The present invention relates to a method of compressed sensing of a spectrally-sparse signal within a given spectral band, the received signal being mixed (820) over a sensing frame with a pulse train scrolling with a repetition frequency linearly modulated over time within this frame. The result of mixing is filtered (830) by means of a low-pass filtering and sampled (840) at a non-uniform rate equal to the repetition frequency, to result in complex samples representative of the received signal. The spectrum of the received signal can be estimated by weighting by means of the complex samples the spectral values of a pulse into a plurality of frequency equidistributed in the band, and by summing up these weighted values for each of these frequencies. An estimate of the received signal is thereby deduced by inverse Fourier transform. The spectral band can be scanned based on the spectrum thus estimated.

Systems and methods for processing online data are disclosed. One such method includes receiving a plurality of data points in a time-series at a short term storage. The method also includes calculating at least one approximation coefficient based on the plurality of data points using a wavelet transform, including calculating a highest level approximation coefficient, and calculating estimated value based on the highest level approximation coefficient. The method further includes calculating differences between the estimated value and the plurality of data points of the short term storage, and determining whether a maximum difference among the calculated differences is less than a predetermined threshold. The method further includes, based on the maximum difference being greater than or equal to the predetermined threshold, storing the oldest data point of the short term storage in a long term storage.

Systems and methods for performing wavelength conflict detection are provided. These are to detect situations in optical networks where two instances of the same wavelength channel have been added. Wavelength conflict detection is performed for each of a plurality of possible wavelength channels that could be present in an optical signal, each wavelength channel that is present modulated by a pilot tone signal with a respective pilot tone frequency, the pilot tone signal carrying M-ary pilot tone data, M=2.sup.n, n≧1, with a respective one of M different sequences being used to represent each of M possible data values over a data value period. Conflict detection for each wavelength channel involves performing correlation peak detection using each of the M different sequences to determine correlation peaks for each of the M different sequences, and, based on the determined correlation peaks, determining whether multiple instances of the wavelength channel are present in the optical signal.

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 and methods are disclosed for improving data channel design by applying transform domain analytics to more reliably extract user data from a signal. In certain embodiments, an apparatus may comprise a channel circuit configured to receive an analog signal at an input of the channel circuit, and sample the analog signal to obtain a set of signal samples. The channel circuit may further apply a filter configured to perform transform domain analysis to the set of signal samples to generate a first subset of samples, the first subset including fewer transitions and having a higher signal to noise ratio (SNR) than the set of signal samples. The channel circuit may detect first bit transform domain representation values from the first subset, and determine channel bit values encoded in the analog signal based on the set of signal samples and using the first bit transform domain representation values detected from the first subset as side information.

A transmitting device (e.g., a base station, a user equipment (UE)) may pre-generate waveform components, for a transmission to be sent subsequent to a listen before talk (LBT) procedure, based on a waveform generation capability of the transmitting device (e.g., based on their memory storage capability, their ability to combine waveform components in the time domain following a per subband LBT procedure, etc.). Further, certain behavior or rules (e.g., which waveform components are generated, how many subbands are included in a waveform component, etc.) may be expected by both a base station and a UE depending on the waveform generation capability of the transmitting device and the resource allocation. Additionally, resource block group (RBG) configurations (e.g., RBG definitions) for improved resource allocation are also described. A bases station may indicate one or more guard band boundaries to a UE to indicate such RBG configurations that account for guard bands.

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.

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.