Abstract
Mathematical expressions, which are regular deterministic rules for synthesis of generalized binary Barker binary sequences, were proposed in the scientific literature. Sequences, which can be synthesized within the framework of these mathematical expressions, generalize the structural features of known Barker binary sequences. Sets of multiplicative complementary generalized binary Barker sequences allows obtaining a low equivalent peak sidelobe level after joint signal processing, which is 1/Nmax, where Nmax is a maximum length of sequence in a set of sequences. One feature of considered sequences is that the multiplication of results of matched filtering of signal components forms a non-stationary output noise in the case of stationary input noise. This fact affects the noise immunity, detection and other characteristics in signal processing system. The aim of the article is a statistical analysis of output signal in signal processing system for multiplicative complementary generalized binary Barker sequences. The results of the analysis show that the value of variance of the output noise is larger in the main lobe of output signal in comparison with values of variance in its sidelobes. The structure of output signal in the case of signal processing of sets of generalized binary Barker sequences can be represented by some number of separately taken partial lobes, each of which is characterized by constant mean value and variance of signal. Statistical characteristics (probability density functions, mean values, variances) of output signal are also shown and analyzed in the article using an example of signal processing.
Highlights
The set of mathematical models, which are regular deterministic rules for synthesis of generalized binary Barker binary sequences, were proposed in [1], [2]
Sets of multiplicative complementary generalized binary Barker sequences allows obtaining a low equivalent peak sidelobe level after joint signal processing, which is 1/Nmax, where Nmax is a maximum length of sequence in a set of multiplicative complementary generalized binary Barker sequences [3]
The value of variance of this noise is larger in the main lobe of output signal in comparison with the values of variance in its sidelobes
Summary
The set of mathematical models, which are regular deterministic rules for synthesis of generalized binary Barker binary sequences, were proposed in [1], [2]. Sets of multiplicative complementary generalized binary Barker sequences allows obtaining a low equivalent peak sidelobe level after joint signal processing, which is 1/Nmax, where Nmax is a maximum length of sequence in a set of multiplicative complementary generalized binary Barker sequences [3]. In this sense, generalized binary Barker sequences supplement in the theory of signal processing both known Barker binary sequences and Golay complementary series (sequences) [4], which are additive complementary code constructions
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