Chaotic Signals for Cw-ranging Systems - a Baseband System Model for Distance and Bearing Estimation

In this paper the application of chaotic signals in ranging systems is addressed. In [1] the idea of using chaotic signals as ranging signals in continuous wave (CW) systems has been introduced and motivated. Possible benefits where also analysed. This paper describes realisation and signal processing problems in chaos based range and bearing estimation. All the signal processing is performed in the baseband. In order to do this an actuator/sensor pair is introduced, that matches the measurement channel to the baseband signal processing. The channel adaption of this actuator/sensor pair is a linear operation and thus allows signal processing based on the assumption of linear channel properties. An array of such sensors is formed in order to allow bearing estimation of the impinging signal. 1. RANGING SIGNAL GENERATION Discrete time chaotic signals possess favourable properties that suggest their application as signals for CW ranging [2]. Moreover, it is possible to design chaos generators with prescribed statistical properties [3]. Therefore, such signals are well suited to be used as ranging signals and allow signal processing schemes which are adapted to their statistical signal properties. As it becomes apparent in Sec. 3 it is advantageous to use complex valued chaotic signals on the unit circle instead of real valued chaotic signals. The generation of such complex chaotic signals is performed in two steps. At first a -dimensional real valued discrete time chaotic signal is generated by an iterated Markov map. The signal is projected onto the interval by means of the projector : "! # $! !$ &%' (!)#'* $! ! + -,/.0 21(!)#'3$ 42! (1) In the second step the signal values "! are taken as arguments of a nonlinear function that maps $!5,6 ( onto the unit circle of the complex plane 7 "!8,-95 ;: