Basics of communications using chaos

In digital communications, either fixed, chaotic, or random, analog waveforms of finite duration are used to carry the information. To optimize a waveform communications system or determine its noise performance in analytic form, mathematical models of modulation and detection have to be developed. The radio channel transmitting the information bearing signal from the transmitter to the receiver is analog, consequently, the digital information to be transmitted has to be mapped into analog waveforms of finite duration. Since only analog waveforms can be transmitted over a physical telecommunications channel and the data rate is determined by the system specification, the modulator of a digital telecommunications system maps the symbols to be transmitted into analog waveforms of finite duration. The standard deviations of both estimates are inversely proportional to the product of estimation time and the equivalent statistical bandwidth of chaotic basis functions.