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
!