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

covariancedetectionsamplessignalsliding window

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

Best Answer

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.)
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