Mathematical analysis on effectiveness of SS code having negative autocorrelation

In the conventional spread spectrum communication systems, the spreading codes generated by linear shift registers have been used. On the other hand, in previous researches on chip-asynchronous CDMA (code division multiple access) systems, effectiveness of the spreading codes generated by the chaotic dynamical systems have been shown by numerical simulations and mathematical analysis. Effective chaotic codes have negative autocorrelation, which takes a negative value at lag 1 with damped oscillations. In this paper, we analyze effectiveness of such chaotic spreading codes having on Direct Sequence / Spread Spectrum (DS/SS) systems. The results of computer simulations show that BER performance becomes best when we use the PN sequences having negative autocorrelation. Moreover, we mathematically analyze the correlation performance and show that the spreading code with a negative autocorrelation becomes best for DS/SS.