What is this package?

This package calculates the periodic and aperiodic cross-correlation matrices of a set of sequences X of M-members, each of length N.
It returns a 3D matrix of size M x M x 2*(N-1): one M x M matrix for each lag from -(N-1) to (N-1).
It also calculates the peak sidelobe level (PSL) and integrated sidelobe level (ISL) of the set of sequences X.

Funtion descriptions

1. CORRELATION

CORRELATION calculates periodic and aperiodic cross-correlation function estimates.

1. Inputs:
   

   • X: a set of M sequence of length N vectors (N>1).
     
   • CORRTYPE: 'a' - aperiodic cross-correlation (default), 'p' - periodic cross-correlation
     

2. Outputs:
   

   • C: M x M x 2*N-1 matrix of cross-correlation values, M x M is the size of cross-correaltion matrix for each lag -N+1 <= l <= N-1
     
   • k: corresponding lags
     

3. Usage:
   

   • R = correlation(X, 'a');
     
   • C = correlation(X, 'p');
     
   • [R,k] = correlation(X, 'a');
     
   • [C,k] = correlation(X, 'p');
     

2. PSL

PSL calculates the peak sidelobe level for periodic or aperiodic cross-correlation.

1. Inputs:
   

   • R : M x M x 2*N-1 matrix of cross-correlation values.
     

2. Outputs:
   

   • P : max([R(u,v,k){u~=v,k}] U [R(u,v,k){u=v,k~=0}])
     

3. Usage:
   

   • P = psl( R );
     

3. ISL

ISL calculates the integrated sidelobe level for periodic or aperiodic cross-correlation.

1. Inputs:
   

   • R : M x M x 2*N-1 matrix of cross-correlation values.
     

2. Outputs:
   

   • I : sum([R(u,v,k){u~=v,k}]^2 + [R(u,v,k){u=v,k~=0}]^2)
     

3. Usage:
   

   • I = isl( R );