Fully connected uplink and downlink fully connected relay network systems using pseudo-noise spreading and despreading sequences subjected to maximizing the signal-to-interference-plus-noise ratio. The relay network systems comprise one or more transmitting units, relays, and receiving units connected via a communication network. The transmitting units, relays, and receiving units each may include a computer for performing the methods and steps described herein and transceivers for transmitting and/or receiving signals. The computer encodes and/or decodes communication signals via optimum adaptive PN sequences found by employing Cholesky decompositions and singular value decompositions (SVD). The PN sequences employ channel state information (CSI) to more effectively and more securely computing the optimal sequences.

A controller is configured to control the adaptive notch filter and to execute a search technique (e.g., artificial intelligence (AI) search technique) to converge on filter coefficients and to recursively adjust the filter coefficients of the adaptive notch filter in real time to adaptively adjust one or more filter characteristics (e.g., maximum notch depth or attenuation, bandwidth of notch, or general magnitude versus frequency response of notch).

A controller is configured to control the adaptive notch filter and to execute a search technique (e.g., artificial intelligence (AI) search technique) to converge on filter coefficients and to recursively adjust the filter coefficients of the adaptive notch filter in real time to adaptively adjust one or more filter characteristics (e.g., maximum notch depth or attenuation, bandwidth of notch, or general magnitude versus frequency response of notch).

A communication device is configured to correlate a first signal with a second signal at a designated interval, the second signal corresponding to the first signal and being received by the communication device where the other communication device transmits a signal including a pulse as the first signal, convert a correlation computation result that is a result of correlating the first signal with the second signal at the designated interval into a format including a matrix product of an expanded modal matrix and an expanded signal vector, the expanded modal matrix including a plurality of elements indicating the correlation computation result obtained when assuming that the signals are received at respective set times, the expanded signal vector being a vector including a plurality of elements, each of which indicates whether or not there is a signal received at each of the set times and amplitude and phase of the signal.

A communication device is configured to correlate a first signal with a second signal at a designated interval, the second signal corresponding to the first signal and being received by the communication device where the other communication device transmits a signal including a pulse as the first signal, convert a correlation computation result that is a result of correlating the first signal with the second signal at the designated interval into a format including a matrix product of an expanded modal matrix and an expanded signal vector, the expanded modal matrix including a plurality of elements indicating the correlation computation result obtained when assuming that the signals are received at respective set times, the expanded signal vector being a vector including a plurality of elements, each of which indicates whether or not there is a signal received at each of the set times and amplitude and phase of the signal.

A hybrid multi-layer method for decomposing of a source signal to a plurality of decomposed signals that can be used to collectively represent the source signal or recover the source signal. An example embodiment is a method that includes multi-layer (or multi-stage) signal decomposition to generate constant envelope signals without impact on the original signal. In an example embodiment, the method includes signal decomposition to maintain constant envelope properties and limit bandwidth expansion from the signal decomposition. The method includes decomposing a source signal into two first-stage decomposed signals that each have a constant envelope amplitude value. The method further includes iteratively decomposing each of the constant envelope signals into further-stage decomposed signals based on a threshold amplitude value at each iteration. The further-stage decomposed signals have a constant envelope with an envelope amplitude value in dependence of the threshold amplitude value at each iteration.

A hybrid multi-layer method for decomposing of a source signal to a plurality of decomposed signals that can be used to collectively represent the source signal or recover the source signal. An example embodiment is a method that includes multi-layer (or multi-stage) signal decomposition to generate constant envelope signals without impact on the original signal. In an example embodiment, the method includes signal decomposition to maintain constant envelope properties and limit bandwidth expansion from the signal decomposition. The method includes decomposing a source signal into two first-stage decomposed signals that each have a constant envelope amplitude value. The method further includes iteratively decomposing each of the constant envelope signals into further-stage decomposed signals based on a threshold amplitude value at each iteration. The further-stage decomposed signals have a constant envelope with an envelope amplitude value in dependence of the threshold amplitude value at each iteration.

A wireless apparatus configured to be cascaded to another wireless apparatus through a transmission path and to be coupled to an antenna multiplexer, the another wireless apparatus being coupled to the antenna multiplexer, the wireless apparatus includes a processor configured to specify a first time length for a first transmission signal having a first frequency band to pass through the wireless apparatus, specify a second time length for a second transmission signal having a second frequency band to pass through the wireless apparatus, the transmission path, and the another wireless apparatus, specify a difference between the first time length and the second time length, delay the second transmission signal by the specified difference, generate a cancellation signal for an intermodulation distortion that occurs in a received signal due to intermodulation between the first transmission signal and the second transmission signal, and combine the cancellation signal with the received signal.

A wireless apparatus configured to be cascaded to another wireless apparatus through a transmission path and to be coupled to an antenna multiplexer, the another wireless apparatus being coupled to the antenna multiplexer, the wireless apparatus includes a processor configured to specify a first time length for a first transmission signal having a first frequency band to pass through the wireless apparatus, specify a second time length for a second transmission signal having a second frequency band to pass through the wireless apparatus, the transmission path, and the another wireless apparatus, specify a difference between the first time length and the second time length, delay the second transmission signal by the specified difference, generate a cancellation signal for an intermodulation distortion that occurs in a received signal due to intermodulation between the first transmission signal and the second transmission signal, and combine the cancellation signal with the received signal.

Fully connected uplink and downlink fully connected relay network systems using pseudo-noise spreading and despreading sequences subjected to maximizing the signal-to-interference-plus-noise ratio. The relay network systems comprise one or more transmitting units, relays, and receiving units connected via a communication network. The transmitting units, relays, and receiving units each may include a computer for performing the methods and steps described herein and transceivers for transmitting and/or receiving signals. The computer encodes and/or decodes communication signals via optimum adaptive PN sequences found by employing Cholesky decompositions and singular value decompositions (SVD). The PN sequences employ channel state information (CSI) to more effectively and more securely computing the optimal sequences.