Dovetail construction of families of complex-valued spreading sequences with asynchronous orthogonality for SS/CDMA

This paper describes a novel dovetail technique for constructing families of spreading sequences for SS/CDMA which are mutually orthogonal in the asynchronous sense. That is, any two members of the family have periodic crosscorrelation values which are identically zero for all values of the shift index, obviating the need for mutual synchronization. Our goal is to improve the crosscorrelation properties at the possible expense of the autocorrelation. In light of advances in technology we have permitted these sequences to be complex-valued with no uniformity constraint on the sequence element absolute values. From statistical considerations the transition from uniform to nonuniform absolute values is expected to leave the effects of noise unchanged. In principle the advantage in alleviating multiaccess interference (MAI) in SS/CDMA is clear if in fact nonlinearities will not make the technique impractical. The sensitivity to nonlinearities in the transmitter system is investigated and the technique is found to be quite robust in this perturbation. A random walk model proves successful in understanding the statistics of the sequence absolute values. The issue of the size of the family is addressed from the standpoint of the effect on the sequence noiselike quality. As witnessed by its sidelobe ratio. For example, we have found that if a 3 dB sidelobe level is acceptable, the family size may include 85 members of sequence length 1024 within the framework of asynchronous orthogonality. From this base other families are suggested and investigated, including derived phase retention sequences for matched or mismatched schemes. Comparison is made with random complex generation of arbitrary and constant amplitude sequences. The technique uncovers some constant amplitude sequences which are mutually asynchronously orthogonal and have doubly periodic autocorrelations. In the evaluation of the results we use the worst-case correlations in terms of the maxima. The results are presented in terms of the expected value of parameters such as mismatch loss, autocorrelation sidelobe ratio and a measure of orthogonality. It is therefore always possible to find sequences with improved values beyond the expected values of these parameters by performing a proper search procedure. In comparing the dovetail technique with random drawing we find that our technique succeeds in interchanging the base values of crosscorrelation and autocorrelation. Comparison is made between the various techniques and with the widely known Gold codes of similar length, known for their excellent crosscorrelation properties