Computationally Efficient Long Binary Sequence Designs With Low Autocorrelation Sidelobes

The design of binary sequences with low autocorrelation sidelobes is critically important to diverse applications, including radar and sonar as well as communications. Many computational methods have been proposed recently to design binary sequences through optimizing the integrated sidelobe level (ISL), which is a commonly used optimization metric. However, due to the high computational complexities, few of them can be used for long binary sequence designs, which are needed in, for example, low-cost commercial automotive radar systems. To improve the performance of the recently introduced fast Fourier transform (FFT) based CANARY algorithm for long aperiodic binary sequence designs, we introduce a new penalty function into the ISL metric and also propose a new framework of double-loop iterations. These new ideas are also extended to design long periodic binary sequences with low autocorrelation sidelobes and long aperiodic and periodic binary sequences with low correlation zones. The associated cost functions are still optimized efficiently via FFT-based iterations, making the proposed algorithms computationally efficient and, hence, suitable for long binary sequence designs. Moreover, the convergence properties and the computational complexities of these algorithms are analyzed. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithms.