Investigation of the Correlation Properties of Spreading Sequences for Asynchronous CDMA

Abstract

Asynchronous CDMA uses sets of spreading sequences (eg, Gold codes, Kasami sequences, etc.) that are statistically uncorrelated for arbitrarily random starting points. We study various sets of spreading sequences and evaluate their correlation properties. The Fundamental Welch Bound sets the limit below which the crosscorrelation square between any cyclically shifted sequence copies cannot fall. We estimate the correlation for different spreading sequences in relation to this theoretical limit. For this we use a polynomial approximation (by Laurent and Puiseux series). We also consider large sets of spreading sequences, for which the correlation modulus increases by about 2 times (compared to Gold codes). However, in comparison with Gold codes, the cardinality of large sets is increased by more than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> times (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> is the length of the sequence). This is an advantage that will significantly increase the capacity of asynchronous CDMA 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.