Table 3 Procedure for the design of a nearly orthogonal polyphase code set

Step 1: SA

1-a.

Given N (number of radars), L (code length), and P (number of possible phases), initialize the code set matrix S with \(s_{n}[i] \in \left \{\exp \left (j\frac {p}{P}2\pi \right)| p=0,1,\cdots,P-1\right \}\).

1-b.

Set the current temperature t as a predefined initial temperature t ₀.

1-c.

Randomly select an element from S and replace its phase with a phase randomly selected from the remaining P−1 phases.

1-d.

Evaluate the change Δ E of the cost value in (19) after the replacement. Accept the new phase value if Δ E<0; otherwise, accept it with probability \(\exp \left (-\frac {\Delta E}{t}\right)\).

1-e.

Determine if the equilibrium state is reached based on a predefined criterion. If the state is reached, go to 1-f; otherwise, go back to 1-c.

1-f.

If the cost value is changed during the last three consecutive temperature reductions, update (reduce) the temperature t based on a predefined cooling schedule and then go back to 1-c. Otherwise, stop the procedure.

Step 2: iterative code selection for fine tuning

2-a.

Start with the design result S from Step 1.

2-b.

For every element of S, tentatively replace the phase with any of the other P−1 phases possible. If the evaluated cost value is reduced as a result of a phase replacement, accept the phase replacement; otherwise, keep the original phase value.

2-c.

If any of phase in S was changed, that is, any phase replacement was accepted, go back to 2-b. Otherwise, stop the procedure.