Multiple access communication system using chaotic signals and method for generating and extracting chaotic signals

• US 6,999,445 B1
• Filed: 05/27/1999
• Issued: 02/14/2006
• Est. Priority Date: 05/27/1999
• Status: Expired due to Fees

• Current Assignee: Apple Inc.
• Original Assignee: Nortel Networks Corporation
• Inventors: Dmitriev, Alexander Sergeevich, Starkov, Sergey Olegovich, Shirokov, Maxim Evgenyevich, Panas, Andrey Ivanovich, Li, Yong, Tong, Wen, Wang, Rui R.
• Primary Examiner(s): Patel, Ajit
• Assistant Examiner(s): NGUYEN, BINH QUOC
• Application Number:
  US09/979,834
• Time in Patent Office: 2,455 Days
• Field of Search: 370/342, 370/203, 370/335, 370/537, 370/320, 370341-344, 370328-329, 370/441, 370/442, 375/130, 375134-137, 375/140
• US Class Current: 370/342
• CPC Class Codes: H04L 27/001 using chaotic signals for secret or secure communication H04L9/001
• CPC Class Codes: H04L 5/02 Channels characterised by the type of signal

Abstract

A multiple access telecommunication system is provided, which makes use of chaotic signals. Each transmitter has a chaotic system, which has at least one strange attractor in its phase space, and each receiver has chaotic systems, which corresponds to those in the transmitters from which it may receive signals. Each pair of users is assigned a set of periodic unstable orbits from a strange attractor, which that pair of users may use for signalling. At the transmitter side, a multiplexer receives data from plurality of users. These data are multiplexed in time, to produce an asynchronous data stream. The data stream is then mapped to a sequence of chaotic signals, in accordance with the set of trajectories for each transmitter and receiver pair.

Claims

1. A multiple access communicating system including multiple users comprising:

a chaotic signal generating unit including;

a data mixer for receiving and mixing said data from multiple users to generate a common data stream;

a transmitter dynamic chaotic system having at least a variable system of parameter and in its phase space at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting a state of said chaotic system in said phase space, said strange attractor including a set of a countable number of unstable periodic orbits determined by said variable parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable periodic orbit;

a control device for assigning a set of characters to each sender-recipient pair of users, symbols of said characters differing from symbols of characters of at least some other sender-recipient pairs of users, matching one of said unstable orbits to each symbol of each of said characters, successively tuning said dynamic chaotic system to generate chaotic signals which correspond to said unstable orbits corresponding to symbols in said common data stream, and forming an asynchronous chaotic signal sequence from said generated chaotic signals,

a chaotic signal receiving unit provided for a respective user recipient, said chaotic signal receiving unit including;

a selecting system tuned at chaotic signals corresponding to symbols of said characters assigned to said respective recipient in any sender-recipient pair of users in which said respective recipient takes part, said selecting system for receiving said asynchronous chaotic signal sequence and extracting from said asynchronous chaotic signal sequence chaotic signals destined for said respective recipient; and

a communication link connecting said chaotic signal generating unit and said chaotic signal receiving unit;

wherein said communication system is characterised in that;

in said chaotic signal generating unit;

said control device comprises;

iterative means for carrying out a step-by-step iterative process of said dynamic chaotic system to generate a required chaotic signal corresponding to a current symbol in said common data stream, the iterative means carrying out the step-by-step iterative process in a phase space of the dynamic chaotic system that contains a required unstable periodic orbit that is required in accordance with the required chaotic signal;

means for stabilizing a current unstable orbit when a trajectory point on said current unstable orbit appeared in said iterative process falls into a predetermined vicinity of said required unstable orbit; and

means for forming said asynchronous chaotic signal sequence from said stabilized unstable orbits; and

in said receiving unit;

the selecting system comprises;

a selecting dynamic chaotic system provided at said selecting system, said selecting dynamic chaotic system having at least a variable system parameter and at least a strange attractor in its phase space, said strange attractor possessing a set of at least unstable orbits which correspond to said symbols of said characters assigned for said respective recipient; and

a receiver control unit for performing a step-by-step iterative process of said selecting dynamic chaotic system to generate unstable orbits which correspond to chaotic signals destined for said respective recipient, and extracting said, destined chaotic signals.

2. The multiple access communication system to claim 1, wherein

said chaotic signal generating unit further comprises a registry for registering a list of said unstable orbits of said strange attractor;

and

said control unit further comprises;

means for analysing bifurcation characteristics of said transmitter dynamic chaotic system to determine system parameter regions where unstable orbits exist;

means for searching in said determined parameter regions for unstable orbits having predetermined periods to form said list of said unstable orbits in said registry; and

means for selecting a subset of said unstable orbits from said list to form said chaotic signals based on said selected unstable orbits.

3. A chaotic signal generating unit for forming chaotic signals for a multiple access communication system, said chaotic signal generating unit comprising:

a dynamic chaotic system having at least a variable system parameter and in its phase space at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting the state of said chaotic system in said phase space, said strange attractor including a set of a countable number of unstable periodic orbits determined by said system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable orbit

a control device for controlling said dynamic chaotic system to generate chaotic signals corresponding to a plurality of said unstable orbits which are selected according to predetermined rules;

said chaotic signal generating unit being characterised in that;

said chaotic signal generating unit further comprises a registry for registering a list of said unstable orbits of said strange attractor; and

said control device comprises;

means for analysing bifurcation characteristics of said dynamic chaotic system to determine system parameter regions where said unstable orbits exist;

means for searching in said determined parameter regions for unstable orbits having predetermined periods to form said list of said unstable orbits in said registry; and

means for selecting a subset of said unstable orbits from said list to control said dynamic chaotic system to form said chaotic signals based on said subset of said selected unstable orbits.

4. The chaotic signal generating unit as claimed in claim 3 wherein:

said chaotic signal generating unit further comprises a data mixer for receiving and mixing data transmitted from multiple users connected to said chaotic signal generating unit, and generating a common data stream; and

said control device receives said common data stream, and controls said dynamic chaotic system to generate chaotic signals corresponding to said common data stream to form a chaotic signal sequence.

35. A chaotic signal generating unit as claimed in claim 3, wherein a set of characters represented by a set of symbols is assigned to each user, and said registry stores relationship of each symbol and each chaotic signal formed using at least a part of said unstable orbits.

36. A chaotic signal generating unit as claimed in claim 4, wherein said users include in its data a priority data indicating priority of said data, and said data mixer mixes said data based on said priority data.

37. A chaotic signal generating unit as claimed in claim 36, wherein higher priority data uses a unstable orbit having a shorter repetition period than that of lower priority data.

5. A method for forming chaotic signals for multiple access communication, said method comprising the steps of:

constructing at least one dynamic chaotic system having at least a variable system parameter and at least a strange attractor in its phase space, said strange attractor being a plurality of chaotic trajectories and including a set of a countable number of unstable periodic skeletal orbits determined by said system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable orbit;

generating chaotic signals corresponding to a plurality of said unstable orbits which are selected according to predetermined rules;

wherein said method is characterized by the steps of;

providing, while constructing said dynamic chaotic system, an analysis of bifurcation characteristics of said dynamic chaotic system to reveal parameter regions where said unstable orbits exist;

carrying out in said revealed parameter regions a search of unstable orbits having predetermined periods;

forming a list of said unstable orbits found;

selecting, from said formed list, a subset of said unstable orbits, differences between said unstable orbits satisfying predetermined criteria; and

forming said chaotic signals by controlling said dynamic chaotic system so that the chaotic signals correspond to said selected unstable skeletal orbits.

6. The method of claim 5, wherein said step of providing said analysis comprises the steps of:

plotting a bifurcation diagram reflecting behavior modes of said dynamic chaotic system in the whole variable range of said system parameter, and

determining, based on said bifurcation diagram, said parameter regions where said unstable orbits of said dynamic chaotic system exist.

7. The method of claim 6, wherein said step of plotting said bifurcation diagram is performed by the steps of:

direct iterating system equations of said dynamic chaotic system on a mesh of values of said system parameter defining said behavior of said dynamic chaotic system; and

analyzing obtained time series.

8. The method of claim 6, wherein said step of plotting said bifurcation diagram is performed by the steps of:

numerically integrating system equations of said dynamic chaotic system on a mesh of values of said system parameter defining said behavior of said dynamic chaotic system; and

analyzing obtained time series.

9. The method of claim 5, wherein said step of carrying out said search comprises the steps of:

fixing sail system parameter of said dynamic chaotic system;

selecting one of said chaotic trajectories in said phase space of said dynamic chaotic system by determining start conditions on said strange attractor;

determining a return point with a period T, to a predetermined neighborhood of which return point said selected chaotic trajectory returns after a predetermined time T,

solving equations for improving a location of said unstable chaotic orbit with said period T;

defining characteristics of said unstable chaotic orbit with said period T,

entering said unstable chaotic orbit in said list as an unstable skeletal orbit with said period T, if said unstable skeletal orbit with said period T is yet absent in said list; and

continuing said search for other unstable chaotic orbits with said period T.

10. The method of claim 9, wherein said step of continuing said search of other unstable chaotic orbits with said period T is performed on said same chaotic trajectory.

11. The method of claim 9, wherein said step of continuing said search of other unstable chaotic orbits with said period T is performed on other chaotic trajectories.

12. The method of claim 5, wherein said step of selecting said subset of said unstable orbits comprises the step of selecting a subset of chaotic signals of said same period that belong to different attractors of said same dynamic chaotic system having at least two different system parameters.

13. The method of claim 5, wherein said step of selecting said subset of said unstable orbits comprises the step of selecting a subset of chaotic signals of different periods provided in said same dynamic chaotic system.

14. The method of claim 5, wherein said step of selecting said subset of said unstable orbits comprises the steps of selecting a subset of chaotic signals corresponding to unstable skeletal orbits of different dynamic chaotic systems.

15. The method of claim 5, wherein said step of selecting said subset of said unstable orbits comprises the step of selecting a subset of chaotic signals corresponding to unstable skeletal orbits of dynamic chaotic systems having hyper-chaotic attractors.

16. The method of claim 5 further comprising the step of level quantizing said selected chaotic signals.

17. A chaotic signal generating unit for generating a chaotic signal sequence for a multiple access communication system including multiple users transmitting data over said communication system, said chaotic signal generating unit comprising:

a data mixer for receiving and mixing said date from multiple users to generate a common data stream;

a dynamic chaotic system having at least a variable system parameter and in this phase space at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting the state of said chaotic system in said phase space, said strange attractor including a set of a countable number of unstable periodic orbits determined by said variable system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable orbit;

a control device for assigning a set of characters to each sender-recipient pair of users, symbols of said characters differing from symbols of characters of at least some other sender-recipient pairs of users, matching one of said unstable orbits to each symbols of each of said characters, successively tuning said dynamic chaotic system to generate chaotic signals which correspond to unstable orbits corresponding to symbols in said common data stream, and forming an asynchronous chaotic signal sequence from said generated chaotic signals;

said chaotic signal generating unit being characterised in that;

said control device comprises;

iterative means for carrying out a step-by-step iterative process of said dynamic chaotic system to generate a required chaotic signal corresponding to a current symbol in said common data stream, the iterative means carrying out the step-by-step iterative process in a phase space of the dynamic chaotic system that contains a required unstable periodic orbit that is required in accordance with the required chaotic signal;

means for stabilizing a current unstable orbit when a trajectory point on said current unstable orbit appeared in said iterative process falls into a predetermined vicinity of said required unstable periodic orbit to form a stabilized unstable orbit; and

means for forming said asynchronous chaotic signal sequence from said stabilized unstable orbit.

18. The chaotic signal generating unit of claim 17, wherein

said chaotic signal generating unit further comprises a registry for registering a list of said unstable orbits of said strange attractor;

and

said control unit further comprises;

means for analysing bifurcation characteristics of said dynamic chaotic system to determine system parameter regions where unstable orbits exist;

means for searching in said determined parameter regions for unstable orbits having predetermined periods to form said list of said unstable orbits in said registry; and

means for selecting a subset of said unstable orbits from said list to form said chaotic signals corresponding to said unstable orbits.

19. A method for forming an asynchronous data stream for a multiple access communication system including multiple users communicating data therebetween, said method comprising the steps of:

assigning in advance a set of characters to each sender-recipient pair of users, symbols of said characters differing from symbols of characters of at least some other sender-recipient pairs of users;

matching, to each symbol of each of said characters, one of chaotic signals generated by a dynamic chaotic system having at least a variable system parameter and in its phase spaces at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting a state of said chaotic system in the phase space, said strange attractor including a set of a countable number of unstable orbits determined by said system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return on said unstable orbit;

receiving, from multiple users, data consisting of symbols of characters of said users;

forming a common data stream from said symbols being received from said users, in which sequence a symbol following order is defined in accordance with a predetermined rule;

successively tuning said dynamic chaotic system to generate chaotic signals, each of which corresponds to a respective symbol in said common data steam;

forming, in a communication channel, an asynchronous chaotic signal sequence from said chaotic signals generated successively,

wherein said method is characterized in that said stop of successively tuning comprises the steps of;

starting a step-by-step iterative process of said dynamic chaotic system to generate a required chaotic signal corresponding to a currant symbol in said common data stream;

stabilizing a current unstable orbit when a trajectory point on said current unstable orbit appeared in said iterative process falls into a predetermined vicinity of said required unstable orbit; and

forming said asynchronous chaotic signal sequence from said stabilized unstable orbit.

20. The method of claim 19, further comprising, during said iterative process of said dynamic chaotic system and prior to said step of stabilizing, the step of finding a point in said phase space of said dynamic chaotic system which belongs to said required unstable orbit, and which is metrically and evolutionally close to a current point reflecting said current state of said dynamic chaotic system.

21. The method of claim 19, wherein said step of starting said iterative process of said dynamic chaotic system is performed by changing initial conditions of said dynamic chaotic system, and starting said iterative process from a phase space point belonging to said required unstable orbit.

22. The method of claim 19, wherein said step of stabilizing said unstable orbit is performed by changing said system parameter of said dynamic chaotic system, and moving a current point reflecting said current state of said dynamic chaotic system on a stable manifold of said required unstable orbit.

23. The method of claim 22, wherein said step of changing of said system parameter of said dynamic chaotic system is performed by correcting a point movement in said phase space at least once in said iterative process during said period of said unstable orbit.

24. The method of claim 23, wherein said step of correcting said point motion in said phase space is performed on each iterative step during said period of said unstable orbit.

25. The method of claim 19, wherein said step of forming said common data stream is performed in order of said data coming from said users.

26. The method of claim 19, wherein said step of forming said common data stream is performed in view of priorities pre-assigned to each character.

27. The method of claim 19, wherein said step of forming said common data stream is performed in view of priorities pre-assigned to each user.

28. The method of claim 19, wherein said step of forming said common data stream is performed in view of transmission of a predetermined number of symbols per time unit for each priority user.

29. The method of claim 19, wherein said step of forming said common data stream is performed in view of transmission of a predetermined number of symbols per time unit for each priority character.

30. The method of claim 19, wherein said step of assigning a set of characters comprises the step of assigning to each priority user a set of characters having more symbols than a set of characters assigned to each of other users.

31. The method of claim 19, wherein said step of matching chaotic signals comprises the step of providing each priority user with several chaotic signals on each symbol of each character.

32. The method of claim 19, wherein said step of matching chaotic signals comprises the step of providing each priority user with chaotic signals having shorter unstable orbit period than chaotic signals for each of other users.

33. The method of claim 19, wherein said step of matching chaotic signals comprises the step of providing each priority character with chaotic signals having shorter unstable orbit period than chaotic signals for each of other characters.

34. The method of claim 19, wherein, in order to transmit at least one symbol, said step of generating said corresponding chaotic signal is performed more than once.

38. A chaotic signal receiving unit for extracting chaotic signals destined for a respective recipient from an asynchronous chaotic signal sequence in a multiple-access communication system, said asynchronous chaotic signal sequence including chaotic signals, said chaotic signal corresponding to symbols of characters assigned to communicating sender-recipient pairs of users in said communication system, symbols of characters of a particular sender-recipient pair of users differing from symbols of characters of at least some other sender-recipient pairs, each chaotic signal corresponding to an unstable periodic orbit generated by a transmitter dynamic chaotic system having at least a variable system parameter and in its phase space at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting the state of said chaotic system in said phase space, said strange attractor including a set of a countable number of unstable orbits determined by said system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable orbit, said receiving unit comprising:

a selecting system tuned at chaotic signals corresponding to symbols of characters assigned for said respective recipient in any sender-recipient pair in which said respective recipient takes part, said selecting system for receiving said asynchronous chaotic signal sequence and extracting from said asynchronous chaotic signal sequence said chaotic signals destined for said respective recipient;

wherein said receiving unit is characterized in that;

a selecting dynamic chaotic system provided at said selecting system, said selecting dynamic chaotic system having at least a variable system parameter and at least a strange attractor in its phase space, said strange attractor possessing a set of at least unstable orbits which correspond to said symbols of said characters assigned for said respective recipient; and

a receiver control unit for performing a step-by-step iterative process of said selecting dynamic chaotic system to generate unstable orbits which correspond to chaotic signals destined for said respective recipient, and extracting said destined chaotic signals.

39. A method for extracting chaotic signals destined for a specific recipient from an asynchronous chaotic signal sequence in a multiple-access communication system, said asynchronous chaotic signal sequence including chaotic signals, said chaotic signal corresponding to symbols of characters assigned to sender-recipient pairs of users in said communication system, symbols of characters of a particular sender-recipient pair of users differing from symbols of characters of at least some other sender-recipient pairs, each chaotic signal corresponding to an unstable periodic orbit generated by a transmitter dynamic chaotic system having at least a variable system parameter and in its phase space at least a strange attractor comprising a plurality of chaotic trajectories of a depicting point depicting the state of said chaotic system in said phase space, said strange attractor including a set of a countable number of unstable orbits determined by said variable system parameter, each unstable orbit having a repetition period of time in which a chaotic trajectory returns to a predetermined neighbourhood of a return point on said unstable orbit, the method comprising the steps of:

providing each recipient with a selecting system tuned at chaotic signals corresponding to symbols of characters assigned for said specific recipient in any sender-recipient pair in which said specific recipient takes part;

receiving said asynchronous chaotic signal sequence; and

extracting from said asynchronous chaotic signal sequence, said chaotic signals destined for said specific recipient by said selecting system;

wherein said method is characterized by the steps of;

providing said selecting system with a selecting dynamic chaotic system, said selecting dynamic chaotic system having at least a variable system parameter and at least a strange attractor in its phase space, said strange attractor possessing a set of at least unstable orbits which correspond to said symbols of said characters assigned for said respective recipient; and

performing said step of extracting said chaotic signals by performing a step-by-step iterative process of said selecting dynamic chaotic system to generate said unstable orbits corresponding to said chaotic signals destined for said specific recipient.

40. The method of claim 39, wherein said step of extracting said chaotic signals further comprises the step of stabilizing said unstable orbit corresponding to a chaotic signal in said selecting dynamic chaotic system of said specific recipient by appropriately tuning said system parameter of said selecting dynamic chaotic system during said step-by-step iterative process.

41. The method of claim 40, wherein said step of stabilizing comprises the steps of:

estimating, in said phase space of said selecting dynamic chaotic system, a metric proximity of a point corresponding to a received sample of said asynchronous chaotic signal sequence, to points corresponding to each of said unstable orbits belonging to said selecting dynamic chaotic system;

starting said step-by-step iterative process of said selecting dynamic chaotic system at an unstable orbit having a point whose metric proximity estimate is within a predetermined range;

correcting a point motion in said phase space of said selecting dynamic chaotic system on at least one step of said iterative process during a repetition period of said iterated unstable orbit;

further estimating, during said iterative process at each iterative step in said phase space of said selecting dynamic chaotic system, a next metric proximity of a point corresponding to a next received sample of said asynchronous chaotic signal sequence, to a next point of said iterated unstable orbit; and

terminating said iterative process once said next metric proximity estimate falls outside said predetermined range.

42. The method of claim 41, wherein said step of correcting said point motion is performed at every step of said iterative process of said selecting dynamic chaotic system.

43. The method of claim 39, wherein said step of extracting said chaotic signals further comprises the steps of:

estimating, in said phase space of said selecting dynamic chaotic system, a metric proximity of a point corresponding to a received sample of said asynchronous chaotic signal sequence, to points corresponding to each of said unstable orbits belonging to said selecting dynamic chaotic system;

starting said step-by-step iterative process of said selecting dynamic chaotic system at an unstable orbit having a point whose estimated metric proximity is within a predetermined range;

further estimating, during said iterative process at each iterative step in said phase space of said selecting dynamic chaotic system, a next metric proximity of a point corresponding to a next received sample of said asynchronous chaotic signal sequence, to a next point of said iterated unstable orbit; and

terminating said iterative process once said next metric proximity estimation falls outside said predetermined range.

44. The method of claim 43, wherein said selecting dynamic chaotic system is similar to said transmitter dynamic chaotic system of said communication system, and tuned to extract only those unstable orbits which are used by said transmitter dynamic chaotic system for forming chaotic signals for said specific recipient.

45. The method of claim 43, wherein:

said selecting dynamic chaotic system is different from said transmitter dynamic chaotic system of said communication system, and possesses periodic orbits that are used at said transmitter dynamic chaotic system; and

said step of extracting said chaotic signals further comprises the step of synthesizing said selecting dynamic chaotic system with said transmitter dynamic chaotic system.

46. The method of claim 39, wherein said step of extracting said chaotic signals is performed by using multiple selecting dynamic chaotic systems, each of which is tuned to extract a respective one of said chaotic signals for said specific recipient.

47. The method of claim 43, wherein said step of extracting said chaotic signals comprises the steps of:

accumulating said metric proximity estimates during a time interval corresponding to said duration of one repetition of said iterated unstable orbit, and making a decision on extraction of said chaotic signal when said accumulated value does not exceed a predetermined threshold.

48. The method of claim 39, wherein said step of extracting said chaotic signals further comprises the step of quantizing amplitude of said chaotic signals in said asynchronous chaotic signal sequence.

49. The method of claim 39, wherein said step of extracting said chaotic signals further comprises the step of preselecting chaotic signals in said asynchronous chaotic signal sequence, for which a type of said selecting dynamic chaotic system differs from types of selecting dynamic chaotic systems of other recipients.

50. The method of claim 39, wherein said step of extracting said chaotic signals further comprises the step of preselecting chaotic signals in said asynchronous chaotic signal sequence, for which a system parameter set of said selecting dynamic chaotic system differs from parameter sets of selecting dynamic chaotic systems of other recipients.