Table 4 Pseudocode for the NuDE-mECA.

Input: \({\mathbf{S}}_{ref}\), \({\mathbf{S}}_{ech}\),\(M\)

Output: Output signal after clutter suppression \({\mathbf{e}}\)

               1

Compute the mutual ambiguity function \(\left| {\chi (l,k)} \right|^{2}\) according to Eq. (25);

               2

Take the maximum value \(\max \left| {\chi (l,k)} \right|^{2}\) within the range of distance dimension cancellation, for each Doppler frequency ;

               3

Sort the peak values and save to matrix \({\mathbf{F}}\);

               4

Take the first \(A\) Doppler frequencies as the first frequency extraction set \({\mathbf{F}}_{A}\), the power ratio of clutter to noise is greater than 1;

               5

//Refactoring the reference matrix for the first frequency extraction;

For \(a = 1:A\)

  Extract the relevant columns corresponding to \(f^{\prime}_{a}\) in the reference matrix and reconstruct a new reference matrix \({\mathbf{S}}_{A}\)

End For

               6

//Eliminating clutter on each frequency in set \({\mathbf{F}}_{A}\) through multichannel ECA algorithm with \({\mathbf{S}}_{A}\) as input

For \(a = 1:A\)

For \(m = 1:M\)

Solve the orthogonal projection of \({\mathbf{S}}_{A}\) on \({\mathbf{S}}_{ech}\) and obtain the clutter suppression result \({\mathbf{S}}_{ech}^{A}\) after the first frequency extraction

End For

End For

               7

//Compute the clutter suppression ratio \({\text{CA}}_{i}\) of the echo signal after cancellation, comparing with the clutter suppression threshold \({\text{CA}}_{th}\) determines the number of second frequency extractions

For \(i = A:P\)

If \({\text{CA}}_{i} < {\text{CA}}_{th}\) then

Extract \(f^{\prime}_{i}\) from \({\mathbf{F}}\) in sequence, eliminate the clutter corresponding to the Doppler frequency according to Eq. (20), and obtain the result \({\mathbf{S}}_{ech}^{i}\) after the \(i\)-th suppression

Else

Break

End For

               8

Return \({\mathbf{e}} = {\mathbf{S}}_{ech}^{i}\)