Thesis for a degree of Doctor of Technical Science in specialty 05.12.02 – «Telecommunication Systems and Networks». – National Aviation University. – Kyiv, 2020.
The thesis is devoted to solving the actual scientific and engineering problem dealing with a synthesis of binary sequences, which are optimal by the minimax criterion with respect to their autocorrelation function, in terms of a synthesis of regular structures of these binary sequences and their combinatorial systems under additional restrictions on the peak sidelobe level of their autocorrelation function (Barker sequences). The solution of the problem, proposed in the thesis, boils down to a new synthesized kind of binary sequences – generalized binary Barker sequences, which are characterized by regular structures, can be synthesized by means of regular synthesis method and form new multiplicative complementary structures of binary sequences.
The methodology of synthesis and signal processing of generalized binary Barker sequences and their multiplicative complementary structures, developed in the thesis, consists of: (a) the modification (parametric and criteria features) of the expectation-maximization (EM) algorithm with removing components of the Gaussian mixture model and additional clustering criteria for a statistical analysis of cross-correlations between sequences in a system for their further structuring, based on proved theorems on mathematical singularities in the log-likelihood function in the mentioned statistical analysis of cross-correlations; (b) the method of structuring binary sequences with a priori unknown structures, which provides selecting groups of binary sequences with interconnected structures and further detecting these interconnected structures in an explicit form; (c) the regular method for synthesis of generalized binary Barker sequences, based on the deterministic generation rules for these sequences; (d) the method for synthesis and joint signal processing of multiplicative complementary structures of generalized binary Barker sequences, based on the multiplication of results of matched filtering of signal components; (e) the method of a structural decomposition of output signal in signal processing system for multiplicative complementary generalized binary Barker sequences (an output signal can be represented by some number of separately taken partial lobes, each of which is characterized by constant mean value and variance of signal), which allows to perform a statistical analysis of output signal for noise immunity analysis, detection and other purposes in telecommunication system; (f) the method of estimation of energetic parameters of orthogonal signal-code constructions and noise on the physical layer of telecommunication system in case of use of generalized binary Barker sequences.
The classification by types and subtypes of generalized binary Barker sequences, based on statistical clustering using the EM and k-means algorithms, is also justified in the research. The properties of regular structures of generalized binary Barker sequences and properties of their autocorrelation functions are detected and studied. A complete system of mathematical models for analytical description of the autocorrelation function of generalized binary Barker sequences is synthesized. The analytical models for estimation of quality characteristics on the physical layer of telecommunication system in case of use of generalized binary Barker sequences are developed. Spectral and detection features of generalized binary Barker sequences and their comparison with Golay complementary sequences are also studied in the research. In contrast with Golay complementary sequences, generalized binary Barker sequences provide larger values of the processing gain in sidelobes (by 4.1 dB for a considered case), which provides less noise in sidelobes and a lower number of errors of the first genus in the case of the use of generalized binary Barker sequences. At the same time, the main disadvantage of generalized binary Barker sequences in comparison with Golay complementary sequences is that the processing gain in the main central lobe is lower (by 8.9 dB for a considered case), which causes more noise in the main lobe and a greater number of errors of the second genus in the case of the use of generalized binary Barker sequences. With this, the compared systems of sequences are characterized by almost the same total bandwidth, and the fact that generalized binary Barker sequences also provide a lower pulse width in the main lobe after signal processing (by 1.5 times), which provides a greater maximum data transfer rate and spectral efficiency on the physical layer of spread-spectrum telecommunication system (up to 1.5 times).
