Noise-like discrete signals for asynchronous code division radio systems

This article discusses noise-like discrete signals (pseudo-random sequences) for asynchronous code division systems for radio channels. Asynchrony implies the use of sequences that are statistically uncorrelated for an arbitrary cyclically shifted copy of the signals, i.e. their cross-correlation coefficient for arbitrarily chosen starting points is close to zero. The fundamental theoretical limit for this characteristic is the well-known Welch boundary. In this paper, we compare the correlation properties of various sets (Gold codes, Kasami sequences, etc.) with this fundamental limit. The parameters of different codes are estimated, the corresponding bound is shown and compared with the real correlation characteristics of the codes. For the approximation, the Laurent series expansion and the Puiseau series were used. The asymptotic properties were also estimated. The paper also considers new ensembles of noise-like discrete signals for asynchronous systems. These codes are statistically uncorrelated, asymptotically the square of their cross-correlation for arbitrary starting points tends to the theoretical Welch bound. Moreover, the cardinality (power of the set) of new signal ensembles is much higher than that of Gold codes and Kasami sets. Consequently, the practical use of such noise-like discrete signals will increase the capacity of asynchronous code division systems for radio channels and reduce the cost of communication services. In addition, new sets of spreading signals will be useful for the implementation of the so-called. soft capacity, i.e. when, if necessary, the base station can increase the subscriber capacity with a slight decrease in the quality of service.