In Wireless communication, we define a channel matrix H to be a matrix of size N by M, where N is the number of receive antennas at some receiver and M is the number of transmit antennas at some transmitter.
Assume we have two channel instances, H1 and H2, and Id like to study the correlation between these two channels in MATLAB.
For simplicity of exposition, assume
H1 = randn (8,64);
H2= randn(8,64)
then is it correct to say the correlation between the two matrices is
abs(H1' *H2)
Sorry for a long post, basically I just want to find how much correlated the two matrices are in Matlab..
This is not a rigorous description of Canonical Correlation. It is only meant for gentle primer.
Correlation is used for analyzing linear dependency between two sets of data. For e.g. You have heights(V1) and weights(V2) of people. You can easily find the correlation among these two sets of observations.
Now, say that you have a set of observations - {Cholestrol, weight, bloodpressure} and intake of {proteins, carbs, fibre, water}. Total 7 (3+4) sets of observations. Say you want to find out if the observations in the first set are dependent on the second set.
Running a simple correlation analysis would mean 12 correlation estimates. Hence, it cannot scale with dimensions. Secondly, say, Cholesterol is strongly dependent on a combination of (carbs + water), but, when analyzed individually with carbs & water, it may not exhibit strong correlation. Traditional correlation cannot capture all combinations of the dependencies.
This is where the canonical correlation is useful. Very plainly speaking, it analyzes all linear combinations of the first set of data with all linear combinations of the second set of data. It gives out those linear combinations within the first set that are highly (in fact, highest) dependent on the linear combinations in the other set.
You can read more about this here:
R has many packages that implement canonical correlation analysis.