COMPLEX SIGNAL DETECTION AND VECTOR-MATRIX MULTIPLICATION ALGORITHM

Wu Shi Dao
Vietnam National University, Hanoi, Vietnam

DOI: 10.36724/2664-066X-2026-12-2-8-25

SYNCHROINFO JOURNAL. Volume 12, Number 2 (2026). P. 8-25.

Abstract

The problem of joint detection and estimation of carrier frequency parameters and time delays of a low-power noise-like complex signal (NCS), its several copies mismatched in frequency and time delay, or noise-like signals of different structure, is relevant for a number of radio systems, since its solution can be used for time and frequency synchronization in information transmission channels, positioning in radio navigation systems, summation of signals during their multipath propagation or radiation by spaced repeaters, detection of all ground stations using a satellite constellation for the purpose of frequency resource monitoring, etc. The objective of the work is to improve the efficiency of digital algorithms for detecting low-power noise-like NCS, as well as to analyze the joint operation of the corresponding devices with loop circuits for tracking changes in signal parameters at a given accuracy of their final estimation in a multi-stage parallel-sequential detection and synchronization procedure, as well as to develop a unified synchronization quality criterion for a radio system. The subject of the research is digital algorithms for accelerated vector-matrix multiplication applied to the problem of detecting a set of noise-like signals; a multi-stage parallel-sequential procedure for detecting and synchronizing noise-like signals using digital synchronization devices (PSP) and analog loop circuits.

Keywords:  noise-like signals, vector-matrix multiplication, Rademacher functions, Walsh-Hadamard system, complex signals

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