reg lms algorithm -- how do we get d(k) at the receiver

in lms algorithm the aim is to minimize the error e(k)
where e(k) = y(k) - d(k)
and the d(k) is the desired output and y(k) is the actual output
how do we come to know about d(k) at the receiver side
if so what is the necessary for getting it from incoming signal

d(k) is the output comming from the adaptive filter ie. lms filter. y(k) is the actual output. the difference between d(k) and y(k) is the error and weights of the filter will be updated by the error

Q1) how do we come to know about d(k) at the receiver side?
A1) d(k) was previously informed to the receiver. It is called "training data". Therefore receiver side knows it beforehand.

Q2) if so what is the necessary for getting it from incoming signal?
A2) The aim is not to find "d(k)", because as you say it is already known. The aim is to cancel out the distortion due to the channel conditions (fading or additive noise)

thank you very much. your explanation is simple and good

That's true, for training mode of operation. After this mode, equaliser is considered to have converged to optimal structure, and transmission of unknown data starts. Now you calculate error by comparing data after decision slice and signal at the output of equaliser - this is so-called Decision Directed mode.

thank u cheggy
if you can explain it a little bit more it would be appreciated

OK, let's go :

First, equaliser operates in training mode: you send d(k) and your receiver expects d(k) exactly. During propagation channel (h(k)) has changed your signal and now it is x(k)=d(k)*h(k) (* is for convolution). x(k) is what you see at input of equaliser: you change x(k) with adaptive filter with coeficients c(k) in order to create y(k)=x(k)*c(k) that looks like d(k), as much as it's possible. Decision is made on the basis of y(k) values - decisions are d'(k). d'(k) should be equal to d(k) if equaliser works . In training mode you know d(k) and can calculate error of equalisation as e(k)=d(k)-y(k) and use it to adapt values of c(k) in right manner. After some time, c(k) achieves values necessary for reconstruction of d(k) (as much as it's possible ) - and we say that equaliser has converged to proper solution. From this moment, training is not necessary any more, 'couse we have coefficients c(k) that eliminate degradations made by channel! So, we can start sending "useful" data insted of training signal. d(k) is now unknown. Maybe you won't adapt your coefficients c(k) any more, but sometimes (in wireless systems "sometimes" means "often" ) you have to change them - 'couse channel h(k) has changed! But we don't have training sequence any more, so how we know in what directon to perform adaptation? Well, we can use decisions d'(k) that our equaliser makes on unknown data and compare them with output of adaptive filter y(k), i.e. error can be calculated as e(k)=d'(k)-y(k). This is Decision Directed mode (you have only your decisions and nothing else on the world ) - it's performance is worse than in Training mode, but it can be quite OK under some conditions. You work in DD mode until new training begins (if ever ).

Some equalisers work only in DD mode (of course - some conditions have to be satisfied) - this is so called "blind equalisation". You can find many papers on this forum that explain these things with detail. I hope this helped !