Constructing Binary Sequences with Optimal Peak Sidelobe Level: An Efficient Analytical-Computational Interplay

Binary sequence sets with asymptotically optimal auto/cross-correlation peak sidelobe level (PSL) growth have been known in the literature for a long time, and their construction has been studied both analytically and numerically. In contrast, it has been a long-standing problem whether we can construct a family of binary sequences whose auto-correlation PSL grows in an optimal manner. In this paper, we devise a construction of such binary sequences from sequence sets with good correlation properties. A key component of the design follows from the observation that if the PSL of the sequence set grows optimally, then the PSL of the constructed binary sequence will experience an optimal growth as a consequence. The proposed construction is simple-to-implement, and is shown to be accomplished in polynomial-time. With such a construction, we not only bridge between analytical construction and computational search, but also settle the long-standing design problem of binary sequences with an optimal growth of the auto-correlation PSL.