Bifurcation of the Delay Lock Loop in Spread Spectrum Communication

Jiro ISHIKAWA  Hisato FUJISAKA  Chikara SATO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A    No.10    pp.1281-1285
Publication Date: 1995/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
spread spectrum communication,  parametric excitation,  subharmonic oscillation,  bifurcation,  chaos,  manifolds,  

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It is important to analyze a tracking or synchronizing process in Spread Spectrum (SS) receiving system. The most common SS tracking system considered here consists of pseudorandom (PN) generator, Lowpass Filter (LPE) and Voltage Controlled Oscillator (VCO). The SS receiver is to track or synchronize its local PN generator to the received PN waveform by VCO. The fundamental equation of the system is known by a second order nonlinear differential equation in terms of phase difference between local PN generator and received PN waveform. The differential equation is nonautonoumous due to PN function of time t with period T. Picking up the gain of VCO as the main parameter in the system we show that the system has bifurcation from the normal oscillation through subharmonic oscillation to finally chaos. In the final case, chaos is confirmed by investigating maximum Liapunov number and both stable and unstable manifolds.