Weak Sinusoidal Signal Detection with CSI Model in Chaotic Interference

Algorithm 1

Empirical likelihood ratio detection for weak sinusoidal signal.

  Input: Observation 1-D data with the chaotic interference, the parameter delay time and the embedding dimension m, constant .

  Output: optimal values of the parameters , and the values of the statistic .

Set the

1 for j to number of epochs do

2  Calculate with Equations (10) and (11)

3  Calculate with Equation (15).

4  Repeat steps 2 and 3 until the estimated values of and stable.

5 end

6 Set etc.

7 for do

8  Simplifying the original problem at the point as a quadratic programming problem.

9  Set be the optimal solution of the quadratic programming problem.

10  Obtain point with Equation (28).

11  Set .

12 end

13  Set with Equation (31)

14 if (>)

15  the random amplitude sinusoidal signal does exist.

16 else

17  the random amplitude sinusoidal signal does not exist.

18 end