Spread Spectrum Communications System and Method Utilizing Chaotic Sequence

• US 20080304666A1
• Filed: 06/07/2007
• Published: 12/11/2008
• Est. Priority Date: 06/07/2007
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J., Chester, David B.
• Granted Patent: US 7,974,413 B2
• Time in Patent Office: Days
• US Class Current: 380/263
• CPC Class Codes: H04B 1/7075 with code phase acquisition
• CPC Class Codes: H04J 13/0003 Code application, i.e. aspects relating to how codes are applied to form multiplexed channels
• CPC Class Codes: H04J 13/0018 Chaotic
• CPC Class Codes: H04J 13/10 Code generation

Abstract

A method is provided for generating a coherent chaotic sequence spread spectrum communications system. The method includes phase modulating a carrier with information symbols. The method also includes generating a string of discrete time chaotic samples. The method further includes modulating the carrier in a chaotic manner using the string of discrete time chaotic samples. Each of the discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols. The generating step includes selecting a plurality of polynomial equations. The generating step also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The generating step further includes determining a series of digits in the weighted number system based on the RNS residue values. The method further includes synchronizing the chaos generated at the receiver with that generated at the transmitter without periodic transfer of state update information.

Claims

1. A method for coherently modulating and demodulating a chaotic sequence spread spectrum signal, comprising:

channel encoding a carrier with a plurality of information symbols;

generating an identical string of discrete time chaotic samples at a transmitter and a receiver by

selecting a plurality of polynomial equations;

using residue number system (RNS) arithmetic operations to respectively determine a plurality of solutions for said plurality of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values; and

determining a series of digits in a weighted number system based on said plurality of RNS residue values;

modulating said carrier in a chaotic manner using said string of discrete time chaotic samples, each of said discrete time chaotic samples having a shorter sample time interval than a duration of said plurality of information symbols;

utilizing an accurate time reference to minimize a timing difference uncertainty between each said string of discrete time chaotic samples generated at said transmitter and said receiver;

synchronizing each said string of discrete time chaotic samples in time and frequency; and

maintaining synchronization of said string of discrete time chaotic samples in time and frequency at each said transmitter and said receiver for a duration of an information transfer.

2. The method according to claim 1, further comprising using a Chinese Remainder Theorem process to determine a series of digits in said weighted number system based on said plurality of RNS residue values.

3. The method according to claim 1, wherein said determining a series of digits step further comprises identifying a number in said weighted number system that is defined by said plurality of RNS residue values.

4. The method according to claim 1, wherein said determining a series of digits step further comprises identifying a truncated portion of a number in said weighted number system that is defined by said plurality of RNS residue values.

5. The method according to claim 4, further comprising selecting said truncated portion to include any serially arranged set of digits comprising a portion of said number in said weighted number system.

6. The method according to claim 5, further comprising selecting said truncated portion exclusive of a most significant digit comprising said number in said weighted number system.

7. The method according to claim 1, further comprising selecting a value for each of N moduli in a RNS used for solving each of said plurality of polynomial equations.

8. The method according to claim 7, further comprising selecting each said modulus for each of said plurality of polynomial equations so that each said polynomial equation is irreducible.

9. The method according to claim 7, further comprising selecting each said modulus for each of said plurality of polynomial equations so that solutions iteratively computed via a feedback mechanism for said polynomial equations are chaotic.

10. The method according to claim 1, further comprising selecting said polynomial equations to include at least a cubic type polynomial equation.

11. The method according to claim 1, further comprising selecting each of said plurality of polynomial equations to be identical exclusive of a constant value.

12. The method according to claim 11, further comprising selecting said constant value so that a polynomial equation is irreducible for a predefined modulus.

13. The method according to claim 1, further comprising selecting said polynomial equation to be at least one of a constant or varying function of time.

14. The method according to claim 1, further comprising iteratively computing said plurality of solutions using a feedback mechanism.

15. The method according to claim 14, further comprising selecting said feedback mechanism to include selectively defining a value of a variable of a polynomial equation for each solution iteratively computed, said value based on a previous iteratively computed solution of said polynomial equation.

16. The method according to claim 1, wherein said weighted number system is a binary number system.

17. The method according to claim 1, further comprising synchronizing said strings of discrete time chaotic samples at said receiver exclusive of a constant or periodic transfer of state update information.

18. A system for coherently modulating and demodulating a chaotic sequence spread spectrum signal, comprising:

a channel encoder configured for channel encoding a carrier responsive to a plurality of information symbols;

a chaotic sequence generator configured for generating a continuous string of discrete time samples, each of said discrete time samples having a shorter sample time interval than a duration said plurality of information symbols, said chaotic sequence generator comprising;

a computing means configured for using residue number system (RNS) arithmetic operations to respectively determine a plurality of solutions for a plurality of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values; and

a mapping means configured for determining a series of digits in a weighted number system based on said plurality of RNS residue values;

a multiplier operatively coupled to said chaotic sequence generator and said channel encoder, said multiplier configured for modulating said carrier in a chaotic manner using said string of discrete time samples;

an accurate time reference configured for minimizing a timing difference uncertainty between said strings of discrete time chaotic samples generated at said transmitter and said receiver; and

at least one processing means configured for initially synchronizing said strings of discrete time chaotic samples in time and frequency and for maintaining synchronization of each said string of discrete time chaotic samples in time and frequency at each of said transmitter and said receiver for a duration of an information transfer.

19. The system according to claim 18, wherein said mapping means is further configured for determining a series of digits in said weighted number system based on said plurality of RNS residue values using a Chinese Remainder Theorem process.

20. The system according to claim 18, wherein said mapping means is further configured for identifying a number in said weighted number system that is defined by said plurality of RNS residue values.

21. The system according to claim 18, wherein said mapping means is further configured for identifying a truncated portion of a number in said weighted number system that is defined by said plurality of RNS residue values.

22. The system according to claim 21, wherein said mapping means is further configured for selecting said truncated portion to include any serially arranged set of digits comprising a portion of said number in said weighted number system.

23. The system according to claim 22, wherein said mapping means is further configured for selecting said truncated portion exclusive of a most significant digit when all possible weighted numbers represented by greater than P-1 bits but less than P bits, said P is a fewest number of bits required to achieve a binary representation of said weighted numbers.

24. The system according to claim 18, wherein said computing means is further configured for utilizing a modulus selected for each of said plurality of polynomial equations so that each said polynomial equation is irreducible.

25. The system according to claim 18, wherein said computing means is further configured for utilizing a modulus selected for each of said plurality of polynomial equations so that solutions iteratively computed via a feedback mechanism for said polynomial equations are chaotic.

26. The system according to claim 18, wherein said plurality of polynomial equations include at least a cubic type polynomial equation.

27. The system according to claim 18, wherein said plurality of polynomial equations are identical exclusive of a constant value.

28. The system according to claim 27, wherein said constant value is selected so that a polynomial equation is irreducible for a predefined modulus.

29. The system according to claim 18, wherein said plurality of polynomial equations are at least one of a constant or varying function of time.

30. The system according to claim 18, further comprising a feedback mechanism configured for selectively defining a variable “

x”

of a polynomial equation as a solution computed in a previous iteration.