Sliding window algorathim to find the covariance matrix and the received signal model in radar detection ?

Hi,

    I need to use sliding window algorithm,but it's the first time that I face to use it , so I need help to implement the following in matlab :

   I have a radar_noise vector x with size (5000*1),how can I find covariance matrix by using sliding window algorithm?

    Also I have a radar_received signal vector s with size (5000*1),how can I use sliding window to find the received signal model ,providing that :

 The number of Quantization =2.
  The number of samples = 32.

The reposted thread :

The signal model used is as follows:

Consider a radar system utilizing an Ns-element array with inter-element spacing d.

The radar transmits an Mt-pulse waveform in its coherent processing interval (CPI).

The received data can then be partitioned in both space and time, by using a sliding window,into an (N*M) space-time snapshot X'.

This partitioning will result in K = (Ns -N +1)(Mt -M +1) snapshot matrices being generated for processing.

The columns of these space-time snapshots are then stacked into inter-leaved column vectors xk of size (NM*1).

The K columns are then arranged as the columns of the (NM*K )matrix X. The signal model used is then:

X =ast' -N

where both s and t are space-time vectors and a is a complex amplitude.

N is the (NM * K ) zero-mean Gaussian clutter-plus-noise matrix with independent and identically distributed (iid) columns nk approximately CN (0,C),where CN is complex Gaussian noise and C is the covariance matrix.

The space-time clutter-plus-noise covariance matrix is defined as C, where E[N * Hermitian(N)] and E[.] is the expectation operator.

Thanks

[Walter Roberson]

Your previous Question, in which you set out your mathematical model, was the most important posting you have yet made, as it set out what you are really trying to accomplish and the mathematical model you are following for it.

Unfortunately, you removed that posting and went back to a line of questions that absolutely positively cannot give you the results you need.

[zayed]

I will repost it again.

Answer 1

[Walter Roberson]

Here is the code to construct the best covariance matrix possible from your vector x:

covx = rand(length(x)) .* repmat(x, 1, length(x));
covx = (covx+covx.')/2;
covx = cov(x) ./ max(abs(covx(:)));
covx(1:length(x)+1:end) = 1;

This will have no relationship at all to the covariance matrix that would be generated by the model you mentioned in your previous Question, but it is the best covariance matrix you can generate without the additional data that is provided by that model (data which you do not make available to this present question.)

[zayed]

can you explain what each line in the code do,because I don't recognize where T come from

[Walter Roberson]

Sorry, I renamed a variable while I was going.

[zayed]

Would you please explain each line so that I can understand the process.

[Walter Roberson]

It creates a symmetric matrix of correlations, normalizes them, and ensures that the diagonal is exactly unitary (which takes care of round-off errors amongst other issues.)

[zayed]

It works ,thank you,and i will accept the answer.But is it the same as

E(x*Hermitian(x)) ,where E is expectation operator .

Also I need the answer of the rest posted thread to be completed,please.

Answer 2

[Honglei Chen]

You may want to take a look at corrmtx.

doc corrmtx

[Walter Roberson]

That would be correlation matrix, but zayed needs a covariance matrix.

[zayed]

I think I should use the sliding window algorithm

[Honglei Chen]

covariance matrix is just corrmtx(x-mean(x)), although I'm assuming the signal is WSS here. As to the sliding window, my understanding is to segment the data and make sure a covariance matrix can be generated. If that's the case, corrmtx does do sliding window.

[zayed]

It gives error using corrmtx(x-mean(x))

??? Error using ==> corrmtx

Not enough input arguments.

[Walter Roberson]

Unfortunately I am not licensed for that toolbox so I cannot test this out.

[Honglei Chen]

You need to give a second input specifying the size of your desired covariance matrix. See the doc for details.