A data communication method in which input digital data is received and encoded into an encoded waveform having zero crossings representative of the input digital data. The encoding includes generating the encoded waveform based upon a continuous piecewise function having sinusoidal components. The continuous piecewise function may be used in generating a plurality of symbol waveforms, each of which occupies a period of the encoded waveform and represents bits of the input digital data. The plurality of symbol waveforms are defined so that a value of a phase offset used in the continuous piecewise function is different for each of the plurality of symbol waveforms, thereby resulting in each symbol waveform having a different zero crossing. An encoded analog waveform is generated from a representation of the encoded waveform and transmitted to a receiver.

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, 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.

A method of recovering information encoded by a modulated sinusoidal waveform having first, second, third and fourth data notches at respective phase angles, where a power of the modulated sinusoidal waveform is reduced relative to a power of an unmodulated sinusoidal waveform within selected ones of the first, second, third and fourth data notches so as to encode input digital data. The method includes receiving the modulated sinusoidal waveform and generating digital values representing the modulated sinusoidal waveform. A digital representation of the unmodulated sinusoidal waveform is subtracted from the digital values in order to generate a received digital data sequence, which includes digital data notch values representative of the amplitude of the modulated sinusoidal waveform within the first, second, third and fourth data notches. The input digital data is then estimated based upon the digital data notch values.

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.

Probabilistic shaping quadrature amplitude modulation (QAM) based on Maxwell-Boltzmann distribution is particularly important in coherent optical communication, which can approach the Shannon limit more desirably in the case of a finite signal-to-noise ratio. However, standard coherent optical digital signal processing algorithms are not optimal for demodulation of PS higher-order QAM signals. The invention provides a probabilistic shaping QAM dynamic equalization method that intercepts multiple inner rings after clock recovery and updates the convergence radius and area of a conventional blind dynamic channel equalization algorithm using a peak density K-means clustering algorithm. The clustering algorithm gives centroid labels and a quantity of classifications required for K-means, which does not require a large number of iterations of K-means, thereby reducing the complexity and improving the accuracy. The updated decision area and decision radius reduce errors in the dynamic equalization algorithm, thereby improving the accuracy of probabilistic shaping QAM digital signal processing.

5G and 6G wireless networks can use artificial intelligence models to optimize performance by measuring the rate of message faults, and in particular the rate of various types of faults. For example, the amplitude faults include a modulation amplitude distorted by a small or large amplitude change, and whether the faults cluster in the high or low amplitude modulation portions of a constellation chart, among many other inputs related to network operations. The artificial intelligence model can be configured to predict the subsequent network performance according to each modulation scheme available to the network, thereby enabling the network to select a more effective modulation scheme. Alternatively, the artificial intelligence model can select the preferred modulation scheme and recommend the change to the network operators, or it can implement the change automatically if enabled to do so.

This disclosure describes systems, methods, and devices related to enhanced constellation shaping. A device may generate payload bits associated with a frame to be sent to a first station device. The device may generate a first output bits having a first length based on the application of a first mask of one or more masks to the payload bits. The device may generate a second output bits having a second length based on the application of a second mask of the one or more masks. The device may compare the first length of the first output bits to the second length of the second output bits. The device may select the first mask or the second mask based on the comparison. The device may convert the payload bits using the selected mask before passing through a shaping encoder to generate shaped bits. The device may cause to send the frame bits and an indication of the selected mask to the first station device.

In 5G and 6G, a message received with even a single-bit fault generally discarded and a retransmission is requested. However, the faulted message contains a wealth of information that the receiver can use to avoid, or at least mitigate, such faults thereafter. Disclosed is a method for comparing a faulted message with an unfaulted copy, thereby determining which part of the message is faulted, and specifically how it was faulted. For example, the fault may have been an amplitude fault in which a demodulated amplitude differs by one level from the initially modulated amplitude, or it may be a phase fault in which the received phase differs by one phase level, or there may be a displacement by multiple amplitude or phase levels (a non-adjacent fault). Different mitigation strategies are disclosed for each situation, including AI models configured to select a suitable modulation scheme to combat specific faults.