Abstract: A processor coupled to a first communication device produces and transmits a first encoded vector and a second encoded vector to a second communication device via a communication channel that applies a channel transformation to the encoded vectors during transmission. A processor coupled to the second communication device receives the transformed signals, constructs a matrix based on the transformed signals, detects an effective channel thereof, and identifies left and right singular vectors of the effective channel. A precoding matrix is selected from a codebook of unitary matrices based on a message, and a second encoded vector is produced based on a second known vector, the precoding matrix, a complex conjugate of the left singular vectors, and the right singular vectors. A first symbol of the second encoded vector and a second symbol of the second encoded vector are sent to the first communication device for identification of the message.

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: A method includes selecting a block size, via a processor of a communications system, and identifying a set of constellation points of a constellation diagram, based on a received set of bits and the constellation diagram. The constellation diagram is associated with a modulation scheme. A set of symbol blocks, based on the set of constellation points, is generated. Each symbol block from the set of symbol blocks has a size equal to the block size and includes a subset of constellation points from the set of constellation points. A unitary braid division multiplexing (UBDM) transformation is applied to each symbol block from the set of symbol blocks to produce a set of complex numbers. The set of complex numbers is then sent via the processor.

Abstract: A system includes first and second sets of communication devices. A processor coupled to the first set of communication devices produces a first encoded vector and transmits the first encoded vector to the second set of communication devices via a communication channel that applies a channel transformation to the first encoded vector during transmission. A processor coupled to the second set of communication devices receives the transformed signal, detects an effective channel thereof, and identifies left and right singular vectors of the effective channel. A precoding matrix is selected from a codebook of unitary matrices based on a message, and a second encoded vector is produced based on a second known vector, the precoding matrix, a complex conjugate of the left singular vectors, and the right singular vectors. The second encoded vector is sent to the first set of communication devices for identification of the message.

Abstract: A method of encoding data includes identifying multiple complex number pairs of a data vector and generating a transformed data vector by applying a non-linear transformation to each complex number pair from the multiple complex number pairs. The non-linear transformation includes modifying a phase of a first complex number from each complex number pair. The phase modification is based on a value associated with a second complex number from each complex number pair. A signal representing the transformed data vector is sent to multiple transmitters for transmission to multiple receivers. A signal representing the non-linear transformation is sent to a compute device for transmission of the non-linear transformation to the multiple receivers prior to transmission of the signal representing the transformed data vector from the multiple transmitters to the multiple receivers, for recovery of the data vector at the multiple receivers.

Abstract: An apparatus includes a first communication device with multiple antennas, operably coupled to a processor and configured to access a codebook of transformation matrices. The processor generates a set of symbols based on an incoming data, and applies a permutation to each of the symbols to produce a set of permuted symbols. The processor transforms each of the permuted symbols based on at least one primitive transformation matrix, to produce a set of transformed symbols. The processor applies, to each of the transformed symbols, a precode matrix selected from the codebook of transformation matrices to produce a set of precoded symbols. The codebook of transformation matrices is accessible to a second communication device. The processor sends a signal to cause transmission, to the second communication device, of multiple signals, each representing a precoded symbol from the set of precoded symbols, each of the signals transmitted using a unique antenna from the plurality of antennas.

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: An apparatus includes a first communication device with multiple antennas, operably coupled to a processor and configured to access a codebook of transformation matrices. The processor generates a set of symbols based on an incoming data, and applies a permutation to each of the symbols to produce a set of permuted symbols. The processor transforms each of the permuted symbols based on at least one primitive transformation matrix, to produce a set of transformed symbols. The processor applies, to each of the transformed symbols, a precode matrix selected from the codebook of transformation matrices to produce a set of precoded symbols. The codebook of transformation matrices is accessible to a second communication device. The processor sends a signal to cause transmission, to the second communication device, of multiple signals, each representing a precoded symbol from the set of precoded symbols, each of the signals transmitted using a unique antenna from the plurality of antennas.

Abstract: An apparatus includes a first communication device with multiple antennas, operably coupled to a processor and configured to access a codebook of transformation matrices. The processor generates a set of symbols based on an incoming data, and applies a permutation to each of the symbols to produce a set of permuted symbols. The processor transforms each of the permuted symbols based on at least one primitive transformation matrix, to produce a set of transformed symbols. The processor applies, to each of the transformed symbols, a precode matrix selected from the codebook of transformation matrices to produce a set of precoded symbols. The codebook of transformation matrices is accessible to a second communication device. The processor sends a signal to cause transmission, to the second communication device, of multiple signals, each representing a precoded symbol from the set of precoded symbols, each of the signals transmitted using a unique antenna from the plurality of antennas.

Abstract: A system includes first and second sets of communication devices. A processor coupled to the first set of communication devices produces a first encoded vector and transmits the first encoded vector to the second set of communication devices via a communication channel that applies a channel transformation to the first encoded vector during transmission. A processor coupled to the second set of communication devices receives the transformed signal, detects an effective channel thereof, and identifies left and right singular vectors of the effective channel. A precoding matrix is selected from a codebook of unitary matrices based on a message, and a second encoded vector is produced based on a second known vector, the precoding matrix, a complex conjugate of the left singular vectors, and the right singular vectors. The second encoded vector is sent to the first set of communication devices for identification of the message.

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: A method includes generating, via a processor, multiple initial vectors, each including N elements. A code map is applied to each of the initial vectors, to produce an associated spreading code vector. Each of the spreading code vectors includes M elements, where M?N. Using the spreading code vectors, spread signals are produced based on a complex baseband signals. The spread signals are stored in a memory operably coupled to the processor. The first and second spread signals are split into respective sets of spread signals, each uniquely associated with one of multiple transmit antennas. The first and second sets of spread signals are transmitted to respective signal receivers for detection of associated complex baseband signals based on the associated spreading code vectors.

Abstract: A system includes first and second sets of communication devices. A processor coupled to the first set of communication devices produces a first encoded vector and transmits the first encoded vector to the second set of communication devices via a communication channel that applies a channel transformation to the first encoded vector during transmission. A processor coupled to the second set of communication devices receives the transformed signal, detects an effective channel thereof, and identifies left and right singular vectors of the effective channel. A precoding matrix is selected from a codebook of unitary matrices based on a message, and a second encoded vector is produced based on a second known vector, the precoding matrix, a complex conjugate of the left singular vectors, and the right singular vectors. The second encoded vector is sent to the first set of communication devices for identification of the message.

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 of encoding data includes identifying multiple complex number pairs of a data vector and generating a transformed data vector by applying a non-linear transformation to each complex number pair from the multiple complex number pairs. The non-linear transformation includes modifying a phase of a first complex number from each complex number pair. The phase modification is based on a value associated with a second complex number from each complex number pair. A signal representing the transformed data vector is sent to multiple transmitters for transmission to multiple receivers. A signal representing the non-linear transformation is sent to a compute device for transmission of the non-linear transformation to the multiple receivers prior to transmission of the signal representing the transformed data vector from the multiple transmitters to the multiple receivers, for recovery of the data vector at the multiple receivers.

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: A method includes generating, via a processor, multiple initial vectors, each including N elements. A code map is applied to each of the initial vectors, to produce an associated spreading code vector. Each of the spreading code vectors includes M elements, where M?N. Using the spreading code vectors, spread signals are produced based on a complex baseband signals. The spread signals are stored in a memory operably coupled to the processor. The first and second spread signals are split into respective sets of spread signals, each uniquely associated with one of multiple transmit antennas.

Abstract: A method includes selecting a block size, via a processor of a communications system, and identifying a set of constellation points of a constellation diagram, based on a received set of bits and the constellation diagram. The constellation diagram is associated with a modulation scheme. A set of symbol blocks, based on the set of constellation points, is generated. Each symbol block from the set of symbol blocks has a size equal to the block size and includes a subset of constellation points from the set of constellation points. A unitary braid division multiplexing (UBDM) transformation is applied to each symbol block from the set of symbol blocks to produce a set of complex numbers. The set of complex numbers is then sent via the processor.

Abstract: A method includes generating, via a processor, multiple initial vectors, each including N elements. A code map is applied to each of the initial vectors, to produce an associated spreading code vector. Each of the spreading code vectors includes M elements, where M?N. Using the spreading code vectors, spread signals are produced based on a complex baseband signals. The spread signals are stored in a memory operably coupled to the processor. The first and second spread signals are split into respective sets of spread signals, each uniquely associated with one of multiple transmit antennas. The first and second sets of spread signals are transmitted to respective signal receivers for detection of associated complex baseband signals based on the associated spreading code vectors.

Abstract: A method includes generating, via a processor, multiple initial vectors, each including N elements. A code map is applied to each of the initial vectors, to produce an associated spreading code vector. Each of the spreading code vectors includes M elements, where M?N. Using the spreading code vectors, spread signals are produced based on a complex baseband signals. The spread signals are stored in a memory operably coupled to the processor. The first and second spread signals are split into respective sets of spread signals, each uniquely associated with one of multiple transmit antennas. The first and second sets of spread signals are transmitted to respective signal receivers for detection of associated complex baseband signals based on the associated spreading code vectors.