Chaotic Communication System with Modulation of Nonlinear Elements

Abstract

A chaotic communication system employs transmitting and receiving chaotic oscillating circuits. One improvement to first-generation systems is the ability to modulate a nonreactive element in the transmitting circuit, thus increasing modulation bandwidth. Other features include insertion of a gain control amplifier in a chaotic receiver; signal filtering in chaotic transmitters and receivers; use of chaotic modulation techniques for cellular telephony applications; dual-transmitter and receiver systems; a dual receiver synchronization detector; interfaces to communication systems; analog chaotic signal modulation; use of multiple chaotic transmitters and receivers; digital algorithm improvement using a cube-law nonlinear component; a Gb-only receiver; a Gb-only transmitter; and positive slope transmitter and receiver systems.

1 . A method of transmitting information, comprising the steps of: 
 (1) generating a chaotic carrier signal that causes a voltage to oscillate chaotically about a first equilibrium point in a current-voltage phase space of a circuit that exhibits a current-voltage characteristic curve on which the first equilibrium point falls by:    generating a chaotic carrier signal that oscillates about one of two equilibrium points in the current-voltage phase space; and    (2) changing, in response to an information signal, a non-reactive resistive value in the circuit and thereby causing the first equilibrium point to shift to a shifted first equilibrium point in the current-voltage phase space by    causing both equilibrium points to shift in the current-voltage phase space.    
   
   
       2 . The method of  claim 1 , wherein step (2) comprises the step of switching a non-reactive resistive element in the circuit which changes a slope of the current-voltage characteristic curve for a circuit element.  
   
   
       3 . The method of  claim 2 , wherein step (2) comprises the step of switching a resistive element in a Kennedy diode circuit.  
   
   
       4 . The method of  claim 2 , wherein step (2) comprises the step of switching a resistive element in a Caltech diode circuit.  
   
   
       5 . The method of  claim 2 , wherein step (2) comprises the step of switching a resistive element in an SAIC diode circuit.  
   
   
       6 . The method of  claim 1 , wherein step (2) comprises the step of shorting at least two diodes arranged in opposite polarity.  
   
   
       7 . The method of  claim 1 , further comprising the steps of: 
 (3) transmitting a signal resulting from the changed non-reactive resistive value through a communication channel;    (4) receiving the signal transmitted in step (3) in a receiver tuned to synchronize with the chaotic carrier signal generated in step (1); and    (5) providing a demodulated output containing the information signal by detecting periods of synchronization and non-synchronization with the received signal.    
   
   
       8 . The method of  claim 7 , wherein: 
 step (3) comprises the step of transmitting a single-scroll attractor chaotic signal;    step (4) comprises the step of receiving the single-scroll attractor chaotic signal transmitted in step (3); and    step (5) comprises the step of detecting periods of synchronization and non-synchronization with the single-scroll attractor chaotic signal.    
   
   
       9 . The method of  claim 7 , wherein: 
 step (3) comprises the step of transmitting a double-scroll attractor chaotic signal;    step (4) comprises the step of receiving the double-scroll attractor chaotic signal transmitted in step (3); and    step (5) comprises the step of detecting periods of synchronization and non-synchronization with the double-scroll attractor chaotic signal.    
   
   
       10 . The method of  claim 7 , wherein: 
 step (3) comprises the step of transmitting a triple-scroll attractor chaotic signal;    step (4) comprises the step of receiving the triple scroll attractor chaotic transmitted in step (3); and    step (5) comprises the step of detecting periods of synchronization and non-synchronization with the triple-scroll attractor chaotic signal.    
   
   
       11 . The method of  claim 1 , wherein step (2) comprises the step of changing a breakpoint voltage of a piecewise linear response curve of the circuit.  
   
   
       12 . A chaotic transmitting circuit, comprising: 
 an oscillator circuit;    a resistor coupled to the oscillator circuit;    a chaotic circuit, coupled to the oscillator circuit through the resistor, wherein the chaotic circuit exhibits a current-voltage characteristic shape having a slope that intersects a load line defined by the resistor and provides an equilibrium point about which a voltage oscillates chaotically; and    means for changing the slope exhibited by the chaotic circuit in accordance with an information signal that includes means for switching a plurality of resistive values.    
   
   
       13 . The chaotic transmitting circuit according to  claim 12 , wherein the means for switching shifts a voltage breakpoint on the current-voltage characteristic shape exhibited by the chaotic circuit.  
   
   
       14 . The chaotic transmitting circuit according to  claim 12 , wherein the means for switching shifts a slope of a piecewise linear current-voltage characteristic shape exhibited by the chaotic circuit.  
   
   
       15 . The chaotic transmitting circuit according to  claim 12 , wherein the means for switching shifts two slopes of the current-voltage characteristic shape exhibited by the chaotic circuit.  
   
   
       16 . The chaotic transmitting circuit according to  claim 12 , wherein the chaotic circuit comprises circuit elements having values selected so as to cause the chaotic transmitting circuit to oscillate about a single-scroll attractor.  
   
   
       17 . A system comprising a chaotic transmitting circuit according to  claim 12  and further comprising a chaotic receiving circuit comprising circuit components matched to synchronize with the chaotic transmitting circuit.  
   
   
       18 . A chaotic transmitting circuit, comprising: 
 an oscillator circuit;    a resistor coupled to the oscillator circuit;    a chaotic circuit coupled to the oscillator circuit through the resistor, wherein the chaotic circuit exhibits a current-voltage characteristic shape having a slope that intersects a load line defined by the resistor and provides an equilibrium point about which a voltage oscillates chaotically, wherein the chaotic circuit comprises a diode circuit that exhibits a negative piecewise linear resistance; and    a switch coupled to the chaotic circuit, wherein the switch changes a nonreactive resistive value in the chaotic circuit in accordance with an information signal and thereby causes the first equilibrium point to shift to a shifted first equilibrium point.    
   
   
       19 . The chaotic transmitting circuit of  claim 18 , wherein the chaotic circuit element comprises: 
 a first diode arranged in a forward polarity across the oscillator circuit through a first resistor and coupled to a first voltage supply through a second resistor;    a second diode arranged in a reversed polarity across the oscillator circuit through a third resistor and coupled to a second voltage supply through a fourth resistor; and    an op amp coupled to a first group of three resistors, a first of which is coupled between an output of the op amp and a positive input terminal thereof; a second of which is coupled between the output of the op amp and a negative input terminal thereof; and a third of which is coupled between the negative input terminal and ground.    
   
   
       20 . The chaotic transmitting circuit of  claim 19 , 
 wherein the switch modifies a resistive value between the negative input terminal of the op amp and ground.    
   
   
       21 . The chaotic transmitting circuit of  claim 18 , wherein the chaotic circuit element comprises: 
 two forward biased diodes coupled across the oscillator circuit through a first resistor;    two reverse biased diodes coupled across the oscillator circuit through a second resistor; and    an op amp coupled across the oscillator circuit through a resistive feedback network.    
   
   
       22 . The chaotic transmitting circuit of  claim 18 , wherein the chaotic circuit element comprises two diodes arranged in opposite polarity across the oscillator circuit through corresponding resistors, wherein the switch shorts the two diodes in response to the information signal and causes the chaotic transmitting circuit to stop oscillating in a chaotic manner.  
   
   
       23 . The chaotic transmitting circuit of  claim 18 , 
 wherein the oscillator and chaotic circuit comprise circuit elements having values selected so as to cause the chaotic transmitting circuit to oscillate in a single-scroll attractor mode.    
   
   
       24 . The chaotic transmitting circuit of  claim 23 , 
 wherein the oscillator circuit comprises an inductance and a first capacitance;    wherein the chaotic circuit comprises a second capacitance; and    wherein the values of the first capacitance, the second capacitance, the inductance, and the resistance are selected so as to cause the chaotic transmitting circuit to oscillate in a single-scroll attractor mode.    
   
   
       25 . The chaotic transmitting circuit of  claim 18 , 
 wherein the oscillator and chaotic circuit comprise circuit elements having values selected so as to cause the chaotic transmitting circuit to oscillate in a double-scroll attractor mode.    
   
   
       26 . A nonlinear circuit element for use in a chaotic transmitter, comprising: 
 a first pair of diodes coupled in series and biased in a forward direction with respect to first and second circuit terminals;    a second pair of diodes coupled in series and biased in a reverse direction with respect to the first and second circuit terminals;    a first resistor coupled between the first pair of diodes and one of the circuit terminals;    a second resistor coupled between the second pair of diodes and one of the circuit terminals;    an op amp coupled between the first and second circuit terminals through a resistive network;    a fourth resistor coupled to the resistive network; and    a switch that couples the fourth resistor into the resistive network, thus changing a slope of the piecewise linear current-voltage characteristic of the nonlinear circuit element in response to an information signal,    wherein the first resistor, the second resistor, and the resistive network have values selected to bias the nonlinear circuit element such that it exhibits a piecewise linear current-voltage characteristic across the first and second terminals.    
   
   
       27 . A method of communicating between a portable telephone device and a base station, comprising the steps of: 
 (1) generating an information signal at the portable telephone device;    (2) modulating a chaotic carrier signal with the information signal using a chaotic trajectory shifting technique by changing a non-reactive resistive value in a chaotic circuit element to cause a strange attractor trajectory shift; and    (3) transmitting the chaotic trajectory shift-keyed signal generated in step (2) to the base station.    
   
   
       28 . The method of  claim 27 , wherein step (2) comprises the step of generating a chaotic carrier signal that oscillates about two equilibrium points in a current-voltage phase space, and further comprising the step of causing both equilibrium points to shift in the current-voltage phase space.  
   
   
       29 . The method of  claim 27 , wherein step (4) comprises the step of detecting periods of synchronization and non-synchronization between the signal the received chaotic trajectory shift-keyed signal generated and a locally-generated chaotic signal using a circuit matched to a transmitter used to transmit in step (3).  
   
   
       30 . The method of  claim 27 , wherein step (2) comprises the steps of: 
 (a) modulating at a baseband frequency level; and    (b) frequency translating the modulated baseband signal to a radio frequency band.    
   
   
       31 . The method of  claim 27 , wherein step (2) comprises the steps of: 
 (a) modulating at an intermediate frequency band which falls between a frequency band of the information signal and a radio frequency band used by transmitting equipment; and    (b) frequency translating the modulated intermediate frequency signal to the radio frequency band of the transmitting equipment.    
   
   
       32 . The method of  claim 27 , wherein step (2) comprises the steps of: 
 (a) modulating the information signal directly to a radio frequency band; and    (b) directly transmitting the modulated information signal in the radio frequency band.    
   
   
       33 . A chaotic transmitter, comprising: 
 a first chaotic circuit that generates a first chaotic signal having a first strange attractor trajectory;    a second chaotic circuit that generates a second chaotic signal having a second strange attractor trajectory different from that of the first strange attractor trajectory;    a switch coupled to the first and second chaotic circuits, wherein the switch selects either the first chaotic signal or the second chaotic signal in response to an information signal;    a low-pass filter coupled to the output of the switch; and    a summing circuit coupled between the switch and the low-pass filter, wherein the summing circuit sums the output from the switch.    
   
   
       34 . The chaotic transmitter of  claim 33 , wherein the first and second chaotic circuits each generate a single-scroll strange attractor chaotic signal.  
   
   
       35 . The chaotic transmitter of  claim 33 , wherein the first and second chaotic circuits each generate a double-scroll strange attractor chaotic signal.  
   
   
       36 . A method of transmitting an information signal, comprising the steps of: 
 (1) generating a first chaotic signal comprising at least one strange attractor that oscillates about a first equilibrium point;    (2) generating a second chaotic signal comprising at least a second strange attractor that oscillates about a second equilibrium point;    (3) in response to the information signal, selecting an output of either the first chaotic signal or the second chaotic signal;    (4) transmitting the selected output from step (3); and    (5) filtering the output selected in step (3).    
   
   
       37 . The method of  claim 36 , wherein steps (1) and (2) each comprise the step of generating a single-scroll strange attractor chaotic signal.  
   
   
       38 . The method of  claim 36 , wherein steps (1) and (2) each comprise the step of generating a double-scroll strange attractor chaotic signal.  
   
   
       39 . The method of  claim 1 , wherein step (2) comprises the step of continuously varying the non-reactive resistive value over a chaotic operating region in accordance with the information signal.  
   
   
       40 . The apparatus of  claim 12 , wherein the means for changing continuously varies a non-reactive resistance over a chaotic operating region in accordance with the information signal.  
   
   
       41 . The apparatus of  claim 18 , wherein the switch continuously varies the non-reactive resistance over a chaotic operating region in accordance with the information signal.  
   
   
       42 . A method according to  claim 1 , wherein step (1) comprises the step of using a digitally implemented nonlinear circuit having a current-voltage characteristic that satisfies the equation I=−aV−bV 3 , where a and b are constants.  
   
   
       43 . The chaotic transmitting circuit of  claim 12 , wherein the chaotic circuit comprises a digitally implemented circuit having a current-voltage characteristic that satisfies the equation I=−aV−bV 3 , where a and b are constants.  
   
   
       44 . The chaotic transmitting circuit of  claim 18 , wherein the chaotic circuit comprises a digitally implemented circuit having a current-voltage characteristic that satisfies the equation I=−aV−bV 3 , where a and b are constants.  
   
   
       45 . The method of  claim 1 , wherein step (1) comprises the step of using a circuit that exhibits a linear slope in one quadrant of the current-voltage characteristic curve, and wherein step (2) comprises the step of changing the linear slope in the one quadrant.  
   
   
       46 . The apparatus of  claim 12 , wherein the means for changing comprises a voltage source and a switch that shifts a slope in one quadrant of the current-voltage characteristic shape.  
   
   
       47 . The apparatus of  claim 18 , wherein the switch switches a voltage source to shift to the shifted first equilibrium point.  
   
   
       48 . The method of  claim 45 , further comprising the step of filtering an output of the circuit to limit its frequency bandwidth.  
   
   
       49 . The apparatus of  claim 46 , further comprising a filter coupled to an output of the chaotic circuit that limits a frequency bandwidth thereof.  
   
   
       50 . The apparatus of  claim 47 , further comprising a filter coupled to an output of the chaotic circuit that limits a frequency bandwidth thereof.  
   
   
       51 . The method of  claim 1 , wherein step (1) comprises the step of using a circuit that exhibits a positive linear slope, and wherein step (2) comprises the step of changing the positive linear slope.  
   
   
       52 . The apparatus of  claim 12 , wherein the chaotic circuit exhibits a positive linear slope.  
   
   
       53 . The apparatus of  claim 18 , wherein the chaotic circuit exhibits a positive linear slope.  
   
   
       54 . A method of transmitting information, comprising the steps of: 
 (1) generating a chaotic carrier signal characterized by a voltage that oscillates chaotically about a first equilibrium point in a current-voltage plane, wherein the first equilibrium point is defined by an intersection of a current-voltage load line having a first slope and a current-voltage slope line having a second slope opposite in polarity to that the of the first slope;    (2) in response to a time-varying information signal comprising an N-bit symbol, selecting one of a plurality of 2 N  equilibrium points defined by successive intersections of a plurality of current-voltage slope lines having slopes opposite to that of the load line and that intersect the load line at different points;    (3) shifting the first equilibrium point to the one selected equilibrium point such that the chaotic carrier signal oscillates chaotically about the one selected equilibrium point by changing a nonreactive circuit value in a chaotic circuit coupled to a resistor that defines the current-voltage load line; and    (4) transmitting the chaotic carrier signal shifted in step (3).    
   
   
       55 . The method of  claim 54 , further comprising the steps of: 
 (5) receiving the signal transmitted in step (4);    (6) determining which of the plurality of equilibrium points corresponds to the signal received in step (5); and    (7) on the basis of the determination in step (6), generating an information symbol.    
   
   
       56 . A method of interfacing a chaotic transmitting circuit to a communications channel without using a frequency filter, comprising the steps of: 
 (1) buffering an output of the chaotic transmitting circuit to isolate the chaotic transmitting circuit from the communications channel;    (2) removing a direct current voltage component from the buffered output obtained in step (1) by using a direct current power supply and an attenuator circuit; and    (3) matching the amplitude and impedance of the signal obtained from step (2) to the communications channel.    
   
   
       57 . The method of  claim 56 , wherein step (3) comprises the step of using a balanced line driver to match the electrical characteristics of a twisted pair wire communications channel.  
   
   
       58 . Apparatus for interfacing a chaotic transmitting circuit to a communications channel without using a frequency filter, comprising: 
 an isolation circuit that buffers an output of the chaotic transmitting circuit from the communications channel;    a direct current power supply coupled to the isolation circuit through a resistor, wherein the direct current power supply subtracts a direct current voltage from the output of the isolation circuit; and    an attenuator circuit, coupled to the direct current power supply, wherein the attenuator circuit attenuates a signal present at the direct current power supply prior to being introduced into the communications channel,    wherein the communications channel comprises a radio frequency channel.    
   
   
       59 . The apparatus of  claim 58 , wherein the communications channel comprises a cable system.  
   
   
       60 . The apparatus of  claim 58 , further comprising a balanced line driver that matches the electrical characteristics of the apparatus to a dual conductor cable.  
   
   
       61 . The method of  claim 27 , further comprising: 
 (4) in the base station, demodulating the transmitted signal to recover the information signal.