I have been reading about equalization and channel estimation in order to apply to my application of estimating trajectory path for a two-wheeled robot. The application is quite similar to equalization. I am studying the Least Mean Square algorithm (LMS) and have some basic doubts regarding how to determine if equalization is proper or not i.e., if there is a measure to quantify how much of the signal has been estimated properly. I am following this MATLAB implementation.
Doubt 1 :
The cost function for LMS is constructed using the input, so we are minimizing the error function. So, based on my understanding the input is known to the receiver. Hence, the LMS equalizer is not blind. Please correct me if wrong.
On running the code (using the same parameter settings in the code), I cannot understand what is the significance of the fourth tap having a magnitude one. Is this the delta impulse in the third subplot.
Does having a delta function mean that equalization is correct? I had read that for equalization to happen, the convolution of the estimated channel coefficients (here these are the weights of the LMS) and the known channel impulse should be a delta function. Does this graph convey the same? Could somebody please explain this concept of delta impulse and the graph?