of the product of the >separate variances. >Or at least if one is using technical definitions. More loosely >correlation means >having some relation but without the ability to specify numerical >values or functional >forms. A common example is a collection of points around the circle >which will have a >zero covariance or correlation but the values are clearly functionallyrelated.> > > > > > >Thanks you for the responses! In the received signal below what is our variables when making the covariance and correlation analysis? And how does the result of analysis of the covariance and correlation help us estimating the channel H? Y=H.X + N _____________________________ Posted through www.DSPRelated.com
