Covariance of Noise?

Hi,

   If I have zk a noise signal (5000*1),which is complex gaussian noise .How can I find the covariance matrix ,so that I need the next step- to success such that inner matrix multiplication to be correct- also I have zm radar_received signal (5000*1),Also the multiplication is (p')*(inverse of covariance matrix)*(zm).I need the result to be 1*1,where p is target steering vector =exp(2j*pi*f*n),n is # of samples.I need to do whitening matched filter detection!!!!!!!!!!!

Answer 1

[Walter Roberson]

The covariance of zk with regards to what?

If you are looking for the covariance of zk with itself, then as long as zk is a scalar you are going to get out only a single value (or a 2x2 array of the same value.)

If zk were an M x N matrix with N > 1, then cov(zk) would be N x N -- and thus cov(zk.') would be M x M; perhaps that is what you want. But it would require zk to be an array rather than a vector.

[zayed]

I need the covariance matrix of zk which is a complex gaussian noise signal (5000*1),so do i have to reshape this signal or something like this to get the coviarnce matrix ,but i need all the inner matrix multiplication (p'*inv(M)*zm)to be correct with last result 1*1

[Walter Roberson]

What size is p, and what size is zm? If we know those sizes then we can work out the size that inv(M) has to be.

The covariance of a vector is a single value (a scalar). You can calculate the inv() of that value, but it is simply 1 divided by the value, which would be 1 x 1. p and zm would have to each be 1 x 1 in order for the result to be 1 x 1.

[zayed]

zmis (5000*1) as zk ,do i have to divide them into blocks.then i alter the size of p to be suitable to the multiplication ,how?

[Walter Roberson]

If zm is 5000*1 then inv(M) must be 5000 in its second dimension, and in order for the inv(M) to be non-singular [because if it wasn't non-singular then inv(inv(M)) -> M would not exist) then M must be square and so must be 5000 x 5000. Then since p' is such that p' * inv(M) is 1 x 1, p' would have to be 1 x 5000 and so p itself would have to be 5000 x 1.

So we have deduced that inv(M) must be 5000 x 5000, which occurs when M itself is 5000 x 5000. But in order for a covariance matrix M to come out 5000 x 5000 then the array whose covariance was taken would itself would have to be S x 5000 for some S > 1, and so would have 5000*S elements in it. Your zk matrix only has 5000 elements in it, so unless more data could be added, we would calculate S as being 1 in order to match (5000) elements = (5000*S) elements, in contradiction of the requirement that S > 1 in order for the cov() call to succeed.

At this time, I do not seem to find any kind of correlation function that will accept a vector of length N and will return an N x N array of correlations of some kind. I looked through the standard tools such as corrcoef and xcov but the output array sizes would not appear to be what you want.