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Barker sequences (codes) are generally well known in telecommunication systems (DSSS tech nology, synchronization) and radar technology. They are characterized by low sidelobes of normalized autocorrelation function (ACF) |RSL(τ)| ≤ 1/N (N is the length of sequence) [1]. Binary Barker sequences (elements ai ∈ {±1}) are only known for lengths N = 2; 3; 4; 5; 7; 11; 13. There are no these sequences for odd lengths N > 13, but it is unknown about an existence of these sequences for even lengths N > 4 [2, p. 109]. Ternary Barker sequences (elements ai ∈ {0, ±1}) are also known up to length N = 31 [3, p. 23]. There is a known kind of sequences called “Generalized Barker Sequences (Codes)”, they are polyphase sequences which consist of elements ai ∈ {exp(j⋅2πk/M)}, k≤M [4]. Polyphase Barker sequences are known up to length N = 77 [5]. The problem boils down to a controversy concerning the existence of sequences or systems of sequences with a greater length that would make it possible to obtain after their processing an ACFsignal with a low value of side lobes and a narrow central-lobe (as that of the Barker sequences). One of the solutions of this problem is the complementary sequences [6]. They are pairs of sequences of lengths N = 2n⋅10k⋅26m (n ≥ 0, k ≥ 0, m ≥ 0; except for the case n = k = m = 0) with a property that the result of adding of sidelobes of their ACF is equal to zero. Complementary sequences are used in pulse compression radar systems, telecommunication systems IEEE 802.11b/g and other applications. Although the complementary sequences are a good technical solution, the optimal ACF structure synthesis problem still hasn’t been solved in general, and there may be some other kinds of sequences that can, for instance, provide better noise stability of radio systems and consistency with some digital modulation techniques, e.g., QAM. New systems of binary sequences, that give the similar correlation properties after signal processing as that of the Barker sequences, are suggested and analyzed. The author considers processing of such systems, as well as ways of their application to radio systems and their comparison with complementary sequences.

Barker-like systems of sequences and their processing