Any two N × N costas signals must have at least one common ambiguity sidelobe if N > 3—A proof

Costas signals have an ambiguity function that approaches the ideal "Thumbtack" configuration. To increase the main lobe/side-lobe ratio without increasing the number of frequencies (signal dimension, N) it may be possible to stagger Costas signal pulses whose ambiguity sidelobe patterns do not coincide. We prove here that Costas signals of the same dimension, with completely different ambiguity sidelobe patterns, do not exist for N > 3.