Introduction. Perfect polyphase unimodular sequences, i. e. sequences with ideal periodic autocorrelation and single amplitude of symbols are widely used in modern radio communications and radar. A special place among them is occupied by perfect ternary sequences (PTSs) with elements {–1, 0, 1}. In fact, these are binary sequences with the alphabet {–1, 1}, but with zero symbols in some positions. It is known that PTSs are quite numerous and their length in comparison with perfect binary sequences is not limited from above. The charge for this is a peak factor greater than one, which causes energy losses in the receiver. A large number of research papers and books are devoted to the design of PTSs and the study of their properties. In particular, the handbook on sequence design by Fan and Darnell (1996) which provides an overview of the then known PTS families has become widely famous. However, over the past two decades, numerous new PTS families were discovered, some theorems on their existence were obtained, and connections were established between them and circulant weighing matrices. Therefore, there is a need for a new review of existing PTSs.Objective. The article is devoted to a retrospective review of existing PTSs and their generation devices.Materials and methods. Considered and analyzed domestic and foreign sources of information (books, journal papers, conference proceedings, patents).Results. Along with solving an informational bibliographic problem, the review shows the relationship between PTSs obtained at different times, their connection with circulant weighing matrices, and also describes the block diagrams of generators of some PTS families.Conclusion. A brief retrospective review of PTSs for their almost 60 years history is presented and the generators of some PTS families are considered. The results of the study are relevant for use in modern radio communications and radar systems and in particular, in CW and LPI radars.
New nonexistence results on circulant weighing matrices
