Probabilistic constellation shaping (PCS) is applied to a desired probability distribution over the 2-D constellation points. Constellation points are partitioned into multiple disjoint sets in which all the constellation points within a subset have the same energy level (i.e., amplitude) or distance from the origin on the complex plane. Each of the sets may be further subdivided into smaller disjoint sets of constellation points to facilitate labeling of the constellation points. The sets may be indexed from 0 to the total number of disjoint sets to form an index set. The desired distribution may then be applied over the index set either using a distribution matcher (DM) or using a lookup table. The desired distribution may be generated before forward error correction (FEC) encoding that preserves the generated amplitude distribution through FEC encoding of data bits. The scheme may map the FEC encoded data bits to the constellation points, such that the probability of occurrence of each signal set (with a specific energy level) follows the desired probability distribution within a fixed codeword length. In addition, PCS can be applied to both square and non-square constellations, which may or may not be arranged on a Cartesian grid.

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. In various embodiments, transmitter and receivers utilize symbol waveforms based on a PSW alphabet designed using methods that may include specifying the location of particular polynomial roots, such as placing roots at the symbol time boundaries with amplitude zero, to minimize symbol boundary discontinuities, translating the nearest polynomial root to a particular point in the complex plane, directly editing the location of one or more polynomial roots, adjusting the complex conjugate of an edited PSW root in order to keep the PSW real-valued, and shaping one of more PSWs using polynomial convolution with polynomial versions of the raised cosine, root raised cosine, Gaussian, or other band-limiting filters. Stochastic methods for PSW optimization are also introduced.

A modulation device includes a mapping circuit configured to map information bits to signal points on a plurality of concentric rings, when a signal space arrangement in which the number of signal points on all of the plurality of rings is the same is used as a basis, reduce the number of signal points on an innermost ring or a plurality of rings from inner to outer rings from among the plurality of rings, generate a new ring outside the signal space arrangement used as the basis, and arrange, on the generated ring, signal points which achieve the same frequency utilization efficiency as that of the signal space arrangement used as the basis.

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 modulation device includes a mapping circuit configured to map information bits to signal points on a plurality of concentric rings, when a signal space arrangement in which the number of signal points on all of the plurality of rings is the same is used as a basis, reduce the number of signal points on an innermost ring or a plurality of rings from inner to outer rings from among the plurality of rings, generate a new ring outside the signal space arrangement used as the basis, and arrange, on the generated ring, signal points which achieve the same frequency utilization efficiency as that of the signal space arrangement used as the basis.

A transmission device that improves data reception quality includes: a weighting synthesizer that generates a first precoded signal and a second precoded signal from a first baseband signal and a second baseband signal, respectively; a phase changer that applies a phase change of i to the second precoded signal; an inserter that inserts a pilot signal into the second precoded signal applied with the phase change; and a phase changer that applies a phase change to the second precoded signal applied with the phase change and inserted with the pilot signal. satisfies /2 radians<< radians or radians<<3/2 radians. Each of the first baseband signal and the second baseband signal is modulated via a modulation scheme of quadrature amplitude modulation (QAM) using non-uniform mapping.

A UE of a wireless communication network first receives a modulation and coding scheme index I.sub.MCS for demodulating a physical layer data channel of the network. The UE then demodulates the physical layer data channel with a non-square quadrature amplitude modulation (NS-QAM) having a modulation order and code rate corresponding to a spectral efficiency (SPEFF) substantially equal to a SPEFF of a square QAM (S-QAM) SPEFF indicted by the I.sub.MCS, where the NS-QAM has an effective channel code rate no larger than the code rate for which the UE may skip decoding a transport block in an initial received transmission.

Disclosed herein is a method for transmitting digital data in a super channel, in which a set of carriers are packed in a predetermined bandwidth. The set of carriers comprises higher and lower edge carriers having the highest and lowest wavelengths, respectively, among said set of earners, wherein data is transmitted via the higher and lower edge carriers using a corresponding modulation format, each modulation format using a constellation diagram comprising a number of symbols, wherein a binary address is associated with each symbol. Said method comprises the steps of: separating digital data to be transmitted via each of said higher and lower edge carriers into corresponding first and second data streams, and for each of said higher and lower edge carriers, mapping the data of the first data stream to predetermined first bit positions within the binary symbol addresses and the data of the second data stream to predetermined second bit positions within the binary symbol addresses, wherein said first bit positions are bit positions which have an error probability less than the average error probability of all bit positions.

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.

A method for modulation in a transmitter for transmitting a signal in a wireless communication system according to an embodiment of the present invention comprises: a step for determining a modulation scheme; a step for, if the determined modulation scheme corresponds to a specific modulation scheme, converting encoded information bits to quadrature amplitude modulation (QAM) symbols in accordance with a predetermined QAM modulation order, selecting a sequence corresponding to an element of an integer vector in a predetermined sequence set, repeating the converted QAM symbols for a predetermined sequence length, and outputting signals by multiplying the repeated QAM symbols and the selected sequence; and a step for transmitting the outputted signals to a receiver.