The number of spreading sequences required for direct-sequence code-division multiple-access (DS-CDMA) systems depends on the number of simultaneous users in the system. Often a sequence family provides more sequences than are required; in many cases the selection of the employed sequences is a computationally intensive task. This selection is a key consideration, as the properties of the sequences assigned affect the error performance in the system. In this paper, a branch and bound algorithm is presented to perform this selection based on two different cost functions. Numerical results are presented to demonstrate the improved performance of this algorithm over previous work.

Large area (LA) sequences form a class of ternary spreading sequences which exhibit an interference free window. In addition, these sequences have low correlation properties outside this window. Work to date has concentrated on examining the parameters and performance of LA sequences with reference to only a small number of example families. In this paper we develop general conditions which an LA family must satisfy. The development of these conditions allows for the production of computationally efficient tests to determine whether a given family is an LA family. In particular, these tests can form the basis for algorithms to construct LA families, allowing for a larger number of families with the potential for higher energy efficiency than those of previous work.

Numerous spread spectrum applications require families of long spreading sequences, often used at very high chip rates. In this paper, an algebraically simple way of generating long sequences by combining shorter polyphase sequences is presented, aimed at asynchronous spread spectrum systems. The approach is motivated by the fact that polyphase sequences offer increased design options, in terms of the supported range of correlation characteristics, while combination sequences allow for simpler generation of long sequences. It leads to the definition of combination Oppermann sequences, the properties of which are investigated in this paper. Numerical results indicate that the families of these proposed combination sequences provide favourable aperiodic correlations. The presented family of combination Oppermann sequences is therefore suitable for applications that rely on rapid synchronisation and are required to provide multiple access to the system.

In this paper we introduce periodic Oppermann sequences, which constitute a special class of polyphase sequences. The properties of these sequences are presented, and indicate that periodic Oppermann sequences are suitable for combination to generate families of longer sequences. Numerical examples show that periodic Oppermann sequences can be designed for ranging or synchronisation applications or for supporting multiple access spread spectrum communication systems.