Receiver estimation engine for a chaotic system

• US 6,744,893 B1
• Filed: 08/25/1999
• Issued: 06/01/2004
• Est. Priority Date: 08/25/1999
• Status: Expired due to Term

• Current Assignee: Southwest Research Institute
• Original Assignee: Southwest Research Institute
• Inventors: Fleming-Dahl, Arthur
• Primary Examiner(s): Barrón, Gilberto
• Assistant Examiner(s): Zand, Kambiz
• Application Number:
  US09/382,523
• Time in Patent Office: 1,742 Days
• Field of Search: 380/263, 380/46, 380/274
• US Class Current: 380/263
• CPC Class Codes: H04L 27/001 using chaotic signals for secret or secure communication H04L9/001

Abstract

A chaotic receiver estimation engine and method of use. The estimation engine synchronizes and recovers data and performs its decision and tracking processes by mapping probability calculation results onto chaotic dynamics via a strange attractor geometrical approximation. Restrictive standard chaotic synchronization requirements of either a stable/unstable subspace separation or a chaotic system inversion are not required. The receiver determines and models both the logical zero and logical one versions of the strange attractor and the transmitted chaotic sequence probability density function (PDF). Two estimates of the transmitted value are created from each received iterate by probability and the transmitted PDF calculations. A third estimate is generated from the chaotic processing of the previous receiver final decisions. The three estimates are combined using a probability-based weighted average to form the initial current decision. A final current decision incorporates chaotic dynamics by mapping the initial decision onto the geometrical model of the attractors via a minimum Euclidean distance metric.

Claims

1. A nonlinear chaotic receiver comprising a component for receiving a chaotic encoded digital signal transmission from a chaotic transmitter, synchronizing the chaotic receiver with the chaotic transmitter and recovering the contents of the encoded chaotic digital signal transmission using a chaotic strange attractor model and a chaotic probability density function model, wherein:

a. synchronization of the chaotic receiver with the chaotic transmitter and recovery of the contents of the encoded chaotic digital signal transmission occurs in the same calculations and results concurrently from the same calculations,

b. the chaotic encoded digital signal transmission is a data sequence comprising a first through N number of iterates, wherein the first iterate represents a first value in the data sequence and the Nth iterate represents a last value in the data sequence; and

c. the chaotic strange attractor model comprises;

i. a strange attractor generated by combining Henon and mirrored Henon attractors, wherein the Henon and mirrored Henon attractors are generated by starting with one or more arbitrary points within an area of phase space that stretches and folds back onto itself, and inputting the points to a set of Henon equations, the result being the Henon attractor, and taking a mirror image of the Henon attractor to form the mirrored Henon attractor;

ii. the strange attractor represented as a set of parabolas displayed on a Cartesian coordinate system; and

iii. the parabolic regions of validity of the strange attractor determined.

2. A nonlinear chaotic receiver according to claim 1, wherein the chaotic attractor model further comprises determining any existing fixed point on the strange attractor that repeats itself through multiple iterations of the chaotic transmission.

3. A nonlinear chaotic receiver according to claim 1, wherein the data sequence of the received chaotic encoded digital signal transmission is randomly selected from the group consisting of a first logical state for the Henon attractor and a second logical state for the mirrored Henon attractor.

4. A nonlinear chaotic receiver according to claim 3, wherein the chaotic probability density function models the probability of the first and second logical states of the Henon and mirrored Henon attractors as a random selection.

5. A nonlinear chaotic receiver according to claim 1, wherein the strange attractor is generated by using image calculations on a Henon map.

6. A nonlinear chaotic receiver according to claim 1, wherein the strange attractor is represented in a Cartesian coordinate system as a crescent-like shape which occupies all four quadrants of the Cartesian coordinate system.

7. A nonlinear chaotic receiver according to claim 6, wherein the strange attractor is modeled as a set of four parabolas.

8. A nonlinear chaotic receiver comprising a component for receiving a chaotic encoded digital signal transmission from a chaotic transmitter, synchronizing the chaotic receiver with the chaotic transmitter and recovering the contents of the encoded chaotic digital signal transmission using a chaotic strange attractor model and a chaotic probability density function model, wherein:

a. synchronization of the chaotic receiver with the chaotic transmitter and recovery of the contents of the encoded chaotic digital signal transmission occurs in the same calculations and results concurrently from the same calculations;

b. the chaotic encoded digital signal transmission is a data sequence comprising a first through N number of iterates, wherein the first iterate represents a first value in the data sequence and the Nth iterate represents a last value in the data sequence;

the nonlinear chaotic receiver further comprising means for determining the contents of the encoded chaotic digital signal transmission including;

c. three estimates generated for each iterate received and an initial decision calculated for each iterate;

d. the initial decision mapped onto the chaotic attractor to form a final decision for each estimate; and

e. a discount weight calculated to reduce the impact of the initial decisions whose receive values are close to zero.

9. A nonlinear chaotic receiver according to claim 8, wherein the three estimates comprise:

a. a first estimate which is the value of the received iterate;

b. a second estimate which is a minimum error probabilistic estimate; and

c. a third estimate which is a final decision of the previous iterate processed through Henon and mirrored Henon equations.

10. A nonlinear chaotic receiver according to claim 9, wherein the initial decision for each iterate comprises combining the three estimates to form the initial decision through a weighted average using probability calculations using the first, second and third estimates.

11. A nonlinear chaotic receiver according to claim 8, further comprising means for determining a synchronization estimate to synchronize the chaotic receiver with a chaotic transmitter that generates the encoded chaotic digital signal transmission.

12. A nonlinear chaotic receiver according to claim 11, wherein the means for determining a synchronization estimate comprises synchronizing the chaotic receiver with a plurality of chaotic processes used in generating the observed chaotic quantity.

13. A nonlinear chaotic receiver according to claim 12, wherein the means for determining a synchronization estimate comprises determining the synchronization data by mapping an initial decision onto the chaotic attractor to generate a final decision for each estimate and the synchronization data is the chaotic system in which the final decision resides.

14. A nonlinear chaotic receiver comprising:

a. a receiver estimation engine for synchronizing the chaotic receiver with a chaotic transmitter and recovering the value of an encoded chaotic digital signal transmission, the receiver estimation engine comprising;

i. a signal-to-noise ratio (SNR) estimator;

ii. a maximum a posteriori (MAP) estimator;

iii. a feedback estimator;

iv. wherein the chaotic receiver and the chaotic transmitter synchronization and the encoded digital signal transmission recovery occur concurrently while executing the same set of calculations within the receiver estimation engine;

b. a decision and weighting function within the receiver estimation engine comprising;

i. probability of transmit value estimates determined using the SNR estimator, the MAP estimator and the feedback estimator for each received iterate;

ii. an initial decision calculated for the iterate;

iii. a discount weight calculated for a final decision for received values in close proximity to zero;

c. within the receiver estimation engine, the final estimate of each iterate determined based on the initial decision from the decision and weighting function; and

d. within the receiver estimation engine, the final decision of iterates 1 through N combined to recover the encoded digital signal transmission data sequence.

15. A nonlinear chaotic receiver according to claim 14, wherein the SNR estimator comprises:

a. an instantaneous maximum likelihood SNR;

b. a current average SNR value calculated as a running weighted average of the instantaneous maximum likelihood SNR; and

c. the current average SNR value is used as feedback to the instantaneous maximum likelihood SNR to determine if a local instantaneous maximum likelihood value close to the current average SNR value exists.

16. A nonlinear chaotic receiver according to claim 15, wherein the instantaneous maximum likelihood SNR is determined for each iterate using a lookup-table.

17. A nonlinear chaotic receiver according to claim 15, wherein the instantaneous maximum likelihood SNR for each iterate is determined using a Newton-Raphson iterative root approximation optimization technique.

18. A nonlinear chaotic receiver according to claim 15, wherein the instantaneous maximum likelihood SNR for each iterate is determined using a modified Newton-Raphson root approximation.

19. A nonlinear chaotic receiver according to claim 14, wherein the MAP estimator comprises:

a. a transmit probability density function window constructed for each iterate centered about the received value using channel noise power and probability density function characteristics; and

b. a maximum value of a windowed transmit probability density function.

20. A nonlinear chaotic receiver according to claim 19, wherein the probability density function is modeled as a summation of deterministic functions.

21. A nonlinear chaotic receiver according to claim 19, wherein the modeled transmit probability density function includes using weighted Gaussian functions to approximate PDF defining characteristics.

22. A nonlinear chaotic receiver according to claim 19, wherein the MAP estimator comprises an empirical windowed transmit PDF waveform stored in memory at receiver initialization.

23. A nonlinear chaotic receiver according to claim 19, wherein the MAP estimator comprises a windowed transmit PDF waveform stored in memory at receiver initialization, wherein a transmit PDF waveform is generated from a summation of deterministic functions.

24. A nonlinear chaotic receiver according to claim 19, wherein the MAP estimator comprises a transmit PDF waveform windowed via in-line computations of closed form equations modeling the transmit PDF waveform as a summation of weighted Gaussian functions.

25. A nonlinear chaotic receiver according to claim 19, wherein the MAP estimator comprises a simplified MAP estimator having a calculation process that achieves computational efficiency on Gaussian noise probability density functions via the natural logarithm function.

26. A nonlinear chaotic receiver according to claim 25, wherein the simplified MAP estimator comprises the windowed natural logarithm of an empirically determined transmit PDF waveform.

27. A nonlinear chaotic receiver according to claim 25, wherein the simplified MAP estimator comprises the windowed natural logarithm of a transmit PDF model waveform consisting of a summation of deterministic functions.

28. A nonlinear receiver according to claim 15, wherein the instantaneous maximum likelihood SNR estimate comprises:

a. a two dimensional probability model of the received probability density function;

b. the two dimensional model sliced along an SNR axis;

c. the maximum likelihood SNR for the current received value determined by using the two dimensional probability model in a Newton-Raphson iteration; and

d. a current average SNR value used as feedback to the instantaneous maximum likelihood SNR estimator to determine if a local maximum instantaneous likelihood value close to the current average SNR value exists.

29. A method in a computer system of receiving and recovering the contents of a chaotic encoded digital signal transmission comprising:

a. receiving a chaotic encoded digital signal transmission from a chaotic transmitter;

b. synchronizing the chaotic receiver with the chaotic transmitter; and

c. recovering the contents of the encoded chaotic digital signal transmission using a chaotic strange attractor model and a chaotic probability density function model,

d. wherein;

i. the synchronizing of the chaotic receiver with the chaotic transmitter and recovering of the contents of the encoded chaotic digital signal transmission occurs in the same calculations and results concurrently from the same calculations;

ii. the receiving a chaotic encoded digital signal transmission is a data sequence comprising a first through N number of iterates, wherein the first iterate represents a first value in the data sequence and the Nth iterate represents a last value in the data sequence;

iii. the using of a chaotic strange attractor model comprises;

1. generating a strange attractor by combining Henon and mirrored Henon attractors, wherein the Henon and mirrored Henon attractors are generated by starting with one or more arbitrary points within an area of phase space that stretches and folds back onto itself, and inputting the points to a set of Henon equations, the result being the Henon attractor, and taking a mirror image of the Henon attractor to form the mirrored Henon attractor;

2. representing the strange attractor as a set of parabolas displayed on a Cartesian coordinate system; and

3. determining the parabolic regions of validity of the strange attractor.

30. The method according to claim 29, wherein the chaotic strange attractor model comprises:

a. a strange attractor generated by combining Henon and mirrored Henon attractors, wherein the Henon and mirrored Henon attractors are generated by starting with one or more arbitrary points within an area of phase space that stretches and folds back onto itself, and inputting the points to a set of Henon equations, the result being the Henon attractor, and taking a mirror image of the Henon attractor to form the mirrored Henon attractor;

b. representing the strange attractor as a set of parabolas displayed on a Cartesian coordinate system; and

c. determining the parabolic regions of validity of the strange attractor.

31. The method according to claim 29, wherein the chaotic attracter model further comprises determining any existing fixed point on the strange attractor that repeats itself through multiple iterations of the chaotic transmission.

32. The method according to claim 29, wherein the data sequence of the received chaotic encoded digital signal transmission is randomly selected from the group consisting of a first logical state for the Henon attractor and a second logical state for the mirrored Henon attractor.

33. The method according to claim 31, wherein the chaotic probability density function models the probability of the first and second logical states of the Henon and mirrored Henon attractors as a random selection.

34. The method according to claim 29, wherein the strange attractor is generated by using image calculations on a Henon map.

35. The method according to claim 29, wherein the strange attractor is represented in a Cartesian coordinate system as a crescent-like shape which occupies all four quadrants of the Cartesian coordinate system.

36. The method according to claim 34, wherein the strange attractor is modeled as a set of four parabolas.

37. A method according to claim 36, wherein the initial decision is generated using a decision and weighting function.

60. A nonlinear receiver according to claim 37, wherein the synchronizer and final decision function incorporates estimation methods with chaotic dynamics to determine a maximum likelihood chaotic quantity from an observed quantity that is chaotic in nature.

62. The method according to claim 37, wherein the synchronizer and final decision function comprises combining synchronization and message data demodulation into a single set of calculations.

63. The method according to claim 37, wherein the attractors are modeled as a set of geometrical functions having defined regions of validity.

64. The method of claim 62, wherein the synchronizer and final decision function uses an initial decision and maps Cartesian coordinates of the initial decision onto a Cartesian coordinate representation of a chaotic strange attractor.

65. The method according to claim 64, wherein the chaotic strange attractor comprises:

i. generating the strange attractor by combining Henon and mirrored Henon attractors, wherein the Henon and mirrored Henon attractors are generated by starting with one or more arbitrary points within an area of phase space that stretches and folds back onto itself, and inputting the points to a set of Henon equations, the result being the Henon attractor, and taking a mirror image of the Henon attractor to form the mirrored Henon attractor;

j. representing the strange attractor as a set of parabolas displayed on a Cartesian coordinate system; and

k. determining the parabolic regions of validity of the strange attractor.

66. The method according to claim 65, wherein the strange attractor is modeled as a set of four parabolas.

67. The method according to claim 64, wherein a final decision is determined by mapping the initial decision onto the chaotic attractor to form a final decision for each estimate.

38. A method in a computer system of receiving and recovering the contents of a chaotic encoded digital signal transmission comprising:

a. receiving a chaotic encoded digital signal transmission from a chaotic transmitter;

b. synchronizing the chaotic receiver with the chaotic transmitter; and

c. recovering the contents of the encoded chaotic digital signal transmission using a chaotic strange attractor model and a chaotic probability density function model

d. wherein;

i. the synchronizing of the chaotic receiver with the chaotic transmitter and recovering of the contents of the encoded chaotic digital signal transmission occurs in the same calculations and results concurrently from the same calculations;

ii. the receiving a chaotic encoded digital signal transmission is a data sequence comprising a first through N number of iterates, wherein the first iterate represents a first value in the data sequence and the Nth iterate represents a last value in the data sequence; and

e. determining the contents of the encoded chaotic digital signal transmission by;

i. generating three estimates for each iterate received and calculating an initial decision for each iterate;

ii. mapping the initial decision on onto the chaotic attractor to form a final decision for each estimate; and

iii. calculating a discount weight to reduce the impact of the initial decisions whose receive values are close to zero.

39. The method according to claim 38, wherein the three estimates comprise:

a. a first estimate which is the value of the received iterate;

b. a second estimate which is a minimum error probabilistic estimate; and

c. a third estimate which is a final decision of the previous iterate processed through Henon and mirrored Henon equations.

40. The method according to claim 39, wherein the initial decision for each iterate comprises combining the three estimates to form the initial decision through a weighted average using probability calculations using the first, second and third estimates.

41. The method according to claim 38, further comprising determining a synchronization estimate to synchronize the chaotic receiver with a chaotic transmitter that generates the encoded chaotic digital signal transmission.

42. The method according to claim 41, wherein the determining a synchronization estimate further comprises synchronizing the chaotic receiver with a plurality of chaotic processes used in generating the observed chaotic quantity.

43. The method according to claim 42, wherein the determining a synchronization estimate comprises determining the synchronization data by mapping an initial decision onto the chaotic attractor to generate a final decision for each estimate and the synchronization data is the chaotic system in which the final decision resides.

44. A method in computer system of receiving and recovering the contents of a chaotic encoded digital signal transmission comprising:

a. synchronizing a chaotic receiver with a chaotic transmitter and recovering an encoded chaotic digital signal transmission using a receiver estimation engine,

said engine comprising;

i. a signal-to-noise ratio (SNR) estimator;

ii. a maximum a posteriori (MAP) estimator;

iii. a feedback estimator;

iv. wherein the chaotic receiver and the chaotic transmitter are synchronized and the encoded digital signal transmission are recovered concurrently when executing the same set of calculations within the receiver estimation engine;

b. using a decision and weighting function within the receiver estimation engine comprising;

i. determining the probability of transmit value estimates using the SNR estimator, the MAP estimator and the feedback estimator for each received iterate;

ii. calculating an initial decision for the iterate;

iii. calculating a discount weight for a final decision for received values in close proximity to zero;

c. determining the final value of each iterate based on the initial decision from the decision and weighting function; and

d. combining the final decision of iterates 1 through N to recover the encoded digital signal transmission data sequence.

49. The method according to claim 44, wherein the MAP estimator comprises:

a. determining and storing the transmit sequence PDF;

b. determining the channel noise PDF;

c. constructing a basic window with channel noise PDF reversed along a ransom variable axis;

d. constructing an iterated window by centering the basic window on a currently received iterate value;

e. multiplying the transmit PDF by the iterate window to form a windowed transmit PDF; and

f. setting the MAP estimate to a random variable value corresponding to the maximum PDF value in the windowed transmit PDF.

50. The method according to claim 49, wherein the PDF is modeled as a summation of deterministic functions.

51. The method according to claim 49, wherein modeling the transmit probability density function comprises using a weighted Gaussian function to approximate PDF defining characteristics.

52. The method according to claim 49, wherein the MAP estimator comprises windowing an empirical transmit PDF waveform stored in memory at receiver initialization.

53. The method according to claim 49, wherein the MAP estimator comprises windowing a transmit PDF waveform stored in memory at receiver initialization, where the transmit PDF waveform is generated from a summation of deterministic functions.

54. The method according to claim 49, wherein the MAP estimator comprises windowing a transmit PDF waveform via in-line computations of closed form equations modeling the transmit PDF waveform as a summation of weighted Gaussian functions.

55. The method according to claim 49, wherein the MAP estimator comprises a simplified MAP estimator having a calculation process that achieves computational efficiency on Gaussian noise probability density functions via the natural logarithm function.

56. The method according to claim 55, wherein the simplified MAP estimator windows the natural logarithm of an empirically determined transmit PDF waveform.

57. The method according to claim 55, wherein the simplified MAP estimator windows the natural logarithm of a transmit PDF model waveform consisting of a summation of deterministic functions.

58. The method according to claim 44, wherein the MAP estimator is a simplified MAP estimator comprising:

a. at receiver initialization;

i. determining the transmit sequence PDF;

ii. taking and storing the natural logarithm of the transmit sequence PDF;

b. determining channel noise power;

c. processing equation (104) for the maximum value in the windowed transmit PDF; and

d. processing equation (100) to find the MAP estimate where the MAP estimate is a random variable value corresponding to the maximum PDF value resulting from equation (104).

45. The method according to claim 92, wherein the SNR estimator comprises:

a. calculating an instantaneous maximum likelihood SNR;

b. calculating a current average SNR value as a running weighted average of the instantaneous maximum likelihood SNR; and

c. using the current average SNR value as feedback to the instantaneous maximum likelihood SNR to determine if a local instantaneous maximum likelihood value close to the current average SNR value exists.

46. The method according to claim 45, wherein the instantaneous maximum likelihood SNR is determined for each iterate using a lookup-table.

47. The method according to claim 45, wherein the instantaneous maximum likelihood SNR for each iterate is determined using a Newton-Raphson iterative root approximation optimization technique.

48. The method according to claim 45, wherein the instantaneous maximum likelihood SNR for each iterate is determined using a modified Newton-Raphson root approximation.

59. The method according to claim 45, wherein the instantaneous maximum likelihood SNR estimate comprises:

e. constructing a two dimensional probability model of the received probability density function;

f. slicing the two dimensional model along an SNR axis;

g. determining the maximum likelihood SNR for the current received value by using the two dimensional probability model in a Newton-Raphson iteration; and

h. using a current average SNR value as feedback to the instantaneous maximum likelihood SNR estimator to determine if a local maximum instantaneous likelihood value close to the current average SNR value exists.

61. A computer-readable medium containing instructions for controlling a computer system for receiving and recovering the contents of a chaotic encoded digital signal transmission comprising:

e. recovering the value of an encoded chaotic digital signal transmission using a receiver estimation engine, said engine comprising;

i. a signal-to-noise ratio (SNR) estimator;

ii. a maximum a posteriori (MAP) estimator;

iii. a feedback estimator;

f. using a decision and weighting function within the receiver estimation engine comprising;

i. determining the probability of a received value using the SNR estimator, the MAP estimator and the feedback estimator for each received iterate;

ii. calculating an initial decision for the iterate;

iii. calculating a discount weight for a final decision for received values in close proximity to zero;

g. determining the final value of each iterate based on the initial decision from the decision and weighting function; and

h. combining the final decision of iterates 1 through N to recover the encoded digital signal transmission data sequence.