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Symmetric key cryptography |
Chaotic communication system and method using modulation of nonreactive circuit elements6980656
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.
Claims
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; 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,
wherein the circuit exhibits a piecewise-linear current-voltage characteristic comprising three linear segments, two of the linear segments having a first slope in the phase space and the third linear segment having a second slope in the phase space; and wherein step (2) comprises the step of changing either the first slope or the second slope but not both slopes in response to the information signal.
2. 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; 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,
wherein the circuit exhibits a piecewise-linear current-voltage characteristic comprising three linear segments, two of the linear segments having a first slope in the phase space and the third linear segment having a second slope in the phase space; and wherein step (2) comprises the step of changing both the first slope and the second slope in response to the information signal.
3. 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,
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.
4. 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,
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 double-scroll attractor mode.
5. 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,
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,
wherein the means for switching shifts an equilibrium point of the single-scroll attractor among at least three different positions on the current-voltage characteristic shape, each position corresponding to a different information symbol contained in the information signal.
6. 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
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,
wherein the chaotic circuit comprises:
a first op amp coupled across the oscillator circuit through the resistor, wherein the first op amp is further coupled to a first group of three resistors, a first of which is coupled between an output of the first op amp and a positive input terminal thereof; a second of which is coupled between the output of the first op amp and a negative input terminal thereof; and a third of which is coupled between the negative input terminal and a ground; and
a second op amp coupled across the oscillator circuit through the resistor, wherein the second op amp is further coupled to a second group of three resistors, a first of which is coupled between an output of the second op amp and a positive input terminal thereof; a second of which is coupled between the output of the second op amp and a negative input terminal thereof; and a third of which is coupled between the negative input terminal and the ground.
7. The chaotic transmitting circuit of claim 6, wherein the switch changes a non-reactive resistive value between the negative input terminal of the second op amp and the ground.
8. A communication system comprising a transmitter and a receiver, wherein the transmitter comprises
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 causes a voltage to oscillate about a first equilibrium point on a current-voltage characteristic curve of the chaotic circuit element; and
a switch coupled to the chaotic circuit element, 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; and wherein the receiver comprises
a second oscillator circuit;
a second resistor coupled to the second oscillator circuit;
a second chaotic circuit coupled to the second oscillator circuit through the second resistor; and
a detector coupled to the second oscillator circuit and the second chaotic circuit;
wherein the second oscillator circuit and the second chaotic circuit comprise circuit components selected such that they cause the receiver to synchronize with the transmitter when the transmitter transmits according to the first equilibrium point; and
wherein the detector detects whether the receiver is synchronized and, in response to detecting synchronization, generates a signal.
9. The system of claim 8, wherein the transmitter and the receiver each oscillate chaotically about a single-scroll attractor.
10. The system of claim 8, wherein the transmitter and the receiver each oscillate chaotically about double-scroll attractors.
11. A chaotic receiver comprising:
an input terminal for receiving a chaotically modulated signal;
an oscillating circuit coupled to the input terminal;
a chaotic circuit comprising a capacitor and a negative resistance element, wherein the chaotic circuit is coupled to the oscillating circuit through a resistor, wherein the chaotic circuit causes a voltage to oscillate about an equilibrium point corresponding to a current-voltage characteristic curve of the negative resistance element;
a synchronizing resistor coupled between the input terminal and the negative resistance element; and
a comparator, coupled across the synchronizing resistor, wherein the comparator generates an output signal when a voltage drop across the synchronizing resistor reaches a predetermined level; and
wherein the synchronizing resistor has a value that satisfies the relation
where fLC is the fundamental frequency of the oscillator circuit, and where C, is the capacitance of the capacitor.
12. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator coupled to the input terminal;
a chaotic circuit comprising a capacitor and a negative resistance circuit;
a gain control amplifier coupled between the oscillator and the chaotic circuit, wherein the gain control amplifier amplifies a voltage present at the oscillator before it reaches the chaotic circuit;
a synchronizing resistor coupled between the input terminal and the chaotic circuit; and
a detection circuit, coupled to the synchronizing resistor, wherein the detection circuit detects periods of synchronization and non-synchronization between the modulated chaotic signal and the chaotic circuit and generates an output corresponding to periods of synchronization and non-synchronization,
wherein the gain control amplifier provides an amplification of between 2.4 dB to 3 dB.
13. A chaotic communication system comprising:
a transmitter that generates a chaotic carrier signal modulated in accordance with an information signal; and
a receiving system having an input terminal that receives the chaotic carrier signal modulated by the transmitter, wherein the receiving system comprises
an oscillator subsystem coupled to the input terminal;
a gain control amplifier coupled to the output of the oscillator subsystem;
a chaotic subsystem coupled to the output of the gain control amplifier;
a synchronizing subsystem coupled to the chaotic subsystem and to the input terminal, which causes the chaotic subsystem to synchronize to the chaotic carrier signal; and
a detector coupled to the chaotic subsystem and the input terminal, wherein the detector detects periods of synchronization and non-synchronization;
wherein the gain control amplifier amplifies a signal produced by the oscillator subsystem and drives the chaotic subsystem with the amplified signal, and wherein the chaotic subsystem generates a signal that synchronizes with the modulated chaotic signal when the transmitter transmits a symbol of information.
14. A chaotic transmitter, comprising:
an oscillator;
a resistor coupled to the oscillator;
a chaotic circuit comprising a negative resistance, wherein the chaotic circuit is coupled to the oscillator circuit through the resistor;
an isolation amplifier coupled to the chaotic circuit;
a filter coupled to the output of the isolation amplifier that limits a frequency bandwidth present at the chaotic circuit; and
means for modulating a circuit element of the chaotic transmitter in accordance with an information signal,
wherein the means for modulating comprises a switch that switches a reactive component in the oscillator, thereby changing a strange attractor trajectory generated by the transmitter.
15. A chaotic transmitter, comprising:
an oscillator;
a resistor coupled to the oscillator;
a chaotic circuit comprising a negative resistance, wherein the chaotic circuit is coupled to the oscillator circuit through the resistor;
an isolation amplifier coupled to the chaotic circuit;
a filter coupled to the output of the isolation amplifier that limits a frequency bandwidth present at the chaotic circuit; and
means for modulating a circuit element of the chaotic transmitter in accordance with an information signal,
wherein the means for modulating comprises a switch that switches a reactive component in the chaotic circuit, thereby changing a strange attractor trajectory generated by the transmitter.
16. A chaotic transmitter, comprising:
an oscillator;
a resistor coupled to the oscillator;
a chaotic circuit comprising a negative resistance, wherein the chaotic circuit is coupled to the oscillator circuit through the resistor;
an isolation amplifier coupled to the chaotic circuit;
a filter coupled to the output of the isolation amplifier that limits a frequency bandwidth present at the chaotic circuit; and
means for modulating a circuit element of the chaotic transmitter in accordance with an information signal,
wherein the means for modulating comprises a switch that changes a non-reactive resistive value in the chaotic circuit, thereby changing a current-voltage characteristic of the negative resistive element.
17. The chaotic transmitter of claim 16, wherein the transmitter oscillates about a single-scroll attractor.
18. The chaotic transmitter of claim 16, wherein the transmitter oscillates about a double-scroll attractor.
19. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
a first filter, coupled to the input terminal, which filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
an oscillator coupled to an output of the first filter;
a chaotic circuit comprising a negative resistor, wherein the chaotic circuit is coupled to the oscillator;
a synchronizing circuit coupled between the first filter and the chaotic circuit, wherein the synchronizing circuit generates a voltage difference in response to an out-of-synchronization condition between the filtered modulated chaotic signal and the chaotic circuit;
a second filter, coupled to a first portion of the synchronizing circuit, which filters a buffered version of the filtered modulated chaotic signal;
a third filter, coupled to a second portion of the synchronizing circuit, which filters a signal generated by the chaotic circuit; and
a detection circuit, coupled to the second and third filters, wherein the detection circuit detects periods of synchronization and non-synchronization between the modulated chaotic signal and the chaotic circuit and generates an output corresponding to periods of synchronization and non-synchronization.
20. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
a first filter, coupled to the input terminal, which filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
an oscillator coupled to the input terminal;
a chaotic circuit comprising a circuit element that exhibits a nonlinear current-voltage characteristic, wherein the chaotic circuit is coupled to the oscillator;
a synchronizing circuit coupled between the first filter and the chaotic circuit, wherein the synchronizing circuit generates a voltage difference in response to an out-of-synchronization condition between the filtered modulated chaotic signal and the chaotic circuit;
a second filter, coupled to a first portion of the synchronizing circuit, which filters a buffered version of the filtered modulated chaotic signal;
a third filter, coupled to a second portion of the synchronizing circuit, which filters a signal generated by the chaotic circuit; and
a detection circuit, coupled to the second and third filters, wherein the detection circuit detects periods of synchronization and non-synchronization between the modulated chaotic signal and the chaotic circuit and generates an output corresponding to periods of synchronization and non-synchronization.
21. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
a first filter, coupled to the input terminal, which filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
an oscillating circuit coupled to the first filter;
a chaotic circuit comprising a circuit element that exhibits a nonlinear current-voltage characteristic, wherein the chaotic circuit is coupled to the oscillating circuit through a second filter;
a third filter, coupled to the output of the first filter, which further filters the output of the first filter;
a synchronizing circuit coupled between the third filter and the chaotic circuit, wherein the synchronizing circuit generates a voltage difference in response to an out-of-synchronization condition between a signal from the third filter and the chaotic circuit;
a fourth filter, coupled to a first portion of the synchronizing circuit, which filters a buffered version of the filtered modulated chaotic signal;
a fifth filter, coupled to a second portion of the synchronizing circuit, which filters a signal generated by the chaotic circuit; and
a detection circuit, coupled to the fourth and fifth filters, wherein the detection circuit detects periods of synchronization and non-synchronization between the modulated chaotic signal and the chaotic circuit and generates an output corresponding to periods of synchronization and non-synchronization.
22. A chaotic telephone device comprising:
a chaotic transmitter that receives a first information signal and generates in response thereto a first chaotic trajectory shifted signal modulated in accordance with the first information signal;
a chaotic receiver that receives a second chaotic trajectory shifted signal modulated in accordance with a second information signal and generates in response thereto a demodulated version of the second chaotic trajectory shifted signal; and
an interface circuit that couples the chaotic transmitter and chaotic receiver to a radio-frequency telephone circuit, wherein the radio-frequency telephone circuit communicates with a ground-based telephone network through one or more radio frequency transmission stations,
wherein the chaotic transmitter modulates using a first set of strange attractor parameters that match a set of strange attractor parameters in a corresponding receiver associated with the one or more radio frequency transmission stations; and wherein the chaotic receiver demodulates using a second set of strange attractor parameters in a corresponding transmitter associated with the one or more radio frequency transmission stations.
23. A chaotic telephone device comprising:
a chaotic transmitter that receives a first information signal and generates in response thereto a first chaotic trajectory shifted signal modulated in accordance with the first information signal;
a chaotic receiver that receives a second chaotic trajectory shifted signal modulated in accordance with a second information signal and generates in response thereto a demodulated version of the second chaotic trajectory shifted signal; and
an interface circuit that couples the chaotic transmitter and chaotic receiver to a radio-frequency telephone circuit, wherein the radio-frequency telephone circuit communicates with a ground-based telephone network through one or more radio frequency transmission stations,
wherein the chaotic receiver comprises:
an oscillator;
a chaotic circuit comprising a circuit element that exhibits a nonlinear current-voltage characteristic; and
a gain control amplifier coupled between the oscillator and the chaotic circuit, wherein the gain control amplifier amplifies a voltage present at the oscillator before it reaches the chaotic circuit.
24. A chaotic telephone device comprising:
a chaotic transmitter that receives a first information signal and generates in response thereto a first chaotic trajectory shifted signal modulated in accordance with the first information signal;
a chaotic receiver that receives a second chaotic trajectory shifted signal modulated in accordance with a second information signal and generates in response thereto a demodulated version of the second chaotic trajectory shifted signal; and an interface circuit that couples the chaotic transmitter and chaotic receiver to a radio-frequency telephone circuit, wherein the radio-frequency telephone circuit communicates with a ground-based telephone network through one or more radio frequency transmission stations,
wherein the chaotic receiver further comprises a synchronizing resistor coupled between an input of the chaotic receiver and the chaotic circuit; and
further comprising a detection circuit, coupled to the synchronizing resistor, wherein the detection circuit detects periods of synchronization and non-synchronization between the second modulated chaotic signal and the chaotic circuit and generates an output corresponding to periods of synchronization and non-synchronization.
25. A chaotic telephone device comprising:
a chaotic transmitter that receives a first information signal and generates in response thereto a first chaotic trajectory shifted signal modulated in accordance with the first information signal;
a chaotic receiver that receives a second chaotic trajectory shifted signal modulated in accordance with a second information signal and generates in response thereto a demodulated version of the second chaotic trajectory shifted signal; and
an interface circuit that couples the chaotic transmitter and chaotic receiver to a radio-frequency telephone circuit, wherein the radio-frequency telephone circuit communicates with a ground-based telephone network through one or more radio frequency transmission stations,
wherein the chaotic transmitter comprises:
an oscillator circuit;
a resistor coupled to the oscillator circuit;
a chaotic circuit comprising a circuit element that exhibits a nonlinear current-voltage characteristic, wherein the chaotic circuit is coupled to the oscillator circuit through the resistor;
an isolation amplifier coupled to the chaotic circuit;
a filter coupled to the output of the isolation amplifier that limits a frequency bandwidth present at the chaotic circuit; and
means for modulating a circuit element of the chaotic transmitter in accordance with the first information signal.
26. 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;
(3) transmitting the chaotic trajectory shift-keyed signal generated in step (2) to the base station; and
(4) in the base station, demodulating the transmitted signal to recover the information signal,
wherein step (2) comprises the step of using a nonlinear circuit element that exhibits a piecewise linear current-voltage characteristic comprising three linear segments, two of the segments having a first slope in the phase space and the third segment having a second slope in the phase space, and where step (2) comprises the step of changing either the first slope or the second slope but not both slopes in response to the information signal.
27. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal;
a first chaotic circuit coupled to the oscillator circuit and tuned to a first strange attractor;
a second chaotic circuit coupled to the oscillator circuit and tuned to a second strange attractor; and
means for detecting a difference between the modulated chaotic signal received at the input terminal and respective signals generated by the first and second chaotic circuits,
further comprising a third chaotic circuit coupled to the oscillator circuit and tuned to a third strange attractor; wherein the means for detecting a difference further detects a difference between the modulated chaotic signal received at the input terminal and a signal generated by the third chaotic circuit.
28. A method of demodulating a signal modulated according to a chaotic trajectory shift-keying technique, comprising the steps of:
(1) receiving a modulated chaotic signal modulated according to a chaotic trajectory shift-keying technique;
(2) using the modulated chaotic signal to drive an oscillator;
(3) using the modulated chaotic signal and an output of the oscillator to drive a first chaotic circuit tuned to a first strange attractor;
(4) using the modulated chaotic signal and an output of the oscillator circuit to drive a second chaotic circuit tuned to a second strange attractor; and
(5) detecting a difference between the modulated chaotic signal and respective signals generated by the first and second chaotic circuits,
further comprising the step of using the modulated chaotic signal and an output of the oscillator circuit to drive a third chaotic circuit tuned to a third strange attractor, and wherein step (5) comprises the step of detecting a difference between the modulated chaotic signal and a signal generated by the third chaotic circuit.
29. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal;
a first chaotic circuit coupled to the oscillator circuit and tuned to a first strange attractor;
a second chaotic circuit coupled to the oscillator circuit and tuned to a second strange attractor; and
means for detecting a difference between the modulated chaotic signal received at the input terminal and respective signals generated by the first and second chaotic circuits,
wherein the means for detecting comprises:
a plurality of synchronizing resistors each of which generates a voltage drop in response to a difference between the modulated chaotic signal and a corresponding one of the first and second chaotic circuits;
means for buffering the plurality of synchronizing resistors and generating buffered outputs therefrom;
means for attenuating the buffered outputs; and
means for subtracting the buffered outputs to generate a detected signal.
30. A method of demodulating a signal modulated according to a chaotic trajectory shift-keying technique, comprising the steps of:
(1) receiving a modulated chaotic signal modulated according to a chaotic trajectory shift-keying technique;
(2) using the modulated chaotic signal to drive an oscillator;
(3) using the modulated chaotic signal and an output of the oscillator to drive a first chaotic circuit tuned to a first strange attractor;
(4) using the modulated chaotic signal and an output of the oscillator circuit to drive a second chaotic circuit tuned to a second strange attractor; and
(5) detecting a difference between the modulated chaotic signal and respective signals generated by the first and second chaotic circuits,
wherein step (5) comprises the steps of:
(a) generating a voltage drop in response to a difference between the modulated chaotic signal and a corresponding one of the first and second chaotic circuits;
(b) buffering the plurality of synchronizing resistors and generating buffered outputs therefrom;
(c) attenuating the buffered outputs; and
(d) subtracting the buffered outputs to generate a detected signal.
31. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal;
a first chaotic circuit coupled to the oscillator circuit and tuned to a first strange attractor;
a second chaotic circuit coupled to the oscillator circuit and tuned to a second strange attractor; and
means for detecting a difference between the modulated chaotic signal received at the input terminal and respective signals generated by the first and second chaotic circuits,
wherein the means for detecting a difference comprises at least two synchronizing resistors, each respectively coupled between the oscillator and one of the first and second chaotic circuits, the chaotic receiver further comprising:
first and second subtractor circuits, each coupled across a corresponding one of the two synchronizing resistors;
a third subtractor circuit, coupled to the first and second subtractor circuits, wherein the third subtractor circuit generates a difference signal from the first and second subtractor circuits;
an absolute value circuit, coupled to the third subtractor circuit, which generates an absolute value signal from the third subtractor circuit; and
a squaring circuit that generates a squared version of the absolute value signal.
32. A method of demodulating a signal modulated according to a chaotic trajectory shift-keying technique, comprising the steps of:
(1) receiving a modulated chaotic signal modulated according to a chaotic trajectory shift-keying technique;
(2) using the modulated chaotic signal to drive an oscillator;
(3) using the modulated chaotic signal and an output of the oscillator to drive a first chaotic circuit tuned to a first strange attractor;
(4) using the modulated chaotic signal and an output of the oscillator circuit to drive a second chaotic circuit tuned to a second strange attractor; and
(5) detecting a difference between the modulated chaotic signal and respective signals generated by the first and second chaotic circuits,
wherein step (5) comprises the step of generating a voltage drop in response to a difference between the modulated chaotic signal and a corresponding one of the first and second chaotic circuits, the method further comprising the steps of:
(6) generating first and second difference signals corresponding to first and second voltage drops from the first and second chaotic circuits;
(7) subtracting the first and second difference signals and generating a third difference signal therefrom;
(9) generating an absolute value signal from the third difference signal; and
(10) generating a squared version of the absolute value signal.
33. A chaotic receiver, comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal;
a first chaotic circuit coupled to the oscillator circuit and tuned to a first strange attractor;
a second chaotic circuit coupled to the oscillator circuit and tuned to a second strange attractor; and
means for detecting a difference between the modulated chaotic signal received at the input terminal and respective signals generated by the first and second chaotic circuits,
wherein the means for detecting a difference comprises at least two synchronizing resistors, each respectively coupled between the oscillator and one of the first and second chaotic circuits, the chaotic receiver further comprising:
first and second subtractor circuits, each coupled across a corresponding one of the two synchronizing resistors;
first and second absolute value circuits, each coupled to a corresponding one of the first and second subtractor circuits;
a third subtractor circuit, coupled to the first and second absolute value circuits, which generates a subtracted absolute value signal; and
a squaring circuit that generates a squared version of the subtracted absolute value signal.
34. A method of demodulating a signal modulated according to a chaotic trajectory shift-keying technique, comprising the steps of:
(1) receiving a modulated chaotic signal modulated according to a chaotic trajectory shift-keying technique;
(2) using the modulated chaotic signal to drive an oscillator;
(3) using the modulated chaotic signal and an output of the oscillator to drive a first chaotic circuit tuned to a first strange attractor;
(4) using the modulated chaotic signal and an output of the oscillator circuit to drive a second chaotic circuit tuned to a second strange attractor; and
(5) detecting a difference between the modulated chaotic signal and respective signals generated by the first and second chaotic circuits,
wherein step (5) comprises the step of generating a voltage drop in response to a difference between the modulated chaotic signal and a corresponding one of the first and second chaotic circuits, the method further comprising the steps of:
(6) generating first and second difference signals corresponding to first and second voltage drops from the first and second chaotic circuits;
(7) generating first and second absolute value signals from the first and second difference signals;
(8) subtracting the first and second first and second absolute value signals and generating therefrom a subtracted absolute value signal; and
(9) generating a squared version of the subtracted absolute value signal.
35. 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; 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,
wherein step (2) comprises the step of changing the non-reactive resistive value to one of a plurality of uniquely coded vectors within a chaotic operating region which, when received at a matched receiver, will generate a corresponding unique code.
36. 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,
wherein the means for changing sets the non-reactive resistive value to one of a plurality of uniquely coded vectors within a chaotic operating region which, when received at a matched receiver, will generate a corresponding unique code.
37. 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
a switch coupled to the chaotic circuit, wherein the switch chances 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,
wherein the switch sets the non-reactive resistive value to one of a plurality of uniquely coded vectors within a chaotic operating region which, when received at a matched receiver, will generate a corresponding unique code.
38. A method of transmitting information, comprising the steps of:
(1) in response to receiving a time-varying N-bit code representing a unit of information, selecting a corresponding one of a Plurality of 2N transmitters each of which generates a chaotic strange attractor signal that is distinct from others in the Plurality of 2N transmitters;
(2) transmitting through a communications channel the chaotic strange attractor signal selected in step (1);
(3) receiving the chaotic strange attractor signal transmitted in step (2);
(4) matching the signal received in step (3) to one of a plurality of 2N receivers each of which is matched to a corresponding one of the plurality of 2N transmitters; and
(5) on the basis of the receiver matched in step (4), recovering the N-bit code received in step (1).
39. A receiving system comprising:
a receiving circuit that receives a time-varying signal comprising a plurality of discrete portions of each of a plurality of chaotic strange attractor signals;
a plurality of 2N receivers each of which is tuned to one of a corresponding number of 2N transmitters;
a plurality of detectors each of which detects whether a corresponding one of the plurality of 2N receivers has received a matching signal; and
a switching circuit which, in response to one of the detectors detecting a corresponding match, generates an N-bit code representing a transmitted unit of information.
40. A system comprising:
a transmitting system capable of transmitting N bits of information, comprising:
a plurality of 2N transmitters each of which generates a chaotic strange attractor signal that is distinct from others in the plurality of 2N transmitters;
a switch which, in response to receiving a time-varying N-bit code representing a unit of information, selects a corresponding one of the Plurality of 2N transmitters; and
a transmission circuit that transmits the selected chaotic strange attractor signal across a transmission channel, and
a receiving system, comprising:
a receiving circuit that receives a time-varying signal comprising a plurality of discrete portions of each of a plurality of chaotic strange attractor signals;
a plurality of 2N receivers each of which is tuned to one of the 2N transmitters;
a plurality of detectors each of which detects whether a corresponding one of the plurality of 2N receivers has received a matching signal; and
a switching circuit which, in response to one of the detectors detecting a corresponding match, generates an N-bit code representing a transmitted unit of information.
41. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal and driven by the modulated chaotic signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a different voltage offset, and wherein the upper and lower slope circuits cooperate with the oscillator circuit to generate a local chaotic signal;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the modulated chaotic signal at the input terminal and the local chaotic signal;
a detector coupled to the synchronizing circuit which detects periods of synchronization and non-synchronization;
a first analog-to-digital converter coupled to the oscillator circuit;
a second analog-to-digital converter coupled to the upper slope circuit; and
a third analog-to-digital converter coupled to the lower slope circuit;
wherein the detector detects periods of synchronization and non-synchronization with respect to the output of each of the first, second, and third analog-to-digital converters.
42. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal and driven by the modulated chaotic signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a different voltage offset, and wherein the upper and lower slope circuits cooperate with the oscillator circuit to generate a local chaotic signal;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the modulated chaotic signal at the input terminal and the local chaotic signal;
a detector coupled to the synchronizing circuit which detects periods of synchronization and non-synchronization;
a first filter, coupled between the input terminal and the oscillator circuit, wherein the first filter filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
a second filter, coupled to a first portion of the synchronizing circuit, wherein the second filter filters a buffered version of the filtered modulated chaotic signal; and
a third filter, coupled to a second portion of the synchronizing circuit, wherein the third filter filters a signal generated by the chaotic circuit; and
wherein the detector is coupled to respective outputs of the second and third filters.
43. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal and driven by the modulated chaotic signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a different voltage offset, and wherein the upper and lower slope circuits cooperate with the oscillator circuit to generate a local chaotic signal;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the modulated chaotic signal at the input terminal and the local chaotic signal;
a detector coupled to the synchronizing circuit which detects Periods of synchronization and non-synchronization;
a first filter, coupled between the input terminal and the synchronizing circuit, wherein the first filter filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
a second filter, coupled to a first portion of the synchronizing circuit, wherein the second filter filters a buffered version of the filtered modulated chaotic signal; and
a third filter, coupled to a second portion of the synchronizing circuit, wherein the third filter filters a signal generated by the chaotic circuit; and
wherein the detector is coupled to respective outputs of the second and third filters.
44. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal and driven by the modulated chaotic signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a different voltage offset, and wherein the upper and lower slope circuits cooperate with the oscillator circuit to generate a local chaotic signal;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the modulated chaotic signal at the input terminal and the local chaotic signal;
a detector coupled to the synchronizing circuit which detects periods of synchronization and non-synchronization;
a first filter, coupled between the input terminal and the oscillator circuit, wherein the first filter filters the modulated chaotic signal and produces a filtered modulated chaotic signal;
a second filter coupled between the chaotic circuit and the oscillating circuit;
a third filter, coupled to an output of the first filter, which further filters the output of the first filter;
wherein the synchronizing circuit is coupled between the third filter and the chaotic circuit, and wherein the synchronizing circuit generates a voltage difference in response to an out-of-synchronization condition between a signal from the third filter and the chaotic circuit;
a fourth filter, coupled to a first portion of the synchronizing circuit, which filters a buffered version of the filtered modulated chaotic signal; and
a fifth filter, coupled to a second portion of the synchronizing circuit, which filters a signal generated by the chaotic circuit;
wherein the detection circuit is coupled to respective outputs of the fourth and fifth filters.
45. A chaotic receiver comprising:
an input terminal that receives a modulated chaotic signal;
an oscillator circuit coupled to the input terminal and driven by the modulated chaotic signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a different voltage offset, and wherein the upper and lower slope circuits cooperate with the oscillator circuit to generate a local chaotic signal;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the modulated chaotic signal at the input terminal and the local chaotic signal; and
a detector coupled to the synchronizing circuit which detects periods of synchronization and non-synchronization;
wherein the upper slope circuit satisfies the relation I=GbV+GaVbp-GbVbp; wherein the lower slope circuit satisfies the relation I=GbV-GaVbp+GbVb, where I is the current through each respective slope circuit, Gb is a first slope constant, V is the voltage across the respective slope circuit, Ga is a second slope constant, and Vbp is a breakpoint voltage.
46. 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; and
a low-pass filter coupled to the output of the switch
wherein the first chaotic circuit exhibits a first current slope that is offset to intersect a load line in an upper quadrant of a current-voltage characteristic curve; and wherein the second chaotic circuit exhibits a second current slope that is offset to intersect the load line in a lower quadrant of the current-voltage characteristic curve.
47. 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; and
(4) transmitting the selected output from step (3),
wherein step (1) comprises the step of generating a first chaotic signal that oscillates about a first equilibrium point in an upper quadrant of a current-voltage phase space of a chaotic circuit element, and wherein step (2) comprises the step of generating a second chaotic signal that oscillates about a second equilibrium point in a lower quadrant of the current-voltage phase space.
48. A chaotic receiving circuit, comprising:
an input terminal that receives a chaotically modulated signal;
a resistor coupled to the input terminal, wherein the resistor defines a current-voltage load line;
an oscillator circuit coupled to the input terminal through the resistor and driven by the chaotically modulated signal;
a chaotic circuit comprising an upper slope circuit that implements a first current-voltage function in an upper quadrant of a current-voltage response plane and a lower slope circuit that implements a second current-voltage function in a lower quadrant of the current-voltage response plane, wherein the first and second current-voltage functions have a positive slope but are offset by a voltage difference and respectively intersect the current-voltage load line in the upper and lower quadrants of the current-voltage response plane;
a synchronizing circuit, coupled to the oscillator circuit and the chaotic circuit, wherein the synchronizing circuit detects differences between the chaotically modulated signal and signals respectively present at the upper and lower slope circuits; and
a detector coupled to the synchronizing circuit which recovers an information signal on the basis of the differences.
49. The chaotic receiving circuit of claim 48, further comprising a plurality of upper slope detector circuits and a plurality of lower slope detector circuits, wherein each upper slope circuit and each lower slope circuit intersects the current-voltage load line at a different point, each point corresponding to a symbol of information.
50. The chaotic receiving circuit of claim 48, wherein the detector comprises a first analog-to-digital converter coupled to an output of the oscillator circuit, a second analog-to-digital converter coupled to upper slope circuit, and a third analog-to-digital converter coupled to the lower slope circuit, wherein the outputs of the first, second, and third analog-to-digital converters are used to recover the information signal.
51. 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; and
a low-pass filter coupled to the output of the switch,
wherein the first chaotic circuit exhibits a first positive linear current slope that is offset to intersect a load line in an upper quadrant of a current-voltage characteristic curve; and wherein the second chaotic circuit exhibits a second positive linear current slope that is offset to intersect the load line in a lower quadrant of the current-voltage characteristic curve.
52. 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); and
(3) matching the amplitude and impedance of the signal obtained from step (2) to the communications channel,
wherein step (3) comprises the step of matching the amplitude and impedance of the signal obtained from step (2) to a light emitting diode.
53. A method of interfacing a chaotic receiving circuit to a communications channel without using a frequency filter, comprising the steps of:
(1) buffering a modulated chaotic signal received from the communications channel to isolate the chaotic receiving circuit from the communications channel;
(2) amplifying the buffered signal; and
(3) adding a direct current component to the amplified buffered signal obtained in step (2), wherein the direct current component corresponds to a direct current component subtracted at a corresponding transmitter,
further comprising the step of, prior to step (1), passing the modulated chaotic signal through a balanced input buffer/amplifier that matches electrical characteristics of a dual conductor communications channel to the chaotic receiving circuit.
54. Apparatus for interfacing a chaotic receiving circuit to a communications channel without using a frequency filter, comprising:
a buffering circuit that buffers a modulated chaotic signal received from the communications channel to isolate the chaotic receiving circuit from the communications channel;
an amplifier coupled to the buffering circuit that amplifies an output of the buffering circuit; and
a direct current voltage offset circuit coupled to the amplifier, wherein the direct current voltage offset circuit adds a direct current component to the amplified buffered signal, wherein the direct current component corresponds to a direct current component subtracted at a corresponding transmitter,
further comprising a differential input amplifier, coupled to the buffering circuit, wherein the differential input amplifier rejects common-mode input components and amplifies differential components.
Description
TECHNICAL FIELD
This invention relates generally to information transmission techniques involving modulation and demodulation of a chaotic carrier signal. Many aspects of the invention involve transmitting information by modulating various characteristics of nonreactive circuit elements of a chaotic transmitter. The invention has broad application to communications systems, radar systems and other systems that transmit and receive information over wire, radio frequencies, light (including fiber optic) and acoustic channels.
BACKGROUND OF THE INVENTION
Techniques for modulating carrier signals in order to transmit information between two points are well known. In systems employing frequency modulation, for example, a carrier signal is modulated by changing the frequency of the signal in accordance with an information signal such as a human voice. Amplitude-modulated systems change the amplitude of a fixed-frequency signal in accordance with an information signal. Other modulation techniques have been developed over the years to optimize transmission characteristics, to optimize signal bandwidth, and to overcome noisy transmission environments.
So-called "chaotic" signals provide a particularly interesting, simple, and useful means of modulating information signals in a manner that can increase noise immunity and reduce the power levels needed to transmit information. As explained in the aforementioned application, which is bodily incorporated herein, these signals can be modulated in various ways to transmit information. The modulation bandwidth available when using such techniques, however, has been determined to be generally limited to 10 to 15% of the tank circuit frequency in the transmitting circuit. This limitation is believed to be due to the fact that changing lump parameters in the transmitter causes a certain amount of settling time before the receiver can synchronize with the changed transmitter parameters.
The present inventors have discovered a technique for modulating the transmitting signal in a manner that results in much faster signal stability, thus reducing the amount of time required to synchronize the receiver and increasing the modulation bandwidth dramatically. Other features and advantages provided by the present invention will become apparent upon reading this specification in conjunction with the figures.
The following description begins by reviewing the subject matter of the aforementioned application as a departure point for explaining the principles of the present invention. Circuits, principles and embodiments described in the aforementioned application will be referred generally to as "first-generation," while those newly presented in this application will be referred to generally as "second-generation" or "improved." These labels are not intended in any way to be limiting. Moreover, many of the second-generation circuits and principles can be used in conjunction with first-generation circuits and vice versa.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A is a diagram of a Chua circuit according to the prior art.
FIG. 1B is a communications system according to the prior art.
FIG. 1C is a diagram indicating the resistance—voltage characteristic of a non-linear resistor used in a Chua circuit.
FIG. 1D is a diagram of the operating regimes of a Chua circuit mapped into a lump parameter plane.
FIG. 2A is a schematic of a transmitter of a first-generation system wherein a capacitor 237 is switched to modulate a chaotic signal.
FIG. 2B shows a conventional receiver that can be used with the transmitter of FIG. 2A.
FIG. 3A shows another embodiment of a first-generation transmitter that produces a vocabulary of chaotic signals.
FIG. 3B shows a receiver for use with the embodiments of FIG. 3A and FIG. 4A.
FIG. 4A shows another embodiment of a first-generation transmitter that produces a vocabulary of chaotic signals in which all such signals can be mapped to the same combinations of the lump parameter plane of FIG. 1D.
FIG. 4B shows another embodiment of a first-generation receiver for use with the embodiments of FIG. 3A and FIG. 4A, this receiver being usable with a simple counter circuit for determining a beat frequency.
FIG. 4C shows another receiver for use with the embodiment of FIG. 3A and
FIG. 4B using a synchronizing resistor 385.
FIG. 4D shows another receiver usable with a simple counter circuit for determining a beat frequency using a synchronizing resistor formed from a combination of resistors.
FIG. 4E shows another receiver similar to that of FIG. 4D, but which adds an emitter follower 353 to isolate the oscillator portion 361 from point 287.
FIG. 4F shows a receiver including a simple counter circuit for determining a beat frequency, wherein resistors provide a synchronizing element to lock the incoming voltage of the communications channel and the receiver generated voltage. In this embodiment, voltage follower 363 isolates the receiver generated signal from the incoming signal and allows the receiver generated signal to feedback into the oscillator portion of the Chua circuit to cause faster synchronization.
FIG. 5 shows a generalized communications system with a synchronizing filter 550 according to a first-generation embodiment of the invention.
FIG. 6A shows a conventional transmitter with a Kennedy non-linear diode that can be modulated according to the principles of a second-generation system.
FIG. 6B shows a conventional transmitter with a Caltech non-linear diode that can be modulated according to the principles of a second-generation system.
FIG. 6C shows a transmitter with a novel non-linear diode that can be modulated in accordance with the principles of a second-generation system.
FIG. 7A shows how a switch 735c can be used to modulate voltage-current characteristics of a nonlinear diode in accordance with a second-generation embodiment.
FIG. 7B shows generally how an information signal 736 can be used to make and break a switch 735c (or other switch-like device) to modulate a negative resistance in accordance with a second-generation embodiment.
FIG. 7C shows the effects of changing various resistive values in a Caltech diode (FIG. 6B) and Kennedy diode (FIG. 6A) on slope.
FIG. 8 shows how the slope of the current-voltage characteristic curve for a nonlinear element can be changed in order to change the rotation of a strange attractor phase plane according to a second-generation embodiment. FIG. 9A shows modulation limits for Ga and Gb according to a second-generation transmitter.
FIG. 9B maps current-voltage characteristic curves between a modulated transmitter and a receiver.
FIG. 9C shows how positive breakpoints can be established for a nonlinear diode according to various second-generation embodiments.
FIG. 10 shows a field effect transistor 1001 placed across diodes 652 and 655 to implement on-off keying according to a second-generation embodiment.
FIG. 11 shows a gain control amplifier 1146 inserted into a receiving circuit that reduces or eliminates the need for an automatic gain control (AGC) amplifier on the input at point 1191.
FIG. 12 shows a general case of a gain control amplifier 1202 embedded in a receiving circuit.
FIG. 13 shows a transmitter including an operational amplifier 1308 that isolates a filter 1309 from the chaotic subsystem 222 according to a second-generation embodiment of the invention.
FIG. 14A shows low-pass filtering characteristics of a transmitter according to a second-generation embodiment of the invention.
FIG. 14B shows bandpass filtering characteristics of a transmitter according to a second-generation embodiment of the invention.
FIG. 15 shows a receiver including noise filters 1593, 1594 and 1597 to filter out noise components introduced by the transmission channel according to a second-generation embodiment of the invention.
FIG. 16 shows a receiver including noise filters 1666, 1694 and 1697 to filter out noise components introduced by the transmission channel according to a second-generation embodiment of the invention.
FIG. 17 shows a receiver including filters 1793, 1766, 1794, 1797 and 1721, wherein filter 1721 works with automatic gain control amplifier 1746 to further reduce noise generated in subsystem 1726.
FIG. 18A shows a cell phone system incorporating a baseband modem using chaotic modulation principles according to a second-generation embodiment of the invention.
FIG. 18B shows a cell phone system using chaotic modulation principles at the intermediate frequency level according to a second-generation embodiment of the invention.
FIG. 18C shows a cell phone system using chaotic modulation principles at the radio frequency level according to a second-generation embodiment of the invention.
FIG. 19A shows a second-generation system employing various principles of the present invention, including a transmitter with a nonlinear element 1904 modulated with an information signal, and a receiver including a nonlinear element 1905 and a synchronizing resistor Rsync.
FIG. 19B shows a current/voltage curve 1910 for a nonlinear diode superimposed over a load line 1911.
FIG. 19C shows two "single-scroll" attractors 1920 and 1930 orbiting around equilibrium points at the intersection of a nonlinear diode current-voltage characteristic curve and a load line, illustrating a DC analysis of a transmitter.
FIG. 19D shows how the current-voltage characteristic curve can be changed at the transmitter to move the equilibrium points between three different positions while slope Ga and the breakpoint positions are held constant.
FIG. 19E shows a strange attractor moving with the equilibrium point as a nonlinear circuit element is modulated with an information signal, causing changes in the slope of part of the characteristic curve.
FIG. 19F shows one technique for changing a nonlinear diode current-voltage characteristic curve using an ideal switch SW1 and a resistor in series with the ideal switch that is also in parallel with one of the nonlinear diode resistors.
FIG. 19G shows the result of modulation on the voltage across the nonlinear diode.
FIG. 20A shows a voltage (V1) versus voltage (V2) versus time (T) plot of a chaotic signal (double scroll strange attractor) without modulation.
FIG. 20B shows the plot of FIG. 20A when modulated with an information signal.
FIG. 20C shows a voltage (V2) versus current (I3) versus time (T) plot of a chaotic signal (double scroll strange attractor) without modulation.
FIG. 20D shows the plot of FIG. 20C when modulated with an information signal.
FIG. 20E shows a voltage (V1) versus current (I3) versus time (T) plot of a chaotic signal (single scroll attractor) without modulation.
FIG. 20F shows the plot of FIG. 20E when modulated with an information signal (single scroll modulation).
FIG. 21A shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1200 ohms (double scroll attractor).
FIG. 21B shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1210 ohms (double scroll attractor).
FIG. 21C shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1220 ohms (double scroll attractor).
FIG. 21D shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 21A.
FIG. 21E shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 21B. As compared to FIG. 21D, the strange attractor on the left side is "squashed."
FIG. 21F shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 21C. As compared to FIG. 21E, the strange attractor on the left side is even more "squashed."
FIG. 21G shows a frequency plot corresponding to the nonlinear diode curve of FIG. 21A.
FIG. 21H shows a frequency plot corresponding to the nonlinear diode curve of FIG. 21B.
FIG. 21I shows a frequency plot corresponding to the nonlinear diode curve of FIG. 21C.
FIG. 22A shows a voltage (V1) versus voltage (V2) versus time (T) plot of a chaotic signal (single scroll strange attractor) without modulation.
FIG. 22B shows the plot of FIG. 22A when modulated with an information signal.
FIG. 22C shows a voltage (V2) versus current (I3) versus time (T) plot of a chaotic signal (single scroll strange attractor) without modulation.
FIG. 22D shows the plot of FIG. 22C when modulated with an information signal.
FIG. 22E shows a voltage (V1) versus current (I3) versus time (T) plot of a chaotic signal (single scroll strange attractor) without modulation.
FIG. 22F shows the plot of FIG. 22E when modulated with an information signal.
FIG. 23A shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1930 ohms (single scroll attractor).
FIG. 23B shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1940 ohms (single scroll attractor).
FIG. 23C shows a nonlinear diode current-voltage characteristic curve where resistor R1 is set to 1950 ohms (single scroll attractor).
FIG. 23D shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 23A.
FIG. 23E shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 23B. As compared to FIG. 23D, the strange attractor is elongated.
FIG. 23F shows a voltage-current phase space map (V1 vs. V2 vs. I3) corresponding to the nonlinear diode curve of FIG. 23C. As compared to FIG. 23E, the strange attractor is even more elongated.
FIG. 23G shows a frequency plot corresponding to the nonlinear diode curve of FIG. 23A.
FIG. 23H shows a frequency plot corresponding to the nonlinear diode curve of FIG. 23B.
FIG. 23I shows a frequency plot corresponding to the nonlinear diode curve of FIG. 23C
FIG. 24 shows a dual-transmitter configuration (1200, 1205) according to a second-generation embodiment of the invention.
FIG. 25 shows a dual-receiver configuration (601, 1370) according to a second-generation embodiment of the invention.
FIG. 26 shows a subtraction circuit for detecting a voltage difference across various points (e.g., point 1450) in FIG. 25.
FIG. 27 shows an absolute value circuit that can be used in conjunction with a detector function.
FIG. 28 shows a dual receiver synchronization detector circuit according to a second-generation embodiment of the invention.
FIG. 29 shows a dual receiver synchronization detector circuit in which signals are subtracted, absolute valued and then subtracted.
FIG. 30 shows a detector circuit for detecting voltage changes between points 287 and 1415 or points 1440 and 1470 in FIG. 25.
FIG. 31 shows a baseband transmitter interface circuit for interfacing a modulated chaotic transmitter to a communication system.
FIG. 32 shows a baseband receiver interface circuit for interfacing a receiver to a communication system.
FIG. 33 shows a system in which a chaotic transmitter and receiver are interfaced to an infrared amplitude modulated subsystem 3090.
FIG. 34 shows how a chaotic transmission and reception system can be interfaced to a radio transmitter/receiver pair 3100 and 3110.
FIG. 35 shows a balanced cable driver circuit 2455 that can be used to pass a chaotic signal over a twisted pair or coaxial cable system.
FIG. 36 shows a balanced cable receiver circuit 2880 that can be used to interface a chaotic receiver 2860 to a twisted pair or coaxial cable system.
FIG. 37A shows curves representing chaotic operating regions for different values of a synchronizing resistor 660 for a Caltech diode implementation (FIG. 6B).
FIG. 37B shows curves representing chaotic operating regions for different values of a synchronizing resistor 608 for a Kennedy diode implementation (FIG. 6A).
FIG. 37C shows what happens when the transmitter capacitor 215 (FIG. 6B) is varied and the receiver capacitors 355 and 1490 (FIG. 25) are set to fixed values with the nonlinear diode characteristic curve set at a fixed value.
FIG. 38 shows a technique for doubling a signal rate using four unmodulated oscillator/transmitters and corresponding receivers.
FIG. 39 shows a technique for increasing the digital signal transmission rate using multiple chaotic transmitters and matched receivers.
FIG. 40 shows how a nonlinear circuit can be replaced with two functions that represent only the Gb slopes, referred to as a "Gb-only" transmitter or receiver.
FIG. 41 shows a detector design in which a nonlinear diode is replaced with +/-Gb slope detectors (5350 and 5340).
FIG. 42 shows a dual receiver design using sample-and-hold circuits with outputs 5380, 5360, and 5370.
FIG. 43 shows a transmitter that modulates only the slope Gb.
FIG. 44 shows a dual-transmitter system that modulates only the slope Gb.
FIG. 45A shows a dual receiver design wherein a nonlinear diode is replaced with a +/- Gb detector and voltage Vb in a negative resistor circuit.
FIG. 45B shows a dual receiver design that is a variation on that of FIG. 45A.
FIG. 46 shows a current-voltage characteristic curve for certain embodiments of the invention that modulate and detect a positive slope.
FIG. 47 shows a receiver in which a nonlinear diode is replaced with a Gb+ detector.
FIG. 48 shows a Gb+ dual receiver design including a sample and hold circuit.
FIG. 49 shows a Gb+ only transmitter using Gb+ slope modulation and voltage modulation.
FIG. 50 shows a digital to analog Gb+ only transmitter.
FIG. 51 shows a current-voltage characteristic curve for certain embodiments of the invention.
FIG. 52 shows a current-voltage characteristic curve for a positive Gb voltage current M-ary modulation system.
I. FIRST-GENERATION EMBODIMENTS AND TECHNIQUES
Referring to FIG. 1A, a circuit 1 known as a "Chua" circuit oscillates chaotically. The term "chaos" applies to dynamic systems that follow simple dynamical rules, but whose state function trajectory is so sensitive to the system's initial conditions that its state after an arbitrary time-period cannot, in practical terms, be predicted. That is, its state could be predicted if it were possible to model the system with an arbitrary degree of precision.
Chaotic systems evolve deterministically, and their chaotic state paths are cyclic, but very complex and with extremely long cycle-lengths. In real systems, however, with extremely long cycle periods, it may be of little practical significance that their behavior is cyclical because the physical systems that generate the behavior may not be sufficiently stable for the system to ever return to the same dynamical system in its same initial state. For example, the component values of an electrical circuit may not remain precisely constant for 600 years.
The Chua circuit is a simple electrical circuit that exhibits chaotic behavior. It has been studied extensively and used to demonstrate many of the chaotic patterns observed in many physical systems. Referring now also to FIG. 1A, the basic Chua circuit includes a non-linear resistance element 10, characterized by a non-linear voltage-current characteristic curve. In a typical configuration, the curve is piece-wise linear with symmetrical slope discontinuities around the zero-axis. That is: IR=GaVR+(½)(Ga-Gb){|vR+Bp|-|vR-Bp|} where Ga and Gb are the slopes of respective linear portions of the piecewise-linear current/voltage curve characterizing the non-linear resistor and BP is the absolute value of the two voltage points at which the discontinuities in the current/voltage curve lie as shown in FIG. 1C. The circuit has a circuit-driving subsystem 2 (e.g., an L-C tank circuit), and a response subsystem 3, which includes for example a capacitance C1 and non-linear resistor 10, wherein the two systems are interconnected through a resistor 25.
Referring to FIG. 1D, a given choice of values of the physical characteristics of the components of the Chua circuit each correspond to a unique operating regime, some values of which may coincide with a chaotic behavior of the Chua circuit. The operating regime may be mapped onto a coordinate system whose axes are the lump parameters, α=C2/C1=C2/C, and β=R2C2/L. By choosing values of R (25), L (30), C1 (15)and C2 (20) so that α and β lie in, for example, a double scroll region 60, a Chua circuit can be made that will oscillate chaotically or quasi-periodically. Any point on the plot corresponds to a different operating behavior and a selected point does not exhaustively define a particular path of state trajectories. A selected point on the curves can correspond to radically different behaviors depending on the initial conditions.
Given a specified physical configuration and a specified initial state specified by V1, V2, and IL, the voltages across C1 (15) and C2 (20) and the current through L (30), the evolution of the Chua circuit's state is deterministic, but chaotic. That is, any Chua circuit with the same physical parameters and initial conditions will follow the same course of states over time and this course will repeat itself over a very long interval (perhaps many years). However, to an observer, the value of (for example) voltage V1 over a period of time shorter than this long interval looks like noise. Also, initial states that differ only slightly can follow widely different state paths. In addition, its power spectral density function is spread over a wide range of frequencies, with a peak at the frequency of the fundamental of the L-C tank circuit formed by L and C2. However, compared to oscillators, such as used to generate carriers for radio transmission, the peak is not pronounced; that is, it is very short and wide.
The Chua circuit, aside from being a classic device for demonstrating, studying, and modeling chaotic real-world systems, has also been proposed as a basis for chaotic signal transmission. Generally a transmitting nonlinear dynamic circuit produces a chaotic signal that can be used to induce a receiving chaotic system to synchronize with it. The parameter of the transmitting chaotic circuit can be modulated or perturbed responsively to an information signal. The parameter can be a scalar, such as a voltage, tapped from the transmitting circuit and used as a signal. The signal is applied to the receiving system, causing the receiving system to synchronize with the transmitted signal. The chaotic signal from the synchronized receiving circuit can be used with the modulated transmitted signal to recover the information signal according to various prior art schemes. The chaotic signals that can be derived from an oscillating Chua circuit are similar to spread-spectrum signals including a range of frequencies. Chua circuits have been made to generate communications signals in frequency bands ranging from audio to radio frequency and in various media.
Various modulation schemes have been proposed. For example, a simple signal summing system adds the information signal to the chaotic scalar. A more complex correlation system uses a signal divider and multiplier at the transmitter and receiver, respectively. In FIG. 1B, a prior art system uses a Chua circuit to transmit signals and receive signals. The system has a transmitting Chua circuit 100 and an identical (in terms of its chaotic oscillating properties) receiving Chua circuit 101. The transmitting Chua circuit 100 oscillates in a chaotic or semiperiodic regime.
Generally, the two chaotic circuits 100 and 101 can be synchronized by driving a portion of the receiving chaotic oscillator 101 with a driving function tapped from the transmitting chaotic oscillator 100. L-C tank circuit 105 of the transmitting Chua circuit 100 is linked through a resistor 81 to the capacitor/non-linear resistor portion 106. The latter portion causes the oscillations of the L-C tank circuit to become chaotic for certain values of the inductor 74, capacitors 71 and 73, and resistor 81 as discussed above with reference to FIG. 1D. The chaotic portion 108 of the identical receiving circuit 101, also a capacitor/non-linear resistor circuit, reproduces the driving signal. That is, the transmitting 100 and receiving 101 circuits follow precisely the same chaotic course of states (assuming no modulation is taking place in the transmitting circuit 100).
It is known that the transmitting 100 and receiving 101 circuits will remain synchronized even when a substantial amount of noise and/or information is injected into the driving signal. Thus, in the prior art embodiment of FIG. 1B, a signal current Ii(t) is injected by a driver 76 that converts a signal voltage through an invertable coding function c(vs(t)). The decoded signal at the receiver is then obtained from the received current signal Id(t) by applying the inverse coding operation to the received current signal Id(t) to obtain a voltage signal containing the information signal.
Note that the term, "synchronous," in this context, characterizes the convergence of two state variables toward identical or linearly related, but continuously changing, sets of values. That is, a change in one variable corresponds to a change in a synchronized variable that is linearly related to the change in the one variable. Thus, plotting one variable against the synchronized variable over time, the result, theoretically, is a straight line. Synchronization of non-linear systems, and the mathematical modeling of such systems, is described in some detail in U.S. Pat. Nos. 5,245,660; 5,473,694; 5,402,334; 5,379,346; 5,655,022; 5,432,697; and 5,291,555, the entirety of each of which is incorporated by reference herein.
Prior art systems have been discussed widely, but few practical working designs are known. The problems with practical synchronization systems are summarized in the introduction of U.S. Pat. No. 5,680,462. Synchronization systems are inherently noisy and error prone due, at least in part, to the time it takes for synchronization to occur in a noisy channel and because noise induces state transitions in the receiver since it causes a breakpoint to be crossed. For example, when a transmitting circuit is perturbed to encode a piece of information (a bit), it takes a finite amount of time for the receiving circuit to begin to follow the trajectory of the transmitted signal. Also, according to the prior art, modulation cannot span too great a range. Otherwise, a tightly locked synchronization, which is, according to the prior art, essential, cannot be maintained. In addition, the practical problems attending achievement of high data throughput, the providing of reliable locking performance, and various purely practical design considerations have not received a great deal of attention. These prior art problems are addressed by the present invention in both the first-generation and second-generation embodiments.
According to one aspect of a first-generation system, the invention provides a spread-spectrum-like communications system that transmits information in a chaotic signal. Other aspects of the invention include: - (a) a method for modulating a chaotic process to generate a signal to encode information in the signal;
- (b) a method for modulating a circuit that generates a chaotic signal in a stable manner.
- (c) transmitting and receiving chaotic circuits that are characterized by rapid synchronization;
- (d) a mechanism for imprinting and extracting information from two chaotic devices synchronized by a chaotic signal in which the information is embedded such that the chaotic signal can serve as the information carrier signal over a communication channel;
- (e) a communications system that permits the modulation of a chaotic process so as to encode multiple independent streams of data on a same chaotic carrier signal, in effect, implementing an N-word vocabulary, where N corresponds to a number of stable chaotic oscillation states that are induced in a transmitter by modification of a property of at least one of a resistance, a capacitance, and an inductance to tune an oscillating circuit of the transmitter.
Briefly, an embodiment of the invention employs a transmitting oscillating circuit capable of chaotic or quasiperiodic oscillation to generate a (chaotic or quasiperiodic) carrier, preferably a voltage tapped through a voltage follower. A property of the transmitting oscillating circuit, in an embodiment, an auxiliary capacitance, is switched on and off to vary the capacitance of an L-C tank portion of a Chua oscillator. The switching is controlled by an information signal to generate a modulated chaotic signal.
Switching is performed with an optical isolator that requires zero output biasing and introduces essentially no capacitance into the circuit. This prevents any effect on the chaotic or quasi-periodic operating regime of the circuit. An autonomous portion of a receiving oscillating circuit, substantially identical in terms of its oscillating properties, is driven by the modulated carrier. This establishes a synchronized chaotic or quasiperiodic oscillation in the receiving circuit. A comparator is used to output the difference between the driving modulated carrier and a synchronized signal tapped from the receiving oscillator at a point corresponding to the transmitting circuit tap used to generate the modulated carrier. This output provides the recovered information signal.
In one embodiment, various elements of the transmitting chaotic circuit are switchably varied to maintain a constant operating regime so that strange attractors, with frequencies covering a wide selectable range, are generated. This is used to form a vocabulary of strange attractors. The frequency can be determined by the receiver in a very simple way by counting pulses formed from a difference between the base signal in the receiving circuit and the received signal. The difference in the frequencies of the signal being transmitted and the base signal generated by the receiver indicates the "word" transmitted. In this way, if the vocabulary consists of N distinguishable oscillating frequencies, then log2(N) bits can be transmitted with each modulating cycle.
According to one embodiment, the invention provides a communications device with a transmitting chaotic circuit. The transmitter has at least one circuit element, the value of which affects a chaotic electrical property of the chaotic circuit. That is, a change in the magnitude of the circuit element changes the oscillating behavior of the chaotic transmitting circuit. The circuit element has multiple component elements, at least one of which is isolated from the chaotic circuit by a switch. The configuration is such that when the switch is switched to a first state, the magnitude has a first value and when the switch is switched to a second state, the magnitude of the component has a second value. This causes the transmitter to oscillate over multiple oscillating regimes each corresponding to one of the values. The chaotic property can be applied to a communications channel to be picked up by a receiver.
Switching the circuit element allows, essentially, a chaotic signal to be modulated. That is, a chaotic signal is tapped from the transmitter (in FIG. 1B, for example, the voltage at the junction of resistor 81 and capacitor 71), applied to a communications channel, and picked up by a receiver. The switch is controllable responsively to an information signal, whereby the chaotic carrier signal is modulated by the information signal. This information signal can be detected by applying the chaotic signal from the channel to a receiving chaotic circuit that synchronizes with the chaotic signal corresponding to one of the chaotic oscillating regimes of the transmitter, but not with another and detecting the alternations between synchronization and desynchronization.
According to another embodiment, the invention provides a communications device with a transmitting chaotic circuit configurable responsively to an information signal. The configurations are such that the transmitting chaotic circuit produces at least three different chaotic signals, each characterized by a different trajectory-versus-time characteristic. The device includes a receiver with an oscillating subportion to which the different chaotic signals can be applied to drive the oscillating subportion. The receiver has a beat detector connected to the oscillating subportion to detect a difference between a fundamental frequency of the oscillating subportion and a current chaotic signal. This allows the information signal to be detected by the detection of beats.
According to still another embodiment, the invention provides a communications receiver with a chaotic oscillator that includes an oscillator portion and a chaotic portion. The chaotic portion has a non-linear resistance element that forms a chaotic oscillator with the oscillator portion when the chaotic portion and the oscillator portions are coupled to pass a current signal therebetween. The oscillator portion is signally coupled to a communications medium carrying a modulated chaotic signal. The chaotic portion is also signally coupled directly to the communications medium such that a voltage of the communications medium is directly applied to the chaotic portion through a circuit path parallel to a coupling allowing the current signal to pass between the oscillator portion and the chaotic portion. Thus, both the chaotic and oscillating portions of the receiver are driven by the incoming chaotic signal from the communications channel.
According to still another embodiment, the invention provides a communications device with a chaotic oscillator connectable to a communications channel. The chaotic oscillator has a tank circuit with at least two capacitors and an inductor. The first of the capacitors is connected to an inductor and a second is selectively connectable to the inductor to combine respective capacitances of the capacitors through a switch. In other words, the capacitors combine their capacities responsively to the switch. The switch has an input for accepting an information signal. The information signal controls the switch so that the chaotic oscillator is selectively alternated between at least two oscillating regimes. The result is that a chaotic transmitter is modulated in accordance with the information signal to generate a chaotic signal which, at each instant, oscillates according to a selected one of the oscillating regimes. A receiver signally coupled to the communications channel has a receiving chaotic oscillator portion for each of the oscillating regimes, each portion being configured to synchronize with a respective one of the at least two chaotic signals. By detecting which portion is in synchrony with the incoming signal, the information signal can be detected.
According to still another embodiment, the invention provides a communications system with transmitting and receiving Chua circuits. At least one component of the transmitting Chua circuit includes at least two subcomponents, at least one of which is selectively isolated from the transmitting Chua circuit by a switch. This is done such that a current oscillating regime of the transmitting Chua circuit is selectively alternated between at least two respective oscillating regimes. The switch is switchable responsively to an information signal. The values of the subcomponents together with a configuration of the switch are such that one of the oscillating regimes is substantially the same as an oscillating regime of the receiving Chua circuit. The result of the latter is that the receiving Chua circuit is synchronizable with the transmitting Chua circuit when the current oscillating regime is the same oscillating regime as the receiver's. A detector is connected to detect when the receiving Chua circuit is in synchrony with a chaotic signal generated by the transmitting Chua circuit. This allows the information signal to be recovered from the chaotic signal (see, e.g., FIG. 4C).
According to still another embodiment, the invention provides a communications receiver with a chaotic oscillator that has an oscillator portion and a chaotic portion. The chaotic portion has a non-linear resistance element that forms a chaotic oscillator with the oscillator portion when the chaotic portion and the oscillator portions are coupled to pass a current signal therebetween. The oscillator portion is signally coupled to a communications medium carrying a modulated chaotic signal. The chaotic portion is also signally coupled directly to the communications medium such that a voltage of the communications medium is directly applied to the chaotic portion through a circuit path parallel to a coupling allowing the current signal to pass between the oscillator portion and the chaotic portion. Thus, both the chaotic and oscillating portions of the receiver are driven by the incoming chaotic signal from the communications channel. In this embodiment, the coupling resistance is a series of three resistors that provide the coupling from the voltage of the communications medium to the chaotic portion of the circuit and provide a voltage divider network for a comparator detector to detect voltage differences between the voltage of the communications medium and the chaotic voltage generated by the receiver chaotic portion of the system (see, e.g., FIG. 4D).
According to still another embodiment, the invention provides a communications receiver system as described in the previous paragraph except the receiver is divided into an oscillator portion and a chaotic portion which are separately driven through emitter followers from the voltage of the communications medium. This allows the voltage of the communications medium to drive the oscillator portion and the chaotic portion of the receiver without direct feedback between the two through the synchronizing resistor. This prevents spontaneous chaotic oscillation in the receiver due to a feedback path from the chaotic portion of the Chua circuit to the oscillator portion of the Chua circuit. The circuit still synchronizes since the voltage of the communications medium is coupled to both the oscillator portion of the receiver and the chaotic portion of the Chua circuit. As a result, the receiver responds only when there is a voltage on the communications medium to stimulate the system (see, e.g., FIG. 4E).
According to still another embodiment, the invention provides a communications receiver system divided into an oscillator portion and a chaotic portion. The oscillator portion is driven by the voltage of the communications medium. The voltage of the chaotic portion is fed back to the oscillator portion through an emitter follower and the synchronizing resistor in a phase locking type arrangement. This allows the voltage of the communications medium to drive the oscillator portion and the voltage of the chaotic portion of the receiver to directly feed back through the synchronizing resistor to quickly synchronize the communications system in the presence of a voltage on the communications channel. This arrangement rapidly synchronizes the communications system. The circuit still synchronizes since the voltage of the communications medium is coupled to the oscillator portion of the receiver and the chaotic portion of the Chua circuit feeds back a portion of the receiver voltage. As a result, the receiver responds only when there is a voltage on the communications medium to stimulate the system (see, e.g., FIG. 4F).
According to still another embodiment, the invention provides a communications receiver system divided into an oscillator portion and a chaotic portion except the nonlinear diode portion has only a Gb component. This allows the oscillator portion of the circuit (e.g., FIG. 41 elements 5340 and 5350) to be driven directly in accordance with the previous embodiments discussed above. By removing the discontinuity caused by diodes 652 and 655 (FIG. 6B), noise in the channel cannot cause the receiver to change scrolls. The circuit still synchronizes since the voltage of the communications medium is coupled to both the oscillator portion of the receiver and the chaotic portion of the Chua circuit. As a result, the receiver responds only when there is a voltage on the communications medium to stimulate the system (see, e.g., FIG. 41). The noise performance has been shown to be approximately an 8-10 dB improvement over a receiver with the diodes in the circuit.
DETAILED DESCRIPTION (FIRST-GENERATION EMBODIMENTS)
Referring again to FIG. 1D, discussed above, the various chaotic oscillating regimes of the Chua circuit are mapped onto an α/β parameter plane. Circuits falling in a double scroll region 60 are characterized by oscillation about two strange attractor equilibrium points ("double scroll"). Circuits falling in a spiral set of oscillating regimes 61 exhibit oscillation about only one strange attractor equilibrium point ("single scroll").
The oscillations of a circuit operating in a single-scroll attractor mode can be seen graphically in FIG. 22A, which plots two voltages V1 and V2 as a function of time for a transmitter without modulation. The two voltages are measured at points 242 and 282, respectively, as shown in one embodiment of FIG. 2A. (In this example, V2 is measured at the L-C tank circuit and V1 is measured at the nonlinear resistance element). While the circuit operates in a non-modulated state, the values of V1 and V2 vary chaotically but generally swirl about an equilibrium point.
The oscillations of a circuit operating in a double-scroll attractor mode can be seen graphically in FIG. 20A, which plots the same two voltages V1 and V2 as a function of time for a circuit that is not modulated. While the circuit operates in a non-modulated state, the values of V1 and V2 vary chaotically but generally swirl about two distinct equilibrium points.
Varying C1 causes the α/β combination to shift as indicated by arrow 130 in FIG. 1D. Varying C2 causes the α/β combination to shift as indicated by arrow 140. Varying R2 or L causes the α/β combination to shift as indicated by arrow 150. As can be seen from the diagram (FIG. 1D), the capacitance C2 of capacitor 20 can be varied over a wide range while still maintaining operation of the circuit in the double scroll oscillating regime 110. A much smaller range of values of capacitance of capacitor 15 (C1) coincides with operation in the double scroll regime 60. The wide range of capacitances for C2 (capacitor 20) that coincide with operation in the double scroll region 60 is exploited in a first embodiment of the invention discussed immediately below.
Referring now also to FIG. 2A, in a first-generation embodiment of the invention, a transmitter 200 includes a modified-Chua circuit. The transmitter 200 generates a modulated chaotic signal responsively to an information signal 236. The transmitter 200 has a primary 220 and auxiliary 237 capacitor. The auxiliary capacitor 237 is selectively switched into the circuit to add selectively to the C2 capacitance of the embedded Chua circuit. By switching the auxiliary capacitor 237 off and on, the transmitter oscillates according to a base oscillating regime and an alternate oscillating regime, respectively. By controlling optoisolator 235 responsively to an information signal 236, an alternating pattern of chaotic oscillations is generated which can be characterized as a modulation of the base chaotic oscillation. This modulated chaotic pattern can be transmitted to a receiver by transmitting a voltage V1 tapped from point 242.
Referring now also to FIG. 2B, the modulated chaotic signal is detected by a receiver 201 containing a modified-Chua circuit whose component properties are chosen to insure that the receiving circuit 201 will exhibit the same oscillating behavior as the base configuration (auxiliary capacitor 237 switched oft) of the Chua circuit of the transmitter 200. The need to match oscillating behaviors is to allow the receiving circuit 201 to synchronize with the received signal 291. One way to match the oscillating behaviors of the transmitting and receiving circuits 200 and 201 is to match the values of the components that determine the oscillating behavior. The resulting transmitted voltage V1, output from the transmitter 200, is applied as input signal 291 to the receiver 201. Note that the component values need not be matched perfectly. It has been found that the receiver's α and β can differ by as much as approximately 5 percent from the transmitter's without substantially affecting the ability of the circuits to synchronize.
The use of an optoelectronic switch 235 avoids any need for output biasing. Also, an optoelectronic switch 235 also adds no significant capacitance to the circuit. A low output biasing and low capacitance of the switching element make it easier to match the component values of the receiving and transmitting circuits 201 and 200 to insure synchronization. Alternatively, a reed switch or a field effect transistor (FET) can be used to isolate the auxiliary capacitor 237 from the main circuit. To provide a lower output biasing requirement, multiple FETs can be employed as a single switch. In the embodiment of FIGS. 2A and 2B, the modulated chaotic signal is produced by varying the capacitance C2 of the tank circuit 231 as described above. That is, in the transmitter 200, the auxiliary capacitor 237 is isolated from the main circuit by an optoelectronic switch 235, which effectively changes the capacitance of capacitor 220 in FIG. 2A.
To modulate the transmitter 200, the capacitance C2 of the tank circuit 231 is modulated by intermittently combining the capacitance of auxiliary capacitor 237 with that of capacitor 220. This capacitance corresponds to the capacitance of capacitor 20 in the unmodified Chua circuit 101; that is, to C2. By intermittently altering this capacitance responsively to the input signal 236, the Chua circuit of the transmitter 200 alternates between two different oscillating patterns.
The voltage signal V1(t) can be transmitted by any means desired. For example, the output chaotic signal V1(t) can be used to modulate an optical carrier, laser carrier, radio carrier, applied directly to a metallic (wire) interface, applied to a speaker and transmitted as sound waves, or transmitted using any other mechanism. The received signal can also be applied through an automatic gain control circuit (not shown in this embodiment) for signal conditioning.
In the embodiment of FIG. 2B, the received signal can be applied through a voltage follower 251, if desired for high input impedance, through a resistor 280, and finally to a bridge point 281 of L-C tank circuit 261. Tank circuit 261 has an inductor 248 and a capacitor 260 and can include a resistor in addition to its inherent resistance. The L-C tank circuit is connected to the chaotic portion of the embedded Chua oscillator of the receiver circuit 201 by a voltage follower 245. Current from the L-C tank circuit 261 is applied through the voltage follower 245 and a resistor 265 whose resistance matches that of the transmitting circuit resistor 225. In other words, the resistance R of the Chua circuits match.
By matching the resistance of 280 to that of resistor 225, tank circuit 261 is driven or pumped by the incoming signal exactly as tank circuit 231 is pumped by chaotic portion 222. When the C2 values of the transmitter tank circuit 231 and the receiving tank circuit 261 are identical (that is, when auxiliary capacitor 237 is isolated from the tank circuit by opto-isolator 235), a time-varying voltage at 281 synchronizes and subsequently tracks that of the incoming signal 291. This synchronization occurs because the incoming signal matches that at corresponding point 282 of the transmitting circuit, so the environments of tank circuit 261 and tank circuit 231 are the same.
Also, the voltage at point 281 is applied through a resistor 265 that is also matched to resistor 225 so the environment of the chaotic part 262 of the receiving circuit 201 is also the same as the environment of the chaotic part 222 of the transmitting circuit 200. Thus, when the transmitter is oscillating about the base strange attractor equilibrium points (base referring to the situation when the auxiliary capacitor 237 is isolated from the transmitter 200 so all the circuit elements of the transmitting 200 and receiving 201 circuits match), tank circuit 261 quickly goes into an oscillating pattern that is in synchrony with that of the transmitter's tank circuit 231. When the auxiliary capacitor 237 is switched on by closing the optoisolator 235, the transmitter circuit 200 oscillates in a pattern that is no longer matched to that of the receiver and the receiver 201 can no longer track the signal perfectly. That is, the transmitting circuit 200 and the receiving circuit 201 no longer synchronize. Note, the value of the combined capacitance C2 can be varied over the range 1 μF to 0.015 μF, a dynamic range of 66:1.
As discussed above, in one embodiment, receiving circuit 201 and the base configuration of the transmitting circuit 200 can be precisely matched, in terms of their oscillating behavior, to insure that receiver 201 will alternately synchronize and go out of synchronization responsively to the transmitter 200. That is, according to this embodiment, the transmitter's and the receiver's behaviors must be substantially matched for the transmitting and receiving circuits 200 and 201 to form an effective communications device. Since β (See FIG. 1D) varies as the square of resistance, precise resistors should be used in the transmitter 200 and the receiver 201. A combination of a 1580 ohm fixed resistor 280 and a 200 ohm, 25-turn pot 265 can be used for resistors 280 and 265 in receiver 201. This allows tuning of the receiver resistors to obtain a precise match to those in the transmitter. Note, if component values of the receiving circuit are chosen to match the values of α and β of the transmitting circuit but depart more substantially from those of the receiving circuit, the receiving circuit can still be driven into synchronization, but the response will not be as strong.
Note that the receiver circuit with the synchronizing resistor added can be configured with components that permit the receiver to produce a detectable pattern at the detector output of a chaotic signal produced by a Chua receiver whose component values do not match the transmitting circuit's precisely. A fully functional communication system can be made since the receiver can produce consistent output beat frequencies from the detector while the receiver circuit tries to follow the input signal. The receiver therefore detects signals that are not synchronized with the receiver chaotic parameters through a received process that shifts the amplitude and phase of the incoming strange attractor. This mode of operation produces a response over a wide range of α/β values as well as frequency ranges for a single specified α/β combination. One can build a vocabulary using this technique even when the chaotic signal attractor frequency is varied and α/β are different. The synchronizing resistor produces this beat frequency effect at the output of the detector.
A comparator 270 detects the alternating pattern of synchronizations and desynchronizations of the receiving circuit 201. The received signal at 286 is compared by comparator 270 with the voltage generated at 287. These two voltages are at corresponding locations 242 and 287 in the transmitting 200 and receiving 201 circuits. When the transmitting 200 and receiving 201 circuits are in synchrony, that is when the voltages follow the same time-dependent trajectory pattern, the comparator output 290 is zero. When the transmitting 200 and receiving 201 circuits are not in synchrony, that is when these voltages do not follow the same time-dependent trajectory pattern, the comparator output 290 is non-zero. A waveform is generated characterized by pulses representing the points where the two waveforms diverge by some voltage difference determined by the sensitivity of comparator 270. The sensitivity (voltage difference trigger) can be set by replacing the fixed comparator 270 with a comparator having hysterisis. Of course there can be a DC component, but that is ignored or filtered out of the comparator output 290.
The following is what occurs in the transmitter as the transmitting circuit 200 is modulated. When the auxiliary capacitor 237 is switched out of the circuit during a first time interval, the transmitting circuit oscillates around the base (strange) attractor at a particular attractor frequency. The circuit, of course, oscillates not at a specific frequency, but about a set of attractors. That is, the modulated signal is chaotically "smeared" over a range of frequencies around the current strange attractor equilibrium point or points.
In the embodiment of FIGS. 2A and 2B, the equilibrium point(s) correspond to the base value of C2, which corresponds to the capacitance of capacitor 220 alone. Note that for some of the operating regimes illustrated in FIG. 1D, the equilibrium point(s) can be dependent on the initial state also. When auxiliary capacitor 237 is switched on by the opto-isolator 235, the transmitting circuit 200 begins oscillating in a different pattern corresponding to a then-current initial state and the new value of C2 equal to the capacitance of capacitor 220 and auxiliary capacitor 237.
When a modulation pattern of successive actuations/deactuations is applied through opto-isolator 235, the transmitting circuit 200 switches between the first (base) signal and the second signal in accordance with the modulation pattern. In the receiver 201, the transmitted V1(t) signal is applied at 281 and through resistor 280. The receiver's L-C tank circuit 261 sees the received V1(t) applied through resistor 280 so that when the base-signal is transmitted, the V1(t) signal applied at 286 causes the voltage at 281, V2′(t), to follow the same time-dependent trajectory as V2(t) of the transmitting circuit 200. Given that V2′(t) in the receiving circuit is substantially identical to V2(t), the V1′(t) in the receiving circuit follows the same time-dependent trajectory as V1(t) of the transmitting circuit 200. Thus, the two circuits are synchronized when the transmitting circuit is oscillating about the base strange attractor(s). When V1(t) received corresponds to the base signal, V1(t) and V1′(t) are substantially identical and an output 290 of comparator 270, to whose inputs V1(t) and V1′(t) are respectively applied, has a nominally zero amplitude. In a practical system, the output of the comparator can have some hysteresis so that the difference must exceed some nominal level to generate a nonzero output.
When optoisolator 235 switches in the auxiliary capacitor 237, transmitting circuit 200 oscillates about the second strange attractor(s). When that happens, the receiving circuit 201 can no longer synchronize in response to the V1(t) applied at 281. This is because C2′ (the capacitance of capacitor 260) no longer matches C2 (the combined capacitance of capacitor 230 and auxiliary capacitor 237). As a result, the pattern of oscillation of V1′(t) is no longer synchronized with V1(t) transmitted and the output 290 of comparator 270 is no longer zero. The changes in output 290 between the nominal zero and nominal oscillating states can be registered through some convenient system, such as a power meter or frequency counter on the output 290, to generate a signal carrying the data in the information signal 236.
The receiving circuit 201 is very sensitive to the chaotic signal of V1(t). That is, the incoming signal can be a very low peak power signal (power within a narrow frequency band about a peak) while still cause the receiving circuit to synchronize with the transmitting circuit. Thus, receiving circuit 201 is able to follow the distinct chaotic time-dependent pattern of the received signal (when the base signal is being transmitted) and only by virtue of its inherent tendency to follow (be driven by) it, is the receiver 201 able to pick up the signal out of the noise. It is very much a resonance phenomenon, even though it is not periodic in the sense of strict linear oscillatory phenomena. This kind of resonance effect allows the power to be so spread over a range of frequencies that the transmitted signal appears to be "buried" in the noise of the channel. The signal can be detected by means of a receiving circuit whose parameters are closely matched with the transmitting circuit or by applying a large FFT engine (1024 point or larger) to the sampled data. The values of the components of the transmitting circuit must be known in order to pick up the data signal masked in the chaotic signal applied to the channel. The sensitivity of the various embodiments described below is so great that an effective communications signal can be characterized by a zero dB signal-to-noise ratio.
Note that a higher signal-to-noise ratio will allow synchronization to be achieved with less precise component matching. To achieve reliable transmission with the lowest signal-to-noise ratio, the precision of component-value-matching should be as high as practical. To achieve precise resistance matching, as mentioned, fixed resistors can be used with 25-turn fine-tuning resistors, either in parallel or series for each resistor 280 and 265.
As discussed above, a large number of different operating regimes are available by modifying C2. However, the receiver 201 may not be capable of distinguishing among these because of the inability of the receiving Chua circuit to track a received signal 291 other than the one generated by the base configuration of the transmitting circuit.
Referring now to FIGS. 3A and 3B, a transmitter 300 has a bank of auxiliary capacitors 237a-237n that can be selectively switched into the tank circuit portion of the transmitter 200′ by respective opto-isolators 235a-235n. Opto-isolators 235a-235n are controlled by a controller 201 responsively to the input signal 236. In all other respects, transmitter 200′ is identical to transmitter 200 of FIG. 2A.
To produce a modulated signal, controller 201 is programmed to receive a data word at 236 and control opto-isolators 235a-235n to switch one or more of them into the circuit to produce a particular chaotic pattern. For example, if opto-isolators 235a and 235b are actuated to switch in auxiliary capacitors 237a and 237b, the capacitances of capacitors 220, 237a, and 237b are combined to produce a corresponding chaotic signal. This unique pattern forms one word or symbol of a vocabulary of possible ones that can be generated by actuating opto-isolators according to the various possible combinations.
Receiver 301 includes a bank of receivers 201a-201n, each the same as shown in FIG. 3B but with different component values chosen to allow each to resonate with a corresponding configuration of the transmitter 200′. That is, the component values for each receiver 201a-201n, are chosen such that each will synchronize with one word of the vocabulary of chaotic signals generated by the transmitter 200′. The outputs of each receiver 201a-201n each correspond to the output 290 of the comparator of FIG. 2B. These are individually applied to a detector 271 that determines which of the outputs 290a-290n is in synchrony with the transmitter 200′ at a given point in time. Detector 271 determines this by indicating which output 290a-290n is nominally equal to zero.
Output 290′ can be a stream of digital words each corresponding to the word transmitted. Thus, at any given instant, signal 290′ can indicate the current, or most recently received, word being applied in the received signal to input 291′. The number of bits that can be transmitted with each cycle of the opto-isolators 235a-235n is equal to the log2 (log base-2) of the number of different capacitor values C2 forming the vocabulary. In this embodiment, the number of receivers 201a-201n matches the size of the vocabulary, that is, the number of symbols or words generated by the transmitter 200′.
Referring to FIGS. 4A and 4B, an alternative embodiment of the invention also produces a vocabulary of signal-words. In this embodiment, the values of the various components are chosen so that all "words" of the vocabulary are produced by configurations that maintain the same α-β combinations. That is, the values of C1, C2, R, and L of the transmitting circuit 400 are varied to produce a variety of selectable chaotic oscillation patterns, each of which coincides with the same α/β combinations. A bank of parallel inductors 330 can be provided that can be switched in by respective opto-isolators to add to the inductance of the fixed inductor 330′. To this end, a bank of parallel capacitors 320 can be provided that can be switched in by respective opto-isolators to add to the capacitance of the fixed capacitor 320′. A bank of parallel capacitors 315 can be provided that can be switched in by respective opto-isolators to add to the capacitance of the fixed capacitor 315′. Finally, a bank of parallel resistors 325 can be provided that can be switched in by respective opto-isolators to change the resistance of fixed resistor 325′.
In the embodiment of FIGS. 4A and 4B, instead of modulating the behavior of the transmitting circuit by varying only one component, the values of combinations of components determining C1, C2, R, and L are varied in such a way as to maintain α=C2/C1 and β=R2C2/L constant under the control of a controller 305. That is, values of the auxiliary capacitors, resistors, and inductors in banks 315, 320, 325, and 330 are chosen so that when predefined combinations of the corresponding opto-isolators are actuated, the oscillating frequency changes (See equation (1), below), but α and β remain the same.
In a first embodiment, the inductance L and the capacitances C1 and C2, only, are varied, maintaining R constant. That is, only the opto-isolators in banks 315, 320, and 330 are switched to modulate the circuit. The fundamental frequency of the tank circuit, given by
varies even though the oscillating regime remains constant. In this embodiment, there is no need to vary R to maintain a constant α and β. Also, the non-linear resistor 310 components do not have to be varied. In one embodiment of the transmitter 400, one combination of values of C1, C2, and L (corresponding to one state of the opto-isolator switches) can be identical to the combination of values corresponding to a receiving circuit 301. This combination of values causes the transmitting circuit to oscillate at a base frequency corresponding to the frequency of the receiver. In a first alternative embodiment, the values of C1, C2, and L are varied, keeping R constant.
The receiver 401, shown in FIG. 4B, consists of a tank circuit 361 and a fast Fourier transform FFT computer 379. The component values of tank circuit 361 are chosen to match the α/β combinations of the transmitter 400. The value of resistor 380, in the first embodiment, can be chosen to match that of the fixed R value of the transmitter. (As mentioned above, R is fixed in the first embodiment. The embodiment depicted in FIG. 4a is capable of variable R values, but a single fixed value is used in the first embodiment. If a fixed R value is to be used, the bank of resistors 325 could be omitted leaving only a single resistor 325′.)
The output 390 of the transmitter 400 is applied (through some transmission medium) to an input 391 of the receiver. The FFT block 379 determines the word transmitted by the transmitter by detecting the difference between the fundamental frequency, given by equation (1), of the instant configuration of the transmitter 400, and the fixed configuration of the tank circuit 361. Fast Fourier transform (FFT) block 379 "sees" this frequency difference because tank circuit 361 attempts to follow the trajectory of the incoming signal applied through resistance 380. Since, however, the incoming signal is at a different frequency, tank circuit 361 is not able to maintain this trajectory and it "falls off the rails." The frequency with which the tank circuit alternately follows and uncouples from the incoming signal applied at 391 is equal to the difference between the fundamental attractor frequency of the transmitter 400 and that of the tank circuit 361. A peak at this difference frequency is indicated by the output 378 of the FFT block. Thus, output 378 indicates each word generated by the transmitter 400.
In an alternative embodiment, the value of R (the resistance determined by the configuration of resistor bank 325) of the transmitter 400 is varied also. In this case, the value of resistor 380 of the receiver 301 can be any of the values used for R in the transmitter 400 or another value.
In the receiving circuit 201 of FIGS. 2A and 2B, the Chua circuit oscillates in synchrony with that of the transmitter 200 when the base signal is received. The resulting output 290 from the comparator 270, as discussed, is a flat (nominally zero) output. However, when the transmitter 200 is placed in a configuration such that it a signal other than the base signal, the comparator output 290 of the receiver 201 becomes substantially non-zero and, also, chaotic due to the lack of synchronization. This would also be the case if the transmitter 400 were connected to the receiver 201 of the prior embodiment. Any signal other than ones that drive the receiver into synchronization will produce a non-zero chaotic signal at the output 290. In other words, if this output 290 were viewed on an oscilloscope, the trace would appear chaotic and it would be difficult if not impossible to tell which "word" of the vocabulary of strange attractors was generating the transmitted signal. This is because V1′ can no longer synchronize with the V1 transmitted.
In the combination of the transmitter 400 and the receiver 301 of the FIG. 4A/4B embodiment, however, the transmitter drives the tank circuit 361 for part of the tank circuit's fundamental cycle but subsequently skips ahead or lags behind (unless, of course, the fundamental frequency of the transmitter is the same as that of the receiver) the driving input voltage applied at 391. This happens at the frequency difference (a beat frequency; the difference between the fundamental frequency of the transmitter (e.g., (1)) and the fundamental frequency of the receiver) and thus forms a detector. The reason the receiver is able to follow the transmitter in this way is that the α and β of the transmitter and receiver are matched and the natural frequency of the tank circuit is an integer multiple of the frequency of the transmitting circuit given by equation (1).
In addition to using a FFT calculator, alternative ways of detecting the beat frequency include an amplitude detector connected across the same terminals as the FFT calculator and which outputs to a counter. The counter can count the number of beats to determine the frequency of the transmitter. Various other alternatives would occur to a practitioner skilled in the art of signal conditioning.
Referring now to FIGS. 4A and 4C, an alternative receiver design employs a synchronizing resistor 385 and comparator input resistors 386 and 387. In this embodiment, the received signal, corresponding to a signal other than the base strange attractor, is applied to the chaotic portion 362 through the synchronizing resistor 385. In the embodiment of FIG. 4C, it has been found, through experiment, that the synchronizing resistor 385 can be adjusted to optimize the ability of the receiver circuit 402 to follow the trajectory of the transmitter signal at portions thereof so that the zero levels of the output 390 are clean and clear. The application of the received |
