Sliding window algorathim to find the covariance matrix and the received signal model in radar detection ?
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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
2 Comments
Walter Roberson
on 28 Dec 2011
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.
Accepted Answer
Walter Roberson
on 28 Dec 2011
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.)
5 Comments
Walter Roberson
on 28 Dec 2011
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.)
More Answers (1)
Honglei Chen
on 28 Dec 2011
You may want to take a look at corrmtx.
doc corrmtx
6 Comments
Walter Roberson
on 29 Dec 2011
Unfortunately I am not licensed for that toolbox so I cannot test this out.
Honglei Chen
on 30 Dec 2011
You need to give a second input specifying the size of your desired covariance matrix. See the doc for details.
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