Generalization of Waveform Communications: The Fourier Analyzer Approach

Abstract

In digital communications, fixed, chaotic, and random waveforms are used. Although the theory of fixed waveform communications is well established, its generalization to include chaotic and random carriers has not yet been carried out. The lack of an exact model prevents the optimization of chaotic and random communication systems.Introducing the Fourier analyzer concepts, this paper develops a unified model which is equally valid for communications with fixed, chaotic and random carriers. It gives an exact measure for the a priori information which is exploited at the receiver to optimize the noise performance. The unified model may be used to determine the performance bounds of different waveform communication systems and offers a systematic approach for the development of optimum detector configurations. Using the model developed, a new classification of digital communication systems is proposed.

Performance of Differential Chaos-Shift-Keying Digital Communication Systems Over a Multipath Fading Channel With Delay Spread

“…The case of sending a symbol of " " may be computed in a likewise fashion, i.e., (11) (12) Using (9) and (10), and assuming that follows a normal distribution under the given conditions, the conditional BER may be computed as (13) where is the bit energy and is represented by (14) and , the complementary error function, is defined as (15) If the logistic map is used, we have and…”

“…Moroever, chaos can also be applied at the coding level, as in the chaos-based direct-sequence code-division-multiple-access (DS-CDMA) schemes studied by Mazzini et al [5], Rovatti et al [6], and Chen et al [7]. In this case, since coherent communication is still applicable in the conventional sense at the waveform communication level [12], performance comparable to conventional systems can be achieved, and if further optimization at the coding level is possible with chaos, as demonstrated by Mazzini et al [5], Rovatti et al [6], improvement over existing DS-CDMA systems is also possible. In short, at the waveform level, all coherent schemes are impractical but their performances have benchmarking values; noncoherent schemes are more practical but their performances are inferior to conventional coherent systems.…”

“…Furthermore, Mazzini et al [18] reported a thorough study of the multipath performance of the chaos-based DS-CDMA scheme. As their system uses chaos at the code-spreading level, their results are not generally applicable to waveform communication systems using chaotic signals [12].…”

Stable non-Gaussian noise parameter modulation in digital communication

“…As an alternative to the conventional digital communication systems, chaos-based digital communication techniques became popular by the beginning of the 1990s and chaotic signals have since been a proper candidate to ensure the security due to their broadband nature [1][2][3][4][5][6]. Chaotic signals have been used to encode the binary message bits with chaos shift keying techniques [4,5].…”

“…This new technique can be called 'stable non-Gaussian noise parameter modulation' since the binary message is encoded by the parameters of the a-stable noise sequence. Although the idea of using a noise-like carrier goes back to the 1950s [6,9], to the best of our knowledge in the literature only this newly introduced technique uses such a random sequence for encoding the message signal instead of using deterministic signals. Such a random sequence for encoding the message signal can then be considered as a random carrier.…”