Chaotic Codes for Cdma Applications

Andreas Abel Andreas Bauer Kristina Kelber Wolfgang Schwarz Technical University Dresden Faculty of Electrical Engineering / IEE Mommsenstra e 13, 01062 Dresden, Germany fabel, [email protected], fbauer, [email protected] Abstract | This paper gives a tutorial-like introduction to the use of chaotic codes in code devision multiple access (CDMA) systems. First, general principles of sharing resources between di erent user pairs, exploiting the same physical channel, are discussed. In the main part suitable code sequences and their properties are treated and especially chaotic codes are considered. Finally, principles of a communication and a measurement example are described and their performance is presented. I. MULTI-USER CHANNELS Objectives and Resources In many communication applications exist several users, who want to transmit informations over one physical channel (multiple access). The resources provided by a physical channel are always restricted according to bandwidth, signal power and access time. A proper functioning of the transmission system requires a sharing of the resources between the potential channel users, upon which they have to agree. Principles of Resource Sharing If several users transmit signals over the same physical channel, each receiver must be able to separate its own signal from a superposition of user signals and noise. Channel separation is done by means of mutually orthogonal signals. Orthogonality of two signals xi(t) and xj(t) is expressed by 0 = 1 Z 1 xi(t)xj(t)dt = 1 2 1 Z 1 Xi(!)X j (!)d!: (1) Here Xi(!) andXj(!) are the Fourier transforms of the signals xi(t) and xj(t). The equality of both integrals is given by Parseval's theorem [1]. Orthogonality can be achieved in several ways: A) Time division. If any two signals xi(t) and xj(t) are di erent from zero on disjoint time intervals only, This work has been supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 358 / Teilprojekt E1) and the EC (ESPRIT project No. 21103) the time integral in (1) vanishes. The user channels are formed by the assignment of disjoint time slots. This method is called TDMA (Time Division Multiple Access). B) Frequency division. If any two signal spectra Xi(!) and Xj(!) do not overlap, the frequency integral in (1) vanishes. The user channels are formed by frequency assignment. This method is called FDMA (Frequency Division Multiple Access). C) Code division. The signals overlap in time and frequency, but the time integral in (1) (correlation integral) still becomes zero. The desired signal is extracted by correlation. The user channels are formed by an assignment of signals (codes) from an orthogonal set. This approach is termed CDMA (Code Division Multiple Access). II. CDMA INFORMATION PROCESSING SCHEME In this section the essential components of a CDMA information processing scheme are described. The approach is to perform the signal processing in the baseband using correlation based methods. This divides the CDMA channel coder into two parts, a classical modulation/demodulation part and a baseband CDMA signal processing scheme. (a) transmitted signal Modulator baseband signal signal information