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Infinite Sets of the Phase-Coded Sequences with the One-Level Periodic Autocorrelation Function


A.N. Leukhin, N.V. Parsaev

Paper is devoted to a synthesis problem of discrete phase-code sequences with the one-level periodic autocorrelation function. A number of known discrete codes with the ideal correlation features (a level of side lobes is equal to the zero) is finite for the given length. This paper the analytical expressions for infinite sets of the discrete phase-coded sequences with the lengths of even numbers, numbers of the multiple four and square numbers with the one-level periodic autocorrelation function are resulted. The problem of the synthesis of discrete phase-coded sequences is reduced to the problem for the solving the system of trigonometric equations of a special kind. It is proved, that Frank codes, codes of a class p and codes of Chu are the special cases of the new synthesized phase-coded se-quences with the zero level of side lobes of the periodic autocorrelation function. Examples of the synthesis of the phase-coded sequences with the zero level of side lobes of the periodic autocorrelation function forming the infinite sets are considered for the lengths of square numbers and for the lengths of numbers of the multiply four.

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