CAZAC sequence generation of any length with iterative projection onto unit circle: principle and first results

Abstract: Constant amplitude zero-autocorrelation (CAZAC) sequences are mainly used for synchronization in communication and radar applications. The state-of-the-art proposes analytical derivation of specific families whose major limitation comes from the alphabet which only represents a fraction of the whole, the longer the sequences, the smaller the fraction. The objective of the paper is threefold, first to present the construction of constant amplitude zero-circular autocorrelation sequences of any length using iterative projection onto Unit Circle (IPUC) algorithm. This algorithm allows, from any random seed, to generate a near-CAZAC sequence. Then, focusing on length-8 sequences, we propose a classification of the IPUC output with an analytical expression of a representative for each identified equivalence class. Finally, the IPUC is applied within a simulated-annealing process to generate near-CAZAC sequences suitable for radar applications with optimized ratio between first and second lobes of the non-circular autocorrelation function.