Michael Peter Kennedy

Communications using chaos/spl Gt/MINUS. III. Performance bounds for correlation receivers

For pt. II, see ibid., vol. 45, p. 1129-40 (1998). In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a typical conventional system, the analog sample functions sent through the channel are weighted sums of one or more sinusoids, called basis functions; in a chaotic communications system, the sample functions are segments of chaotic waveforms. This three-part paper shows in a tutorial manner how the theory of conventional telecommunications systems can be applied to chaotic modulation schemes. In addition, it discusses the latest results in the field of chaotic communications. In Part III, examples are given of chaotic communications schemes with and without synchronization, and the performance of correlator-based systems is evaluated in the context of noisy, bandlimited channels.

FM-DCSK: a novel method for chaotic communications

In binary Differential Chaos Shift Keying (DCSK), each information bit is mapped to the correlation between two pieces of a chaotic waveform. The receiver determines the correlation (which is proportional to the energy per bit) in order to demodulate the received signal. Since a chaotic signal is not periodic, the energy per bit is not constant and can only be estimated, even in the noise-free case. This estimation has a non-zero variance that limits the attainable data rate. This problem can be avoided if the energy per bit is kept constant. In this paper, the DCSK technique is combined with frequency modulation in order to achieve two properties: the excellent noise performance of DCSK is maintained; in addition, the energy per bit is kept constant in order not to limit the data rate. A low-pass equivalent model that significantly speeds up the simulation of an FM-DCSK system is also developed. Finally the noise performance of the proposed FM-DCSK system is given.

Enhanced versions of DCSK and FM-DCSK data transmission systems

Over the past five years many different modulation schemes have been proposed for chaotic communications. Of these, the DCSK and FM-DCSK techniques offer the best noise performance. However, even the noise performance of these schemes is a few dB worse than that of the conventional noncoherent FSK technique. The paper shows how the noise performance of DCSK and FM-DCSK systems can be improved considerably. Two solutions are considered: in the first version more than one information bit is sent using the same reference signal, while in the second version the received noisy sample functions are cleaned by averaging.

Recent results for chaotic modulation schemes

By generalizing the waveform communications concept, this paper develops exact expressions, verified by computer simulations, for the noise performance of the coherent antipodal Chaos Shift Keying (CSK), coherent Differential Chaos Shift Keying (DCSK) and differentially coherent DCSK modulation schemes. We show that the properties of the basis functions have no effect on the noise performance of a modulation scheme, provided that the energy per bit is constant and the basis functions are orthogonal.

Frequency domain analysis of double sampling phase-locked loop

Double sampling phase-locked loop (2-SPLL) is used in frequency synthesis. The unique feature of single sampling PLL is that its phase detector (PD) has a very low unwanted periodic output in steady state. In 2-SPLL, a second sample and hold circuit (S&H) is connected in cascade to suppress further the unwanted periodic PD output. However, the absence of a proper baseband model and design equations prevent the exploitation of all benefits of 2-SPLL. This paper develops a nonlinear baseband model for the 2-SPLL. Then based on the linearized baseband model, analysis is performed in the frequency domain and the frequency responses required to determine the spectrum of the output signal as a function of reference and VCO noise and modulation inputs are developed. Finally, the theoretical results are verified by measurements.