Correlation Properties of Sequences Formed on the Basis of M-Sequences and Walsh Sequences

Composite noise-like signals, such as signals that are obtained by phase varying of harmonic fluctuation at discrete points in time according to pseudorandom code sequences law, are widely used in modern radar, satellite radio-navigation and communication systems. Inherent properties of these signals can improve stability of systems to different types of interference, ensure simultaneous operation in overall bandwidth, increase accuracy of object positioning and solve synchronization problems. Set of such signals should have good correlation properties. Each signal of this set should differ from its time-shifted copies and from any other signal of this set with any time shift. Correlation properties of complex phase-shift keyed signals are uniquely determined by correlation properties of code sequences. Therefore development of effective methods for synthesis of code sequences with good correlation properties is an actual task. Results of analysis of correlation properties of composite code sequences formed on the basis of sequences with two level periodic correlation function and Walsh sequences are presented. Expressions for calculating periodic correlation function, periodic cross-correlation function and meander inverted cross-correlation function are given. Requirements for the components of the composite sequences are defined. A subset of Walsh sequences that can be used to obtain the composite sequences with good correlation properties is specified.

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