Nested code sequences of Barker — Mersenne — Raghavarao

Abstract

Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.

New Composite Barker Codes in the Synchronization System of Broadband Signals

“…The efficiency of using new composite codes was estimated by the parameter ΔP(%) = РBV(%) -P(%), (3) where РBV(%)is the sync pulse peak extraction loss when using composite Barker-Volynskaya codes.…”

“…Broadband signals (BВS) are used in modern multi-channel code division multiplexing systems (CDMA, WCDMA) [1], in 802.11 family of wireless communication systems with Direct Sequence Spread Spectrum (DSSS) [2], in modern radar systems [3]. In the role of special spreading sequences in WCDMA networks, M-sequences, Gould sequences, Barker sequences can be used, in 802.11 wireless communication systems, the Barker sequence of length 11 is used for spreading the spectrum, in modern radar systems, Barker codes of length 11 and 13 are used.…”

The rise in maximum determinant matrix complexity

“…Mathematical objects, such as matrices with small number of their element values (levels), are corresponded by determinant-extreme solutions which find practical use in image processing and noise-immune coding problems [1,2], such as impulse-noise-resistant coding of images transferred via telecommunication channels [3], formation of nested code structures based on Barker codes with improved auto-correlation functions [4], image transformation for better protection from unauthorized use [5], etc.…”