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.

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 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.

In some aspects of the systems, methods, and devices described herein, one or more asymmetric modulation constellations may be utilized. For example, a modulation constellation utilized to modulate data symbols may be asymmetric. In some approaches, an asymmetric modulation constellation may be generated by introducing a phase shift (e.g., cyclic shift, phase rotation) to one or more constellation points of a modulation constellation. An asymmetric modulation constellation may allow detecting phase shifts without ambiguity. For example, a user equipment (UE) may perform channel estimation or phase noise estimation aided by data symbols that are modulated with an asymmetric modulation constellation. In some examples, a UE may receive a message from a network entity indicating a configuration of an asymmetric modulation constellation. The UE may demodulate data symbols of a data signal based on a channel characterization estimate that is associated with the configuration of the asymmetric modulation constellation.

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.

In some aspects of the systems, methods, and devices described herein, one or more asymmetric modulation constellations may be utilized. For example, a modulation constellation utilized to modulate data symbols may be asymmetric. In some approaches, an asymmetric modulation constellation may be generated by introducing a phase shift (e.g., cyclic shift, phase rotation) to one or more constellation points of a modulation constellation. An asymmetric modulation constellation may allow detecting phase shifts without ambiguity. For example, a user equipment (UE) may perform channel estimation or phase noise estimation aided by data symbols that are modulated with an asymmetric modulation constellation. In some examples, a UE may receive a message from a network entity indicating a configuration of an asymmetric modulation constellation. The UE may demodulate data symbols of a data signal based on a channel characterization estimate that is associated with the configuration of the asymmetric modulation constellation.