# Alan J. Michaels, West Melbourne US

## Alan J. Michaels, West Melbourne, FL US

Patent application number | Description | Published |
---|---|---|

20080263119 | Digital Generation of a Chaotic Numerical Sequence - A method is provided for generating a chaotic sequence. The method includes selecting a plurality of polynomial equations. The method 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 method further includes determining a series of digits in a weighted number system (e.g., a binary number system) based on the RNS residue values. According to an aspect of the invention, the method includes using a Chinese Remainder Theorem process to determine a series of digits in the weighted number system based on the RNS residue values. According to another aspect of the invention, the determining step comprises identifying a number in the weighted number system that is defined by the RNS residue values. | 10-23-2008 |

20080294710 | Extending a Repetition Period of a Random Sequence - A method is provided for extending a sequence repetition period of a random number generator in systems based on the availability of random sequences. The method includes performing RNS arithmetic operations to express a random number in a sequence as RNS residue values. Each generated random number has a value between zero and n!−1. The method also includes converting each of the RNS residue values to a relatively prime base number system so that each of the RNS residue values includes at least one digit. The method further includes generating an arbitrary permutation ordering of output sequence numbers using a select combination of digits associated with each of the RNS residue values. The arbitrary permutation ordering is applied to a cyclic structure having n elements. Each of the n elements has an associated output sequence number. | 11-27-2008 |

20080294956 | Encryption Via Induced Unweighted Errors - A method for encrypting data is provided. The method includes formatting data represented in a weighted number system into data blocks. The method also includes converting the data blocks into a residue number system representation. The method further includes generating a first error generating sequence and inducing errors int he data blocks after converting the data blocks into a residue number system representation. It should be understood that the errors are induced in the data blocks by using the first error generating sequence. After inducing errors into the data blocks, the data of the data blocks is formatted into a form to be sorted or transmitted. The method also includes generating a second error generating sequence synchronized with and identical to the first error generating sequence and correcting the errors in the data blocks using an operation which is an arithmetic of a process used in inducing errors. | 11-27-2008 |

20080304666 | Spread Spectrum Communications System and Method Utilizing Chaotic Sequence - 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. | 12-11-2008 |

20080307022 | Mixed Radix Conversion with a Priori Defined Statistical Artifacts - A method is presided for masking a process used in generating a random number sequence. The method includes generating a random number sequence. This step involves selectively generating the random number sequence utilizing a ring structure which has been punctured. The method also includes performing a mixed radix conversion to convert the random number sequence from a first number base to a second number base. The method further includes puncturing the ring structure by removing at least one element therefrom to eliminate a statistical artifact in the random number sequence expressed in the second number base. The first number base and second number base are selected so that they are respectively defined by a first Galois field characteristic and a second Galois field characteristic. | 12-11-2008 |

20080307024 | Mixed Radix Number Generator with Chosen Statistical Artifacts - A method is provided for masking a process used in generating a number sequence. The method includes generating a first sequence of numbers contained within a Galois field GF[M]. The method also includes performing a first modification to a first number in the first sequence of numbers. The first modification includes summing the first number with a result of a modulo P operation performed on a second number of the first sequence that proceeds the first number. M is relatively prime with respect to P. The method further includes performing a second modification to the first random number. The second modification is comprised of a modulo P operation. This second modification is performed subsequent to the first modification. The method includes repeating the first and second modification for a plurality of numbers comprising the first sequence of numbers to generate a second sequence of numbers. | 12-11-2008 |

20090034727 | Chaotic Spread Spectrum Communications System Receiver - A method is provided for coherently demodulating a chaotic sequence spread spectrum signal at a receiver ( | 02-05-2009 |

20090044080 | Closed Galois Field Combination - A method is provided for combining two or more input sequences in a communications system to increase a repetition period of the input sequences in a resource-efficient manner. The method includes a receiving step, a mapping step, and a generating step. The receiving step involves receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[p | 02-12-2009 |

20090110197 | CRYPTOGRAPHIC SYSTEM CONFIGURED FOR EXTENDING A REPETITION PERIOD OF A RANDOM SEQUENCE - A cryptographic system (CS) is provided. The CS ( | 04-30-2009 |

20090196420 | CRYPTOGRAPHIC SYSTEM INCORPORATING A DIGITALLY GENERATED CHAOTIC NUMERICAL SEQUENCE - A cryptographic system (CS) is provided. The CS ( | 08-06-2009 |

20090202067 | CRYPTOGRAPHIC SYSTEM CONFIGURED TO PERFORM A MIXED RADIX CONVERSION WITH A PRIORI DEFINED STATISTICAL ARTIFACTS - A cryptographic system (CS) is provided. The CS ( | 08-13-2009 |

20090245327 | SELECTIVE NOISE CANCELLATION OF A SPREAD SPECTRUM SIGNAL - A method is provided for improving a signal-to-noise ratio in a received signal. The method involves receiving a spread spectrum signal (SSS) with a power level below a noise floor of a receiver. The SSS is generated by modulating a data signal using a spreading sequence (SS) comprised of a random number sequence (RNS). The SS can be generated using a chaos generator or any other deterministic means. The method also involves comparing a magnitude of each number of the RNS which was used to generate the SSS to an adaptable threshold value. The adaptable threshold value is selected based on a minimum magnitude of each number necessary to produce samples having a predetermined signal-to-noise ratio. Notably, samples of the received SSS are excluded from a receiver processing based on a result of the comparison. Similarly, each number of a random number sequence is excluded from the receiver processing based on the comparison. | 10-01-2009 |

20090279688 | CLOSED GALOIS FIELD CRYPTOGRAPHIC SYSTEM - A cryptographic system (CS) comprised of generators ( | 11-12-2009 |

20090279690 | CRYPTOGRAPHIC SYSTEM INCLUDING A MIXED RADIX NUMBER GENERATOR WITH CHOSEN STATISTICAL ARTIFACTS - A cryptographic system ( | 11-12-2009 |

20090296860 | ADAPTIVE CORRELATION - A method is provided for correlating samples of a received signal and samples of an internally generated/stored sample sequence (“IGSSS”). The method involves performing a first iteration of a first-resolution correlation state. The first-resolution correlation state involves: selecting a first N sets of samples from the received signal; selecting a first set of samples from the IGSSS; and concurrently comparing each of the N sets of samples with the first set of samples to determine if a correlation exists between the same. If it is determined that a correlation does not exist between one of the N sets of samples and the first set of samples, then a second iteration of the first-resolution correlation state is performed. If it is determined that a correlation exists between one of the N sets of samples and the first set of samples, then a first iteration of a second-resolution correlation state is performed. | 12-03-2009 |

20090300088 | SINE/COSINE GENERATOR | 12-03-2009 |

20090310650 | FEATURELESS COHERENT CHAOTIC AMPLITUDE MODULATION | 12-17-2009 |

20090327387 | DIGITAL GENERATION OF AN ACCELERATED OR DECELERATED CHAOTIC NUMERICAL SEQUENCE - A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values. | 12-31-2009 |

20100054228 | MULTI-TIER AD-HOC NETWORK COMMUNICATIONS - Ad-hoc wireless network which operates in accordance with a time division multiple access (TDMA) channel scheme. The network includes a plurality of nodes configured for wireless ad-hoc network communications using at least a first tier waveform and a second tier waveform. | 03-04-2010 |

20100091700 | AD-HOC NETWORK ACQUISITION USING CHAOTIC SEQUENCE SPREAD WAVEFORM - Method and system for identifying neighbor nodes in an ad-hoc wireless network including two or more nodes. The method involves generating a beacon signal at a first node of the network for alerting other nodes in the network of the presence of the first node. A digitally generated first spreading sequence is also generated at the first node. Thereafter, the beacon signal is modulated with the first spreading sequence to produce a spread spectrum signal which is then transmitted. The spreading sequence is selected to be a chaotic sequence. | 04-15-2010 |

20100165828 | COMMUNICATIONS SYSTEM EMPLOYING CHAOTIC SPREADING CODES WITH STATIC OFFSETS - Methods for code-division multiplex communications. The method involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC | 07-01-2010 |

20100166041 | COMMUNICATIONS SYSTEM EMPLOYING ORTHOGONAL CHAOTIC SPREADING CODES - Methods for code-division multiplex communications. The methods involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC | 07-01-2010 |

20100226497 | COMMUNICATIONS SYSTEM EMPLOYING ORTHOGONAL CHAOTIC SPREADING CODES - Systems and methods for code-division multiplex communications. The methods involve forming orthogonal or statistically orthogonal chaotic spreading sequences (CSC | 09-09-2010 |

20100309957 | CONTINUOUS TIME CHAOS DITHERING - Embodiments of the present invention provide a system and method for further reducing cyclostationarity and correspondingly energy density in a chaotic spread spectrum data communication channel, by digitally generating a first chaotic sequence of values to form a spreading code. The spreading code is then used to form a digital IF spread spectrum signal having a uniform sampling interval. The digital IF spread spectrum signal is converted to a sampled analog IF spread spectrum signal at a conversion rate substantially equal to the uniform sampling interval. The duration of the sampling interval is then selectively varied in accordance with a first pseudo-random sequence, thereby introducing a known dither in the analog IF spread spectrum signal. After introducing the known dither, the analog IF spread spectrum signal is upconverted to an analog RF spread spectrum signal. The first pseudo-random sequences may be designed to be a chaotic sequence. | 12-09-2010 |

20100310072 | SYMBOL DURATION DITHERING FOR SECURED CHAOTIC COMMUNICATIONS - A system for communicating a sequence of information symbols using a chaotic sequence spread spectrum signal. The system includes a transmitter ( | 12-09-2010 |

20100316090 | DISCRETE TIME CHAOS DITHERING - The invention concerns a chaotic communications system, method and apparatus having a transmitter configured to spread an input data signal over a wide intermediate frequency band, by digitally generating a first chaotic sequence of values to form a spreading code. The spreading code is then used to form a digital IF chaotic spread spectrum signal having a uniform sampling interval. The duration of the sampling interval is then selectively varied in accordance with a first pseudo-random sequence, thereby introducing a known dither in the digital IF chaotic spread spectrum signal. After introducing the known dither, the digital IF chaotic spread spectrum signal is converted to an analog RF spread spectrum signal at a conversion rate that exceeds the sampling interval of the chaotic spread spectrum signal. A corresponding receiver recovers the input data from the spread transmitted signal. This spreading may utilize a chaotic sequence employing discrete time chaos dithering. | 12-16-2010 |

20110002360 | PERMISSION-BASED SECURE MULTIPLE ACCESS COMMUNICATION SYSTEMS | 01-06-2011 |

20110002362 | SYMBOL ESTIMATION FOR CHAOTIC SPREAD SPECTRUM SIGNAL - A communications system includes RF hardware ( | 01-06-2011 |

20110002364 | ANTI-JAM COMMUNICATIONS HAVING SELECTIVELY VARIABLE PEAK-TO-AVERAGE POWER RATIO INCLUDING A CHAOTIC CONSTANT AMPLITUDE ZERO AUTOCORRELATION WAVEFORM - A spread spectrum communication system includes a channel encoder configured for modulating a carrier signal with data to form an information signal. A spreading sequence generator is configured for generating a spreading sequence having a phase angle dependent upon a chaotic sequence and contiguously distributed over a predetermined range. The chaotic sequence also has a magnitude which is selectively dependent upon the pseudo-random number or chaotic sequence. The invention also includes a multiplier configured for forming a spread spectrum signal by multiplying the information signal by the spreading sequence. The spreading sequence generator is responsive to a magnitude control signal for controlling the selective dependency of said magnitude. The magnitude can be constant to form a constant amplitude zero autocorrelation signal. Alternatively, the magnitude can be allowed to vary in selectively controlled chaotic or pseudo-random manner to vary a peak to average power ratio. | 01-06-2011 |

20110002366 | RAKE RECEIVER FOR SPREAD SPECTRUM CHAOTIC COMMUNICATIONS SYSTEMS - A receiver ( | 01-06-2011 |

20110002460 | HIGH-SPEED CRYPTOGRAPHIC SYSTEM USING CHAOTIC SEQUENCES - A cryptographic system ( | 01-06-2011 |

20110002463 | PERMISSION-BASED MULTIPLE ACCESS COMMUNICATIONS SYSTEMS | 01-06-2011 |

20110004792 | BIT ERROR RATE REDUCTION IN CHAOTIC COMMUNICATIONS - A system for chaotic sequence spread spectrum communications includes a transmitter ( | 01-06-2011 |

20110019719 | ADAPTIVE LINK COMMUNICATIONS USING ADAPTIVE CHAOTIC SPREAD WAVEFORM | 01-27-2011 |

20110019817 | PERMISSION-BASED TDMA CHAOTIC COMMUNICATION SYSTEMS | 01-27-2011 |