I am taking a course in Digital communication. I had a topic on the concept called Bipolar Amplitude Shift Keying in which I heard AWGN . It is said it has 3 properties Autocorrelation (dirac delta), Power spectral Density of (N/2) and PDF of Guassian Shape please can anyone explain how this properies make a AWGN unique . Any pointers to web resources will be appreciated. Thanks .

# Additive White Guassian Noise properties (Newbie question)

Started by ●November 6, 2010

Reply by ●November 6, 20102010-11-06

On 11/06/2010 07:06 AM, Deamon wrote:> I am taking a course in Digital communication. I had a topic on the > concept called Bipolar Amplitude Shift Keying in which I heard AWGN . > It is said it has 3 properties Autocorrelation (dirac delta), Power > spectral Density of (N/2) and PDF of Guassian Shape please can anyone > explain how this properies make a AWGN unique . Any pointers to web > resources will be appreciated. Thanks .Unique in what way? Mostly it's pretty good approximation to some common noise phenomenon, with a bit of extra constraints you can make it a pretty good approximation to many (but by no means all) common noise phenomenon, and if you couple it with an error-squared cost function it makes for mathematical analysis that drops tidy closed-form solutions all over the place Like linear systems, Gaussian noise is something that doesn't really exist in the real world, but makes the math tractable enough that you can actually make forward progress with closed-form solutions instead of fumbling around with solutions that either take a year to get an answer instead of an hour, or with computer simulations that are either wrong or so opaque that you don't learn anything by doing them. So we design our systems to approximate linear systems, and so that the noise comes out looking like AWGN, just so that we can have some hint of what the damn things are doing. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html

Reply by ●November 6, 20102010-11-06

On Sat, 06 Nov 2010 08:58:39 -0700, Tim Wescott <tim@seemywebsite.com> wrote:>On 11/06/2010 07:06 AM, Deamon wrote: >> I am taking a course in Digital communication. I had a topic on the >> concept called Bipolar Amplitude Shift Keying in which I heard AWGN . >> It is said it has 3 properties Autocorrelation (dirac delta), Power >> spectral Density of (N/2) and PDF of Guassian Shape please can anyone >> explain how this properies make a AWGN unique . Any pointers to web >> resources will be appreciated. Thanks . > >Unique in what way? > >Mostly it's pretty good approximation to some common noise phenomenon, >with a bit of extra constraints you can make it a pretty good >approximation to many (but by no means all) common noise phenomenon, and >if you couple it with an error-squared cost function it makes for >mathematical analysis that drops tidy closed-form solutions all over the >place > >Like linear systems, Gaussian noise is something that doesn't really >exist in the real world, but makes the math tractable enough that you >can actually make forward progress with closed-form solutions instead of >fumbling around with solutions that either take a year to get an answer >instead of an hour, or with computer simulations that are either wrong >or so opaque that you don't learn anything by doing them. > >So we design our systems to approximate linear systems, and so that the >noise comes out looking like AWGN, just so that we can have some hint of >what the damn things are doing. > >-- > >Tim Wescott >Wescott Design Services >http://www.wescottdesign.com > >Do you need to implement control loops in software? >"Applied Control Theory for Embedded Systems" was written for you. >See details at http://www.wescottdesign.com/actfes/actfes.htmlIsn't AWGN an accurate model for thermal noise? Since that's the main impairment in many receivers, I think it's a pretty accurate representation of the real world. Gaussian distributions occur frequently in nature. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com

Reply by ●November 6, 20102010-11-06

On 11/06/2010 03:28 PM, Eric Jacobsen wrote:> On Sat, 06 Nov 2010 08:58:39 -0700, Tim Wescott<tim@seemywebsite.com> > wrote: > >> On 11/06/2010 07:06 AM, Deamon wrote: >>> I am taking a course in Digital communication. I had a topic on the >>> concept called Bipolar Amplitude Shift Keying in which I heard AWGN . >>> It is said it has 3 properties Autocorrelation (dirac delta), Power >>> spectral Density of (N/2) and PDF of Guassian Shape please can anyone >>> explain how this properies make a AWGN unique . Any pointers to web >>> resources will be appreciated. Thanks . >> >> Unique in what way? >> >> Mostly it's pretty good approximation to some common noise phenomenon, >> with a bit of extra constraints you can make it a pretty good >> approximation to many (but by no means all) common noise phenomenon, and >> if you couple it with an error-squared cost function it makes for >> mathematical analysis that drops tidy closed-form solutions all over the >> place >> >> Like linear systems, Gaussian noise is something that doesn't really >> exist in the real world, but makes the math tractable enough that you >> can actually make forward progress with closed-form solutions instead of >> fumbling around with solutions that either take a year to get an answer >> instead of an hour, or with computer simulations that are either wrong >> or so opaque that you don't learn anything by doing them. >> >> So we design our systems to approximate linear systems, and so that the >> noise comes out looking like AWGN, just so that we can have some hint of >> what the damn things are doing. >> >> -- >> >> Tim Wescott >> Wescott Design Services >> http://www.wescottdesign.com >> >> Do you need to implement control loops in software? >> "Applied Control Theory for Embedded Systems" was written for you. >> See details at http://www.wescottdesign.com/actfes/actfes.html > > Isn't AWGN an accurate model for thermal noise?Yes.> Since that's the > main impairment in many receivers, I think it's a pretty accurate > representation of the real world.If that were true, we wouldn't need spread spectrum. Adjacent channel interference is certainly "noise" if you don't want to receive it, and it's certainly not Gaussian. For years this was dealt with by saying "oh, that's not noise, that's interference". Now we use CDMA, and say "look! it acts just like Gaussian noise!"> Gaussian distributions occur frequently in nature."Long-tail Gaussian" distributions occur frequently in experiments, where some more or less close approximation to a Gaussian process accounts for most of the signal, with the occasional "event" that blows the tails out. We call them "outliers", we throw them out, then we say "look! what's left looks Gaussian!". I'm not saying that Gaussian noise isn't a tremendously useful mathematical tool. I'm not saying that it shouldn't be used (I do, all the time). I'm not even saying it doesn't exist in nature -- I'm just saying that pure real honest-to-gosh Gaussian noise doesn't occur nearly as often as you'd think, given how universally it is assumed (explicitly or implicitly). Only when you ponder just how tractable the math is with the Gaussian assumption, and just how intractable it can get without, does the ubiquitousness of the Gaussian assumption make sense. Like linear systems, Gaussian noise should be recognized as a really simplifying mathematical model. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html

Reply by ●November 6, 20102010-11-06

Tim Wescott wrote:>> >> Isn't AWGN an accurate model for thermal noise? > > Yes.Until the quantum effects and extremities could be ignored.>> Since that's the >> main impairment in many receivers, I think it's a pretty accurate >> representation of the real world. > > If that were true, we wouldn't need spread spectrum.Spread Spectrum is a way to deal with the dispersion in the channel; whereas noise is still the noise.> Adjacent channel > interference is certainly "noise" if you don't want to receive it, and > it's certainly not Gaussian.If noise statistics is not Gaussian, then it could be used to our advantage.> For years this was dealt with by saying > "oh, that's not noise, that's interference". Now we use CDMA, and say > "look! it acts just like Gaussian noise!"Spread Spectrum and CDMA are different concepts with entirely diferent goals. CDMA is equvalent to the random access to a shared channel.> Like linear systems, Gaussian noise should be recognized as a really > simplifying mathematical model.Yes. VLV

Reply by ●November 7, 20102010-11-07

Reply by ●November 7, 20102010-11-07

Deamon <persistence911@gmail.com> writes:> Please could anyone explain this properties of AWGN to me in clear > terms.Hi, A = Additive. This means the noise adds to the signal in a linear way, i.e., there are no nonlinear phenomenom occurring such as gain modulation or other "multiplicative mechanisms" [sklar] in effect. W = White. This is the statistical, or stochastic, notion of "white," meaning that the noise has a "constant spectral density function" [brown]. I won't elaborate further on this as there is already a ton of material explaining it. G = Gaussian. This means that the "distribution" of the noise is Gaussian. See any probability theory book, e.g. [papoulis]. --Randy @BOOK{sklar, title = "{Digital Communications}", author = "{Bernard~Sklar}", publisher = "Prentice Hall P T R", edition = "second", year = "2001"} @book{brown, title = "Introduction to Random Signal Analysis and Kalman Filtering", author = "{Robert~Grover~Brown}", publisher = "John Wiley and Sons", year = "1983"} @book{papoulis, title = "Probability, Random Variables, and Stochastic Processes", author = "{Athanasios~Papoulis}", publisher = "WCB/McGraw-Hill", edition = "Third", year = "1991"} -- Randy Yates % "And all you had to say Digital Signal Labs % was that you were mailto://yates@ieee.org % gonna stay." http://www.digitalsignallabs.com % Getting To The Point', *Balance of Power*, ELO

Reply by ●November 7, 20102010-11-07

There is quite a bit of detail in those four letters. I'm not even trying to give a satisfying answer, just point you to the right directions. A: Additive The noise is strictly added on top of the signal, not for example modulated like phase noise or intermodulation distortion. W: White The power spectral density is uniform. It affects all frequencies evenly G: Gaussian The amplitude probability density function is, erm, Gaussian. N: Noise. It's not someone else's signal, otherwise it would be an "interferer". The "Gaussian" distribution usually results when a large number of independent independent noise processes interact, like all the electrons in a wire. To a communications engineer AWGN might imply in a modulation context that you're looking at error rates in the presence of noise, but no fading channel is present.

Reply by ●November 7, 20102010-11-07

>I'm not saying that Gaussian noise isn't a tremendously useful >mathematical tool. I'm not saying that it shouldn't be used (I do, all >the time). I'm not even saying it doesn't exist in nature -- I'm just >saying that pure real honest-to-gosh Gaussian noise doesn't occur nearly >as often as you'd think, given how universally it is assumed (explicitly >or implicitly). Only when you ponder just how tractable the math is >with the Gaussian assumption, and just how intractable it can get >without, does the ubiquitousness of the Gaussian assumption make sense. > >Like linear systems, Gaussian noise should be recognized as a really >simplifying mathematical model. > >Tim WescottI think its more accurate to say that Gauusian noise is seldom the *only* process at work. Most things in nature is pretty darned close to Gaussian at their root. However, the noise may appear after filtering, and other parallel sources of signal pollution may be at work. Steve

Reply by ●November 8, 20102010-11-08

On Nov 6, 8:06�am, Deamon <persistence...@gmail.com> wrote:> I am taking a course in Digital communication. I had a topic on �the > concept called Bipolar Amplitude Shift Keying �in which I heard AWGN . > It is said it has 3 properties Autocorrelation (dirac delta), Power > spectral Density of (N/2) and PDF of Guassian Shape please can anyone > explain how this properies make a AWGN unique . Any pointers to web > resources will be appreciated. Thanks .Deamon, Consider that the Gaussian is completely defined by the mean and variance. Then consider what the autocorrelation matrix looks like. Then _really_ think about it. Maurice Givens