The even-odd transform (EOT) converts a complex sequence set into another one with even and odd correlation distributions exchanged. The Fukumasa-Kohno-Imai transform (FKIT) converts a real-valued sequence set into a complex one with improved generalized even-odd-equivalent (EOE) correlation distributions. In this work, the EOT is generalized for asynchronous M-PSK/CDMA. A subclass of the generalized EOTs coincides with the FKITs. New bounds on the correlation gains achievable by the FKITs are then derived.

Based on the use of Berlekamp-Massey algorithm, six conjectures for the linear complexity (LC) of some Kronecker sequences of two and three component codes are given. Components were chosen from the families of Gold, Kasami, Barker, Golay complementary and M-sequences. Typically, the LC value is a large part of the code length. The LC value of the outermost code influences mostly on the LC value.

In synchronous CDMA system, the orthogonal spreading sequences are employed to reduce the multiple access interference. However, as the frequency selectivity of the propagation channel strengthens, the orthogonality among different users tends to diminish because of increasing inter-path interference. In this paper, various binary and nonbinary orthogonal sequences are discussed. In order to maintain the orthogonality among different users, a new concept of generalized orthogonality is defined and the corresponding sequences are presented, including binary, quadriphase and nonbinary code sequences. Based on a simplified synchronous CDMA system model, the related system performance is also analyzed and compared for different orthogonal and generalized orthogonal spreading sequences. Our analytical and simulation results show that the generalized orthogonal code sequences are indeed more robust in the multipath propagation channels, compared with the traditional orthogonal code sequences.

Two families of rapidly synchronizable spreading codes are compared using the same component codes. The influence of component code choice is also discussed. It is concluded that correlation, code-division multiple-access (CDMA) and information security (measured by the value of linear complexity) properties of Kronecker sequences are considerably better than those of Combination sequences. Combination sequences cannot be recommended for CDMA use unless the number of active users is few. CDMA performance of Kronecker sequences is almost comparable with that of linear pseudonoise (PN) code families of equal length when a Gold or Kasami code is used as the innermost code and the Barker code is used as the outermost code to guarantee satisfactory correlation and CDMA properties. Kronecker sequences possess a considerably higher value of linear complexity than those of the corresponding non-linear Geffe and majority logic type combination sequences. This implies they are highly non-linear codes due to the Kronecker product construction method. It is also observed that the Geffe type Boolean combiner resulted in better correlation and CDMA performance than with majority logic. The use of the purely linear exclusive-or combiner for considerable reduction of code synchronization time is not found recommendable although it results in good CDMA performance.

This paper presents a generation method of orthogonal spreading codes with different spreading factors (SFs), which are called orthogonal multi-SF spreading codes in this paper, for DS-CDMA mobile radio. The generated orthogonal multi-SF spreading codes have a tree structure and the codes are applied to the forward link such that all users, who transmit data at different rates, are orthogonalized. A group spreading modulator that simplifies the base station transmitter structure is also described. The transmission performance of the orthogonal multi-SF forward link under multi-user and frequency selective Rayleigh fading environments is evaluated by computer simulation to show that its performance is identical to that achieved by using multiple orthogonal spreading codes in parallel (orthogonal multicode forward link). Unlike the orthogonal multicode forward link, only a single Rake combiner is required at a mobile receiver which significantly simplifies the mobile receiver structure.

In this paper, we analyze the multiple access interference of a variable processing gain DS/CDMA system and define discrete partial crosscorrelation functions. We also evaluate the bit error rate of the system using Gaussian approximation and bounding technique. Three kinds of spreading codes (long, short, and random codes) are considered in the analysis of the system. It is shown that the bit error rate of a user is not relevant to the processing gain of interfering users: it is relevant only to the processing gain of the user, transmitted powers, PN sequences, and spreading codes. The performance of short codes turns out to be better than that of long and random codes as in other systems.

It is demonstrated with the Berlekamp-Massey shift-register synthesis algorithm that the linear complexity value of binary complementary sequences is at least 3/4 of the sequence length. For some sequence pairs the linear complexity value can be even 0.98 times the sequence length. In the light of these results strongly non-linear complementary sequences are considered suitable for information security applications employing the spread-spectrum (SS) technique.

It is concluded from numerical examples for the well-known linear PN sequence families of a large range of periods that the mean-square cross-correlation value between sequences is the dominating parameter to the average signal-to-noise power ratio performance of an asynchronous direct-sequence (DS) code-division multiple-access (CDMA) system. The performance parameters derived by Pursley and Sarwate are used for numerical evaluation and the validity of conclusion is supported by reviewing the other related works. The mean-square periodic cross-correlation takes the equal value p (code period) for the known CDMA code families. The equal mean-square cross-correlation performance results from the basic results of coding theory.