Optimal search for binary skew-symmetric sequences with minimal levels of side lobes

2020;
: pp. 410–419
https://doi.org/10.23939/mmc2020.02.410
Received: September 11, 2020
Accepted: October 01, 2020
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
National Army Academy

Signal-code constructions with modulating binary sequences are widely used in multichannel radiocommunication systems, radar, and other information systems.  Among these sequences, there are those that provide the minimum levels of side lobes of the aperiodic autocorrelation function and, accordingly, the required secrecy, noise immunity, resolution, and other important characteristics and parameters.  The paper describes an alternative approach for solving optimization task that involves a complete full search for the optimal binary skew-symmetric sequences with odd dimension $l$ using a criterion of minimum side lobes of the aperiodic autocorrelation function.  The proposed method based on performing two consecutive steps: optimizing in the space of dimension $L < 0.5(l-5)$ of the objective functions with respect to the levels of side lobes of the aperiodic autocorrelation function and solving of an equation system which specifies the aperiodic autocorrelation function.  The right sides of the equation system present the levels of the side lobes that are obtained as the result of completing the first operation.  The developed methodology includes an analysis of the structure of sets of binary sequences; finding correlations between the structural components using the methods of group theory; establishing analytical forms that define the functional relationships between the levels of side lobes of the aperiodic autocorrelation function.  The article presents an example of application and results of modeling of the offered algorithm to identify optimal binary sequences.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 410–419 (2020)