Least Squares and Auto and Cross Correlation I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here:

$Ax=b$ -- I have not exact solution, so I use the least squares equation.
$$A^TAx=A^Tb$$
I can solve and use the equation but I am trying to figure out why cross and auto correlation helps. Can anyone shed some light on that? For example, what do cross and auto correlation represent?

I am learning about signal processing and linerisation of a signal. $A$ is the input unpredistoted signal and $b$ is feedback distorted signal. $x$ is the coefficients that will be used to weight the Look Up Table. $Ax=B$ is solved in the adaptive algorithm box, in the link below.

http://www.altera.com/end-markets/wireless/advanced-dsp/predistortion/wir-digital-predistortion.html
Cross-correlation and auto-correlation are not directly linked to least squares.

Least squares can create a line of best fit for a set of points.

Cross correlation is a measure of the similarity of one signal to another (as a function of time lag to one signal). The discrete (digital) cross-correlation is an array where each element tells you how much the signals correlate with a certain amount of time lag. This operation is performed naively with a sliding window, or faster using Fourier, or other transforms. xcorr(a,b) = IFFT(FFT(a)* conj(FFT(b)))

Auto correlation is a measure of the similarity of a waveform to itself as a function of time.

There are normalised variants of cross-correlation and auto-correlation. These are created by measuring the standard deviation of each signal and dividing the output by the multiple of both. This enables you to classify the level of correlation much more easily. 0 implies no correlation and 1 implies identical signals.