Abstract: A method includes generating, via a first processor of a first compute device, symbols based on an incoming data and decomposing a unitary matrix of size N×N by: 1) applying a permutation to each symbol using a permutation matrix, to produce permuted symbols, and 2) transforming each symbol using at least one primitive transformation matrix of size M×M, M being smaller than or equal to N, to produce transformed symbols. The method also includes sending a signal representing the transformed symbols to a plurality of transmitters for transmission of a signal representing the transformed symbols to a plurality of receivers. A signal representing the unitary matrix is sent to a second compute device for transmission of the unitary matrix to the receivers for recovery of the plurality of symbols at the plurality of receivers.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.

Abstract: A method includes generating a set of symbols based on an incoming data vector. The set of symbols includes K symbols, K being a positive integer. A first transformation matrix including an equiangular tight frame (ETF) transformation or a nearly equiangular tight frame (NETF) transformation is generated, having dimensions N×K, where N is a positive integer and has a value less than K. A second transformation matrix having dimensions K×K is generated based on the first transformation matrix. A third transformation matrix having dimensions K×K is generated by performing a series of unitary transformations on the second transformation matrix. A first data vector is transformed into a second data vector having a length N based on the third transformation matrix and the set of symbols. A signal representing the second data vector is sent to a transmitter for transmission of a signal representing the second data vector to a receiver.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.

Abstract: Techniques of transmitting wireless communications involve generating orthogonal spreading codes for any number of user devices that are linear combinations of sinusoidal harmonics that match the frequencies within the spread bandwidth. Along these lines, prior to transmitting signals, processing circuitry may generate a set of initial code vectors that form an equiangular tight frame having small cross-correlations. From each of these rows, the processing circuitry produces a new spreading code vector using a code map that is a generalization of a discrete Fourier transform. The difference between the code map and a discrete Fourier transform is that the frequencies of the sinusoidal harmonics are chosen to match the particular frequencies within the spread bandwidth and differ from a center frequency by multiples of the original unspread bandwidth. Different transmitters may then modulate respective signals generated with different spreading code vectors.