Hi all, i m not clear about AWGN channel . most paper and book consider that channel is Gaussian and it has zero mean and N0/2 noise spectral desnsity for eatch side. i just clear channel is random it has normal valriable(zero mean) and noise what is the meaning of two sided spectral density is it transmitter side as well as receiver side noise level. What is the relation between AWGN channel and rayleigh fading channel ? could u possible to little bit implent what exactly that........if possible give a example. thanks in advance.
Channel
Started by ●February 20, 2006
Reply by ●February 20, 20062006-02-20
Almas_Uddin_Ahmed wrote:> Hi all, > > i m not clear about AWGN channel . most paper and book consider that > channel is Gaussian and it has zero mean and N0/2 noise spectral > desnsity for eatch side."Additive White Gaussian Noise". That pretty much sums it up -- It's additive, so you add the noise instead of dividing or multiplying on something. It's white, so it has zero mean (and is spread over all frequencies, or at least beyond the bandwidth of your receiver). Finally, the noise is Gaussian, so it's not uniform or a Poisson process or bi-value or anything else.> i just clear channel is random it has normal valriable(zero mean) and > noise"i just clear channel"? I'm not sure what you're asking, but hopefully the answer is that a zero-mean normal variable is Gaussian and on the road to being white.> > what is the meaning of two sided spectral density is it transmitter > side as well as receiver side noise level.That depends on the context of the book you're reading. It probably means the spectrum considering both positive and negative frequencies -- but I don't know.> > What is the relation between AWGN channel and rayleigh fading channel > ?They are both channels. They act differently. A Rayleigh fading channel, well, fades: the noise is multiplicative, and it isn't Gaussian. I _think_ the PD of the multiplicative noise is the result of squaring a process with a Gaussian PD, but I'd have to check. You could, if you needed to (you don't want to) study a channel that has both Rayleigh fading and additive white Gaussian noise.> > could u possible to little bit implent what exactly that........if > possible give a example. > > thanks in advance. >-- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/
Reply by ●February 20, 20062006-02-20
"Almas_Uddin_Ahmed" <almas.mmu@gmail.com> asked in message news:1140462104.705325.182330@g43g2000cwa.googlegroups.com...> Hi all, > > i m not clear about AWGN channel . > > what is the meaning of two sided spectral density is it transmitter > side as well as receiver side noise level.In many communication systems, the "channel noise" actually is thermal noise from the front-end of the receiver; the physical channel itself contributes very little of the channel noise. The Prime Rule for communication systems design is "Put the signal where the noise a'i'nt!" The notion of white noise with two-sided (constant) spectral density is just a reminder to the designer that in this problem, the noise is everywhere, and that the designer cannot pull tricks such as using only that part of the available bandwidth where the noise is low compared to other parts of the available band: the noise power is the same everywhere in the band (and outside the band too for that matter!)
Reply by ●February 20, 20062006-02-20
Dilip V. Sarwate said the following on 20/02/2006 19:35:> "Almas_Uddin_Ahmed" <almas.mmu@gmail.com> asked in message > news:1140462104.705325.182330@g43g2000cwa.googlegroups.com... >> Hi all, >> >> i m not clear about AWGN channel . >> >> what is the meaning of two sided spectral density is it transmitter >> side as well as receiver side noise level. > > The notion of white > noise with two-sided (constant) spectral density is just > a reminder to the designer that in this problem, the noise is > everywhere...It has a far more specific meaning than that. Two-sided spectral density is relevant if you're thinking in terms of a two-sided spectrum, i.e. you're including -ve frequencies, and thinking in terms of complex exponentials. To add up to the same overall noise power as the one-sided model or the baseband representation (BW * N0), clearly the noise spectral density in each half (+ve and -ve) must be (N0 / 2), i.e. total power is (BW * 2) * (N_0 / 2). -- Oli
Reply by ●February 20, 20062006-02-20
Oli Filth <catch@olifilth.co.uk> writes:> Dilip V. Sarwate said the following on 20/02/2006 19:35: >> "Almas_Uddin_Ahmed" <almas.mmu@gmail.com> asked in message >> news:1140462104.705325.182330@g43g2000cwa.googlegroups.com... >>> Hi all, >>> >>> i m not clear about AWGN channel . >>> >>> what is the meaning of two sided spectral density is it transmitter >>> side as well as receiver side noise level. >> The notion of white >> noise with two-sided (constant) spectral density is just >> a reminder to the designer that in this problem, the noise is >> everywhere... > > It has a far more specific meaning than that. Two-sided spectral > density is relevant if you're thinking in terms of a two-sided > spectrum, i.e. you're including -ve frequencies, and thinking in terms > of complex exponentials.Right. Usually two-sided densities are used for complex baseband signals. Remember that a real time-domain signal has a Hermitian-symmetric spectrum, so a complex time-domain signal allows asymmetry in the spectrum, or, looked at the other way, an asymmetric spectrum describes a complex time-domain signal. -- % Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven. %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and %%% 919-577-9882 % Verdi's always creepin' from her room." %%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO http://home.earthlink.net/~yatescr
Reply by ●February 20, 20062006-02-20
Oli Filth wrote:> Dilip V. Sarwate said the following on 20/02/2006 19:35: > >> "Almas_Uddin_Ahmed" <almas.mmu@gmail.com> asked in message >> news:1140462104.705325.182330@g43g2000cwa.googlegroups.com... >> >>> Hi all, >>> >>> i m not clear about AWGN channel . >>> >>> what is the meaning of two sided spectral density is it transmitter >>> side as well as receiver side noise level. >> >> >> The notion of white >> noise with two-sided (constant) spectral density is just >> a reminder to the designer that in this problem, the noise is >> everywhere... > > > It has a far more specific meaning than that. Two-sided spectral density > is relevant if you're thinking in terms of a two-sided spectrum, i.e. > you're including -ve frequencies, and thinking in terms of complex > exponentials. > > To add up to the same overall noise power as the one-sided model or the > baseband representation (BW * N0), clearly the noise spectral density in > each half (+ve and -ve) must be (N0 / 2), i.e. total power is (BW * 2) * > (N_0 / 2).That depends on how BW is defined. For double-sideband AM with a 5 KHz audio bandwidth, you need a 10 KHz RF channel. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 22, 20062006-02-22
Randy Yates said the following on 20/02/2006 23:05:> Oli Filth <catch@olifilth.co.uk> writes: > >> Dilip V. Sarwate said the following on 20/02/2006 19:35: >>> The notion of white >>> noise with two-sided (constant) spectral density is just >>> a reminder to the designer that in this problem, the noise is >>> everywhere...>> It has a far more specific meaning than that. Two-sided spectral >> density is relevant if you're thinking in terms of a two-sided >> spectrum, i.e. you're including -ve frequencies, and thinking in terms >> of complex exponentials. > > Right. Usually two-sided densities are used for complex baseband > signals.Isn't the noise PSD for the complex baseband representation the same as the one-sided (real) passband noise PSD, i.e. N0? Two-sided density becomes relevant when you're looking at the passband signal on a two-sided spectrum. -- Oli
Reply by ●February 23, 20062006-02-23
Hi there, If you consider a transmitted signal s(t), the effect of additive noise on the signal can be represented as r(t) = s(t) + n(t) where r(t) is the signal at the receiver. When you say that n(t) is AWGN, it means that the noise can be "added" to the signal (additive), that the amplitude of n(t) is Gaussian distributed, and the frequency spread N(f) is from -inf to +inf, that is, it's "white". The reason why the noise is modeled as "Gaussian" or "Normal" is that if you model noise from multiple sources as INDEPENDENT random variables of ANY distribution (not necessarily Gaussian), then the pdf of the resulting random variable tends to have a Gaussian distribution when the number of independent sources is large (Central Limit Theorem). Now if s(t) were to be considered a complex signal made up of in-phase and quadrature components, then, using S(t) and N(t) to represent the complex baseband versions of s(t) and n(t) S(t) = s_i(t) + j s_q(t) N(t) = n_i(t) + j n_q(t) R(t) = S(t) + N(t) = [s_i(t) + n_i(t)] + j [s_q(t) + n_q(t)] there is an additive gaussian noise component on each of the in-phase and quadrature components separately The noise signal can be written in the amplitude-phase notation as N(t) = A(t) exp (j phi(t)) where A(t) = sqrt(n_i(t)^2 + n_q(t)^2]) phi(t) = arctan (n_q(t)/n_i(t)) Now it can be shown that A(t) is Rayleigh distributed and phi(t) is uniformly distributed. Regards, - Ravi Almas_Uddin_Ahmed wrote:> Hi all, > > i m not clear about AWGN channel . most paper and book consider that > channel is Gaussian and it has zero mean and N0/2 noise spectral > desnsity for eatch side. > i just clear channel is random it has normal valriable(zero mean) and > noise > > what is the meaning of two sided spectral density is it transmitter > side as well as receiver side noise level. > > What is the relation between AWGN channel and rayleigh fading channel > ? > > could u possible to little bit implent what exactly that........if > possible give a example. > > thanks in advance.
Reply by ●February 23, 20062006-02-23
Dilip,> In many communication systems, the "channel noise" actually > is thermal noise from the front-end of the receiver; the physical > channel itself contributes very little of the channel noise.Why should this be so? I'm inclined to think that in wireless channels for example, atmospheric noise is a significant source of random noise.> The Prime Rule for communication systems design is > "Put the signal where the noise a'i'nt!" The notion of white > noise with two-sided (constant) spectral density is just > a reminder to the designer that in this problem, the noise is > everywhere, and that the designer cannot pull tricks such as > using only that part of the available bandwidth where the > noise is low compared to other parts of the available band: > the noise power is the same everywhere in the band (and > outside the band too for that matter!)Very nicely put! Regards, Ravi
Reply by ●February 23, 20062006-02-23
Ravi Srikantiah wrote:> Dilip, > > >>In many communication systems, the "channel noise" actually >>is thermal noise from the front-end of the receiver; the physical >>channel itself contributes very little of the channel noise. > > > Why should this be so? I'm inclined to think that in wireless channels > for example, atmospheric noise is a significant source of random noise.... Many communications systems use wires, optical fiber, and other isolated channels. Some use radio frequencies high enough so that there is very little man-made noise. The cosmic background noise was investigated and discovered because it was the dominant noise in its band. Interstellar hydrogen radiation at 21 cm isn't strong, but it too is the dominant signal in that band, at least for directional antennas pointed upward. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
