Complex valued spreading sequences with good crosscorrelation properties

This paper examines the performance of sets of pseudorandom (PR) sequences using the criterion of least mean-square (MS) values of the aperiodic cross-correlation (CC). The MS correlation values are averaged over all elements in the set rather than the more traditional approach of taking the MS correlation values of randomly selected elements as representative. This is intended to give an indication of the performance of the set as a whole. This paper introduces a new family of constant amplitude, complex valued sequences designed using the criterion of least MS value of the CC values of all sequences in the set. This family of sequences is compared with well known sequences on the basis of correlation values and frequency characteristics and is shown to offer a wider range and better combination of correlation values. The paper also provides a limit on the lower bound of the value of the MS CC for the new family of complex sequences and members of the family are given for which the average MS value of the CC asymptotically approaches this bound. The potential trade off of CC values for auto-correlation (AC) is also illustrated