Efficient Design of Binary Sequences With Low Autocorrelation Sidelobes

Sequences with low autocorrelation sidelobes are needed in a diverse set of active sensing applications, including radar, sonar, communications, and biomedicine. The recently proposed and widely adopted methods of the Cyclic Algorithm-New (CAN) and Periodic CAN (PeCAN) are known to be computationally efficient, particularly as they employ fast Fourier transform (FFT) operations to design unimodular (i.e., unit-modulus) sequences with good autocorrelation properties. However, these cyclic algorithms cannot be directly used to design binary sequences with good autocorrelation properties due to the extremely multimodal nature of the associated optimization objectives. In this paper, we combine the notion of converging functions with the CAN and PeCAN frameworks, to considerably enhance their performances for binary sequence synthesis. Moreover, the convergence of these algorithms are established and their convergence properties are thoroughly analyzed. Numerical examples are provided to show that the proposed algorithms can outperform existing approaches for aperiodic and periodic binary sequence synthesis, especially for long sequence designs.