An algebraic approach to generate super‐set of perfect complementary codes for interference‐free CDMA

Abstract

This paper introduces an algebraic approach to generate the super-set of perfect complementary (PC) codes suitable for new generation CDMA applications, characterized by isotropic multiple access interference (MAI) free and multipath interference (MI) free properties. The code design methodology proposed in this paper takes into account major impairing factors existing in real applications, such as MAI, MI, asynchronous transmissions, and random signs in consecutive symbols, such that a CDMA system using the generated codes can insure a truly interferencefree operation. Two important facts will be revealed by the analysis given in this paper. First, implementation of an interference-free CDMA will never be possible unless using complementary code sets, such as the PC code sets generated in this paper. In other words, all traditional spreading codes working on an one-code-per-user basis are not useful for implementation of an MAI-free and MI-free CDMA system. Second, to enable the interference-free CDMA operation, the flock size of the PC codes should be made equal to the set size of the codes, implying that a PC code set can support as many users as the flock size of the code set. A systematic search has been carried out to generate the super-set of various PC codes with the help of carefully selected seed codes belonging to distinct sub-sets. This paper will also propose an implementation scheme based on multi-carrier CDMA architecture and its performance is compared by simulations with the ones using traditional spreading codes.

The Application of Frequency Assignment Techniques in Spreading Code Assignment

“…If we consider that data bit transitions occur equally as often as data bit non-transitions, and convert the voltage associated with the interferer to a power, we can (on average) write the power arising from each interferer j as (C 2 . In a QS-CDMA system treat τ as uniformly distributed in [−T + 1, T − 1] and define a Mean Square Cross (MSC) correlation value…”

Performance of multicarrier complementary-coded CDMA under frequency-selective Nakagami-m fading channels

“…where w l ð Þ n is the equivalent combining weight of the nth subcarrier for desired user l. y l ð Þ n i ð Þ represents the discrete-time equivalent of (8).…”

“…Most of the attractive features of OCC were reported in [6,7] to show the superiority of complementary codes in multipath and multiuser scenarios. In [8], a superset of perfect complementary codes was proposed to increase the set size of the OCC to its processing gain. In order to achieve interference-free OCC, the flock size of the signature code must be equal to the set size of the codes.…”

Evolution from symbol‐level space–time coded MIMO to chip‐level space–time coded MIMO: a review

“…It has also been proved that an interference‐free CDMA can only be implemented with the help of orthogonal complementary codes. On the basis of the REAL approach, a large number of orthogonal complementary codes suitable for the next generation CDMA architecture were found , which laid a solid foundation for the development of next generation CDMA technologies.…”