Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations in a wide range of applications, such as interference and spectrum monitoring or clearance, object tracking, transmission channel and noise analyses, radiated power analysis, signal boundary interference, satellite downlink signal identification, pulsed radar monitoring, audio detection and identification, lidar systems, sonar systems, etc.
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.
Systems, devices, and methods of the present invention facilitate secure communication by changing sets of symbol waveforms used transmit data in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency) to enable successful sending of data between a transmitter and receiver employing SWH, but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats, but one symbol waveform alphabet is not reliably able to receive signals sent using the other alphabets. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
H04L 27/34 - Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
4.
Devices, Systems, Software, and Methods for Efficient Data Processing for Fully Homomorphic Encryption, Post-Quantum Cryptography, Artificial Intelligence, and other Applications
Systems, devices, software, and methods of the present invention provide for homomorphically encrypted (HE) and other data represented as polynomials of degree K−1 to be transformed in O(K*log(K)) time into ‘unique-spiral’ representations in which both linear-time (O(K)) addition and linear-time multiplication are supported without requiring an intervening transformation. This capability has never previously been available and enables very significant efficiency improvements, i.e., reduced runtimes, for applications such as Fully Homomorphic Encryption (FHE), Post-Quantum Cryptography (PQC) and Artificial Intelligence (AI). Other efficient operations, such as polynomial division, raising to a power, integration, differentiation and parameter-shifting are also possible using the unique-spiral representations. New methods are introduced based on the unique-spiral representation that have applications to efficient polynomial composition, inversion, and other important topics.
OOO(K)) addition and linear-time multiplication are supported without requiring an intervening transformation. This capability has never previously been available and enables very significant efficiency improvements, i.e., reduced runtimes, for applications such as Fully Homomorphic Encryption (FHE), Post-Quantum Cryptography (PQC) and Artificial Intelligence (AI). Other efficient operations, such as polynomial division, raising to a power, integration, differentiation and parameter-shifting are also possible using the unique-spiral representations. New methods are introduced based on the unique-spiral representation that have applications to efficient polynomial composition, inversion, and other important topics.
Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.
Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
Systems, methods and devices for communicating comprise one or more of a computer-readable media, a computer, a satellite communication device and a mobile device, wherein the at least one of a computer-readable media, a computer, a satellite communication device and a mobile device to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data to at least one of a user, a secondary computer-readable media, a secondary computer, a secondary satellite communication device and a secondary mobile device.
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.
Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations in a wide range of applications, such as interference and spectrum monitoring or clearance, object tracking, transmission channel and noise analyses, radiated power analysis, signal boundary interference, satellite downlink signal identification, pulsed radar monitoring, audio detection and identification, lidar systems, sonar systems, etc.
Systems, transmitters, and methods employing waveform bandwidth compression to transmit information are provided. Transmitters may include an encoder to generate a time-domain amplitude sequence from information in a constant amplitude sinusoidal modulation format; fit a polynomial to the time-domain amplitude sequence, the fitted polynomial spanning at least one transmission time interval; and convert the polynomial to a transmission signal, the transmission signal comprising a sum of sinusoids of differing frequencies, each sinusoid having a continuously time-varying amplitude. A carrier source providing a carrier that is modulated with the transmission signal and transmitted through the system to a receiver, which receives the signal in the constant amplitude sinusoidal modulation format. The sum of sinusoids of differing frequencies having a continuously time-varying amplitude may be generated using instantaneous spectral analysis, to reduce the spectral occupancy of the transmission signal.
Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a Taylor series polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.
Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of data stream in a signal transmission channel of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.
Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations.
Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations.
G01R 21/133 - Arrangements for measuring electric power or power factor by using digital technique
G01R 21/127 - Arrangements for measuring electric power or power factor by using pulse modulation
G01R 23/10 - Arrangements for measuring frequency, e.g. pulse repetition rateArrangements for measuring period of current or voltage by converting frequency into a train of pulses, which are then counted
G01R 23/15 - Indicating that frequency of pulses is either above or below a predetermined value or within or outside a predetermined range of values, by making use of non-linear or digital elements
G01R 23/167 - Spectrum analysisFourier analysis using filters with digital filters
G01R 23/18 - Spectrum analysisFourier analysis with provision for recording frequency spectrum
G06F 17/00 - Digital computing or data processing equipment or methods, specially adapted for specific functions
H04L 27/148 - Demodulator circuitsReceiver circuits with demodulation using spectral properties of the received signal, e.g. by using frequency selective- or frequency sensitive elements using filters, including PLL-type filters
A method for waveform bandwidth compression (WBC) and a system configured to perform the method, which may include the steps of: processing information to produce an input sequence of real-valued amplitude signals; fitting a polynomial to the input sequence covering at least one transmission time interval; converting the polynomial to a transmission signal comprising a sum of sinusoids with continuously time-varying amplitudes; transmitting the transmission signal; and receiving the transmission signal as a time-amplitude sequence. This method may significantly improve the spectral efficiency of existing transmission systems, while at the same time requiring only minimal modification to traditional radio architecture design.
Systems, devices, methods, and computer readable medium for transmitting data using polynomial-based signals. Data may be represented as a message polynomial and convolved with a reference polynomial to generate a transmission polynomial. The transmission polynomial may be converted in a set of sinusoidals with continuously-varying amplitude in a plurality of frequencies prior to transmission of a signal to a receiver. Following transmission, the signal is received and the amplitude values are mapped into bit sequences to recover the data.
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/ or shaping of the polynomial alphabet to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission. In various embodiments, transmitter and receivers utilizing symbol waveforms based on a PSW alphabet designed may be in wireless and/ or wired data transmission systems that may or may not include transmitters and receivers employing traditional modulation formats.
H04L 7/02 - Speed or phase control by the received code signals, the signals containing no special synchronisation information
H04L 7/033 - Speed or phase control by the received code signals, the signals containing no special synchronisation information using the transitions of the received signal to control the phase of the synchronising-signal- generating means, e.g. using a phase-locked loop
H04L 7/06 - Speed or phase control by synchronisation signals the synchronisation signals differing from the information signals in amplitude, polarity, or frequency
22.
Devices, systems, and methods employing polynomial symbol waveforms
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission. In various embodiments, transmitter and receivers utilizing symbol waveforms based on a PSW alphabet designed may be in wireless and/or wired data transmission systems that may or may not include transmitters and receivers employing traditional modulation formats.
Systems, methods and devices for communicating comprise one or more of a computer-readable media, a computer, a satellite communication device and a mobile device, wherein the at least one of a computer-readable media, a computer, a satellite communication device and a mobile device to perform at least one of supplying data as input communication symbols to an encoder, which converts the input communication symbols into transmittable waveforms having a head function and a tail function, which are different. A transmitter transmits transmittable waveforms over a communication channel, which is received by a receiver, then demodulated and output communication symbols carrying the data to at least one of a user, a secondary computer-readable media, a secondary computer, a secondary satellite communication device and a secondary mobile device.
A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.
Methods for communicating are disclosed. A method includes obtaining at least one input communication symbol selected from a set of communication symbols, converting the at least one input communication symbol into at least one transmittable waveform using at least one defined spiral waveform function, and transmitting the at least one transmittable waveform over a communication channel. Example spiral waveform functions include spline-based piecewise functions and Archimedes spiral functions.
A method for waveform bandwidth compression (WBC) and a system configured to perform the method, which may include the steps of: processing information to produce an input sequence of real-valued amplitude signals; fitting a polynomial to the input sequence covering at least one transmission time interval; converting the polynomial to a transmission signal comprising a sum of sinusoids with continuously time-varying amplitudes; transmitting the transmission signal; and receiving the transmission signal as a time-amplitude sequence. This method may significantly improve the spectral efficiency of existing transmission systems, while at the same time requiring only minimal modification to traditional radio architecture design.
A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.
A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.
Methods for communicating are disclosed. A method includes obtaining at least one input communication symbol selected from a set of communication symbols, converting the at least one input communication symbol into at least one transmittable waveform using at least one defined spiral waveform function, and transmitting the at least one transmittable waveform over a communication channel. Example spiral waveform functions include spline-based piecewise functions and Archimedes spiral functions.
Methods for communicating are disclosed. A method includes obtaining at least one input communication symbol selected from a set of communication symbols, converting the at least one input communication symbol into at least one transmittable waveform using at least one defined spiral waveform function, and transmitting the at least one transmittable waveform over a communication channel. Example spiral waveform functions include spline-based piecewise functions and Archimedes spiral functions.
One exemplary embodiment can describe a method for communicating. This can include identifying a set of nonlinear functions used to generate waveforms; generating, a plurality of waveforms having substantially identical amplitudes and substantially identical phases, and designating this plurality of waveforms as a plurality of reference signals; encoding at least one bit of traffic data in an attribute of a waveform; selecting a reference symbol (“refbol”) that encodes the at least one bit of traffic data; transmitting the refbol as a waveform from a transmitter; receiving the refbol at a receiver; and decoding the refbol.
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
A method for Gray coding a symbol alphabet transmitted utilizing a plurality of non-periodic waveforms. The method for Gray coding a symbol alphabet transmitted utilizing a plurality of non-periodic waveforms may include producing a matched filter for each of the non-periodic waveforms, forming an adjacency matrix indicating which symbols are most likely to be confused with each other, ordering the symbols accordingly, and applying a Gray code to the ordered symbols. The method may also include a symbol alphabet with a plurality of symbols that may also include means for building an adjacency matrix describing likelihood of inter-symbol interference and means for ordering the symbols based on the adjacency matrix and for Gray coding the ordered symbols. The method may also include applying a standard Gray code to an ordered symbol list such that successive symbols in the ordered list are assigned bit sequences that differ by one bit.
A software defined radio is disclosed. The software defined radio may utilize a method for encoding a bit stream into non-periodic spiral-based symbol waveforms for transmission and reception. The method includes transmitting a signal constructed from one or more non-periodic modulation sets residing on a memory system of the software defined radio, where each modulation set corresponds to a symbol alphabet and provides non-periodic symbol waveforms corresponding to symbol bit sequences segmented by a microprocessor according to alphabet size. The method also includes receiving the signal constructed from one or more spiral modulation sets, wherein the signal from one or more spiral modulation sets are filtered and then fed to an analog to digital converter, where the signal constructed from the one or more spiral modulation sets is digitized and are fed to the microprocessor. A non-transitory computer storage media may also execute the method.
A software defined radio is disclosed. The software defined radio may utilize a method for encoding a bit stream into non-periodic spiral-based symbol waveforms for transmission and reception. The method includes transmitting a signal constructed from one or more non-periodic modulation sets residing on a memory system of the software defined radio, where each modulation set corresponds to a symbol alphabet and provides non-periodic symbol waveforms corresponding to symbol bit sequences segmented by a microprocessor according to alphabet size. The method also includes receiving the signal constructed from one or more spiral modulation sets, wherein the signal from one or more spiral modulation sets are filtered and then fed to an analog to digital converter, where the signal constructed from the one or more spiral modulation sets is digitized and are fed to the microprocessor. A non-transitory computer storage media may also execute the method.
H04B 1/00 - Details of transmission systems, not covered by a single one of groups Details of transmission systems not characterised by the medium used for transmission
42 - Scientific, technological and industrial services, research and design
Goods & Services
Telecommunication consultation in the nature of technical consulting in the field of signal modulation Engineering services in the field of signal modulation and RF modem design
42 - Scientific, technological and industrial services, research and design
Goods & Services
Telecommunication consultation in the nature of technical consulting in the field of signal modulation Engineering services in the field of signal modulation and RF modem design
39.
Telecommunication signaling using nonlinear functions
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
Methods and systems for communicating are disclosed. A method includes obtaining input communication symbols selected from a set of communication symbols, converting input communication symbols into transmittable waveforms using non-periodic functions, and transmitting transmittable waveforms over a communication channel. Another method includes receiving transmittable waveforms constructed using non-periodic functions and transmitted over a communication channel, and demodulating transmittable waveforms. A system includes a modulator adapted to obtain input communication symbols selected from a set of communication symbols and adapted to convert input communication symbols into transmittable waveforms using non-periodic functions, and a transmitter or transceiver adapted to transmit transmittable waveforms over a communication channel. Another system includes a receiver or transceiver adapted to receive transmittable waveforms transmitted over a communication channel and constructed using non-periodic functions, and a demodulator adapted to demodulate transmittable waveforms.
Methods and systems for communicating are disclosed. A method includes obtaining input communication symbols selected from a set of communication symbols, converting input communication symbols into transmittable waveforms using non-periodic functions, and transmitting transmittable waveforms over a communication channel. Another method includes receiving transmittable waveforms constructed using non-periodic functions and transmitted over a communication channel, and demodulating transmittable waveforms. A system includes a modulator adapted to obtain input communication symbols selected from a set of communication symbols and adapted to convert input communication symbols into transmittable waveforms using non-periodic functions, and a transmitter or transceiver adapted to transmit transmittable waveforms over a communication channel. Another system includes a receiver or transceiver adapted to receive transmittable waveforms transmitted over a communication channel and constructed using non-periodic functions, and a demodulator adapted to demodulate transmittable waveforms.
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
H04B 1/62 - Details of transmission systems, not covered by a single one of groups Details of transmission systems not characterised by the medium used for transmission for providing a predistortion of the signal in the transmitter and corresponding correction in the receiver, e.g. for improving the signal/noise ratio
44.
TELECOMMUNICATION SIGNALING USING NONLINEAR FUNCTIONS
One exemplary embodiment can describe a method for communicating. The method for communicating can include a step for identifying characteristics of a communications channel, a step for identifying a set of nonlinear functions used to generate waveforms, a step for assigning a unique numeric code to each waveform, a step for transmitting a numeric sequence as a series of waveforms, a step for receiving the series of waveforms, and a step for decoding the series of waveforms.
H04B 1/62 - Details of transmission systems, not covered by a single one of groups Details of transmission systems not characterised by the medium used for transmission for providing a predistortion of the signal in the transmitter and corresponding correction in the receiver, e.g. for improving the signal/noise ratio
Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software suitable for signal with either stationary and non-stationary spectrums. The methods that may be used throughout various systems including transmitters receivers, repeater, controllers, monitors, etc. and in software simulators to enable various signal power calculations and analyses, such as frequency spectrum analysis, throughout operating systems and that may be consistently applied in system design and operation simulations.
G01R 21/127 - Arrangements for measuring electric power or power factor by using pulse modulation
G01R 21/133 - Arrangements for measuring electric power or power factor by using digital technique
G01R 23/10 - Arrangements for measuring frequency, e.g. pulse repetition rateArrangements for measuring period of current or voltage by converting frequency into a train of pulses, which are then counted
G01R 23/15 - Indicating that frequency of pulses is either above or below a predetermined value or within or outside a predetermined range of values, by making use of non-linear or digital elements
G01R 23/167 - Spectrum analysisFourier analysis using filters with digital filters
G01R 23/18 - Spectrum analysisFourier analysis with provision for recording frequency spectrum
G06F 17/00 - Digital computing or data processing equipment or methods, specially adapted for specific functions
H04L 27/148 - Demodulator circuitsReceiver circuits with demodulation using spectral properties of the received signal, e.g. by using frequency selective- or frequency sensitive elements using filters, including PLL-type filters
46.
COMMUNICATION DEVICES, SYSTEMS, SOFTWARE AND METHODS EMPLOYING SYMBOL WAVEFORM HOPPING
Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/ or shaping of the polynomial alphabet to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission. In various embodiments, transmitter and receivers utilizing symbol waveforms based on a PSW alphabet designed may be in wireless and/ or wired data transmission systems that may or may not include transmitters and receivers employing traditional modulation formats.
H04L 7/02 - Speed or phase control by the received code signals, the signals containing no special synchronisation information
H04L 7/033 - Speed or phase control by the received code signals, the signals containing no special synchronisation information using the transitions of the received signal to control the phase of the synchronising-signal- generating means, e.g. using a phase-locked loop
H04L 7/06 - Speed or phase control by synchronisation signals the synchronisation signals differing from the information signals in amplitude, polarity, or frequency
A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.
A method for waveform bandwidth compression (WBC) and a system configured to perform the method, which may include the steps of: processing information to produce an input sequence of real-valued amplitude signals; fitting a polynomial to the input sequence covering at least one transmission time interval; converting the polynomial to a transmission signal comprising a sum of sinusoids with continuously time-varying amplitudes; transmitting the transmission signal; and receiving the transmission signal as a time-amplitude sequence. This method may significantly improve the spectral efficiency of existing transmission systems, while at the same time requiring only minimal modification to traditional radio architecture design.
Methods and systems for communicating are disclosed. A method includes obtaining input communication symbols selected from a set of communication symbols, converting input communication symbols into transmittable waveforms using non-periodic functions, and transmitting transmittable waveforms over a communication channel. Another method includes receiving transmittable waveforms constructed using non-periodic functions and transmitted over a communication channel, and demodulating transmittable waveforms. A system includes a modulator adapted to obtain input communication symbols selected from a set of communication symbols and adapted to convert input communication symbols into transmittable waveforms using non-periodic functions, and a transmitter or transceiver adapted to transmit transmittable waveforms over a communication channel. Another system includes a receiver or transceiver adapted to receive transmittable waveforms transmitted over a communication channel and constructed using non-periodic functions, and a demodulator adapted to demodulate transmittable waveforms.
Systems, devices, software, and methods of the present invention provide for homomorphically encrypted (HE) and other data represented as polynomials of degree K-1 to be transformed in O(Klog(K)) time into 'unique-spiral' representations in which both linear-time (O(K)) addition and linear-time multiplication are supported without requiring an intervening transformation. This capability has never previously been available and enables very significant efficiency improvements, i.e., reduced runtimes, for applications such as Fully Homomorphic Encryption (FHE), Post-Quantum Cryptography (PQC) and Artificial Intelligence (AI). Other efficient operations, such as polynomial division, raising to a power, integration, differentiation and parameter-shifting are also possible using the unique-spiral representations. New methods are introduced based on the unique-spiral representation that have applications to efficient polynomial composition, inversion, and other important topics.
