Very Low Correlation Sequence Design with Power Control

Barker sequences and generalized Barker sequences with complex symbols on the unit circle have very limited lengths to achieve maximum aperiodic autocorrelation of 1. In the performed innovation, we consider symbols beyond the unit circle in the complex plain to obtain more degrees of freedom to achieve the desired minimum autocorrelation level with much longer sequences. The sequence symbols are obtained by direct solution of a minimax problem (i.e., minimization of the maximum autocorrelation), with limitation on their maximum power to preserve the sequence randomness. The sequence length is arbitrary and is an input parameter to the algorithm. The developed algorithm leads to excellent results. For instance, sequences with the length of 1000 can simply be obtained with maximum autocorrelation of not only below 1, but even much smaller.