# US 2010/0165828 A1 · Communications system employing chaotic spreading codes with static offsets > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2010/0165828 A1 - Document ID: US20100165828A1 - Status: Published application - Kind: A1 - Application number: 12/345,163 - Filed: 2008-12-29 - Published: 2010-07-01 - Earliest claimed: 2008-12-29 - Assignees: Harris Corporation - Inventors: Alan J. Michaels; David B. Chester - Web page: https://patentgrep.com/patent/US20100165828A1 ## CPC - H04J 13/12: Generation of orthogonal codes - G09C 1/00: Apparatus or methods whereby a given sequence of signs, e.g. an intelligible text, is transformed into an unintelligible sequence of signs by transposing the signs or groups of signs or by replacing them by others according to a predetermined system (cryptographic typewriters G09C3/00) - H04J 13/0018: {Chaotic} - H04K 1/025: {using an analogue chaotic signal} - H04K 1/10: by using two signals transmitted simultaneously or successively - H04L 9/001: {using chaotic signals} - H04B 1/707: using direct sequence modulation - H04L 2209/12: Details relating to cryptographic hardware or logic circuitry - H04L 2209/80: Wireless - H04J: MULTIPLEX COMMUNICATION (transmission in general H04B; peculiar to transmission of digital information H04L5/00; systems for the simultaneous or sequential transmission of more than one television signal H04N7/08; in exchanges H04Q11/00; stereophonic systems H04S) - G09C: CIPHERING OR DECIPHERING APPARATUS FOR CRYPTOGRAPHIC OR OTHER PURPOSES INVOLVING THE NEED FOR SECRECY - H04K: SECRET COMMUNICATION; JAMMING OF COMMUNICATION - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) - H04B: TRANSMISSION ## Abstract Methods for code-division multiplex communications. The method involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC1, . . . , CSCK) having different static offsets using a set of polynomial equations (f0(x(nT)), . . . , fN−1(x(nT)) and/or f0[x((n+v)T+t)], . . . , fN−1[x((n+v)T+t)]). The methods also involve forming spread spectrum communications signals respectively using the orthogonal or statistically orthogonal chaotic spreading codes. The methods further involve concurrently transmitting the spread spectrum communications signals over a common RF frequency band. The spreading codes are generated using different initial values for a variable “x” of a polynomial equation f(x(nT)) and/or different acc-dec values for a variable “v” of a polynomial equation f[x((n+v)T+t)]. The static offsets are defined by the different initial values for a variable “x” and/or different acc-dec values for a variable “v”. ## Claims ### Claim 1 A method for code-division multiplex communications, comprising the steps of: generating a plurality of orthogonal or statistically orthogonal chaotic spreading codes having different static offsets using a set of polynomial equations; forming a plurality of spread spectrum communications signals respectively using said plurality of orthogonal or statistically orthogonal chaotic spreading codes; and concurrently transmitting said plurality of spread spectrum communications signals over a common RF frequency band. ### Claim 2 (depends on 1) The method according to claim 1, wherein said generating step further comprises generating each spreading code of said plurality of orthogonal or statistically orthogonal chaotic spreading codes using a different initial value for a variable “x” of a polynomial equation f(x(nT+t)), where n is an index of time, t is a variable representing an initial time offset, and T is a discrete time interval. ### Claim 3 (depends on 1) The method according to claim 1, wherein said generating step further comprises generating each spreading code of said plurality of orthogonal or statistically orthogonal chaotic spreading codes using a different acc-dec value for a variable “v” of a polynomial equation f[x((n+v)T+t)], where n is an index of time, v is a variable having a value selected to accelerate or decelerate a chaotic sequence generation by at least one cycle, t is a variable representing an initial time offset, and T is a discrete time interval. ### Claim 4 (depends on 3) The method according to claim 3, further comprising the step of selecting said ace-dec variable “v” to be defined by a mathematical expression c modulo where c is a number of cycles for acceleration or deceleration and mi is a value indicating a cycle in which a chaotic sequence starts to repeat. ### Claim 5 (depends on 1) The method according to claim 1, wherein said generating step further comprises using residue number system (RNS) arithmetic operations to determine a plurality of solutions for said set of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values. ### Claim 6 (depends on 5) The method according to claim 5, wherein said generating step further comprises determining a series of digits in a weighted number system based on said RNS residue values. ### Claim 7 (depends on 6) The method according to claim 6, wherein said generating step further comprises selecting a value for each of N moduli in an RNS used for solving said set of polynomial equations. ### Claim 8 (depends on 1) The method according to claim 1, wherein said generating step further comprises selecting a plurality of relatively prime numbers to be used as moduli in solving said set of polynomial equations. ### Claim 9 (depends on 1) The method according to claim 1, further comprising: receiving said plurality of spread spectrum communications signals at a receiver; generating at least one chaotic de-spreading code; and de-spreading at least one of said spread spectrum communications signals using said at least one chaotic de-spreading code. ### Claim 10 (depends on 1) The method according to claim 1, further comprising: receiving said plurality of spread spectrum communications signals at a receiver; generating a plurality of chaotic de-spreading codes; and de-spreading said plurality of spread spectrum communications signals using said plurality of chaotic de-spreading codes. ### Claim 11 (depends on 1) The method according to claim 1, further comprising synchronizing a chaotic de-spreading code in time and frequency with at least one of said plurality of orthogonal chaotic spreading codes. ### Claim 12 A code-division multiplex communication system, comprising: a plurality of transmitters configured for generating a plurality of orthogonal or statistically orthogonal chaotic spreading codes having different static offsets using a set of polynomial equations, forming a plurality of spread spectrum communications signals respectively using said plurality of orthogonal or statistically orthogonal chaotic spreading codes; and concurrently transmitting said plurality of spread spectrum communications signals over a common RF frequency band. ### Claim 13 (depends on 12) The system according to claim 12, wherein said plurality of transmitters is further configured for generating said plurality of orthogonal or statistically orthogonal chaotic spreading codes using different initial values for a variable “x” of a polynomial equation f(x(nT+t)), where n is an index of time, t is a variable representing an initial time offset, and T is a discrete time interval. ### Claim 14 (depends on 12) The system according to claim 12, wherein said plurality of transmitters is further configured for generating said plurality of orthogonal or statistically orthogonal chaotic spreading codes using different acc-dec values for a variable “v” of a polynomial equation f[x((n+v)T+t)], where n is an index of time, v is a variable having a value selected to accelerate or decelerate a chaotic sequence generation by at least one cycle, t is a variable representing an initial time offset, and T is a discrete time interval. ### Claim 15 (depends on 14) The system according to claim 14, wherein said acc-dec variable “v” is defined by a mathematical expression c modulo mi, where c is a number of cycles for acceleration or deceleration and mi is a value indicating a cycle in which a chaotic sequence starts to repeat. ### Claim 16 (depends on 12) The system according to claim 12, wherein said plurality of transmitters is further configured for using residue number system (RNS) arithmetic operations to determine a plurality of solutions for said set of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values. ### Claim 17 (depends on 16) The system according to claim 16, wherein said plurality of transmitters is further configured for determining a series of digits in a weighted number system based on said RNS residue values. ### Claim 18 (depends on 17) The system according to claim 17, wherein said plurality of transmitters is further configured for using a pre-selected value for each of N moduli in an RNS to solve said set of polynomial equations. ### Claim 19 (depends on 12) The system according to claim 12, wherein said plurality of transmitters is further configured for using a plurality of pre-selected relatively prime numbers as modulus to solve said set of polynomial equations. ### Claim 20 (depends on 12) The system according to claim 12, further comprising a receiver configured for receiving said plurality of spread spectrum communications signals, generating at least one chaotic de-spreading code, and de-spreading at least one of said spread spectrum communications signals using said at least one chaotic de-spreading code. ### Claim 21 (depends on 12) The system according to claim 12, further comprising a receiver configured for receiving said plurality of spread spectrum communications signals, generating a plurality of chaotic de-spreading codes, and de-spreading said plurality of spread spectrum communications signals using said plurality of chaotic de-spreading codes. ### Claim 22 (depends on 12) The system according to claim 12, further comprising a receiver configured for synchronizing a chaotic de-spreading code in time and frequency with at least one of said plurality of orthogonal or statistically orthogonal chaotic spreading codes.