Abstract:
Direct Sequence Spread-Spectrum Systems (DS-SSS) and Code Division Multiple Ac-cess (CDMA) Systems have a wide range of applications in wireless communication systems. They are well investigated under assumption that the spreading sequences are perfectly synchronized. However there are not many references presenting their opera-tions under assumption the spreading sequences are not perfectly synchronized, which can have significant consequences on the probability of error properties of these sys-tems. This Report describes design of these systems under assumption that there is not perfect sequence synchronization. The analysis and results are presented for binary and non-binary sequences like chaotic and random sequences. It was found that the signals in the systems can be represented and precisely mathematically described in discrete time domain. However, in that case, a random delay between imperfectly synchronized sequences needs to be expressed in discrete form, which opened a new problem of deriving discrete probability density functions as necessity for the statistical characterization of this delay between the received and locally generated (reference) sequence. Furthermore, the delay has a finite value, i.e., it is limited due to the nature of synchronization, being at most equal to the duration of a chip. Therefore, the derived density functions need to be defined and derived in the form of truncated discrete density functions. Also, the problem of choosing these densities is to be separately solved. Namely, the density functions need to follow real variations of the delay in these kinds of systems.
