A sub-sampling system that is part of a modulator in a transmitter employing a chaos based architecture and including a symbol mapper and a chaos generator. The system includes M-number of channels each receiving a sequence of chaos samples from the generator and a delay device in all of the channels except one that delay the chaos samples at different delay times. The system also includes a sub-sampler in all of the channels that receive the delayed samples, where each sub-sampler outputs every predetermined one of the chaos samples and a register in each channel each storing a predetermined number of the sub-sampled chaos samples. A selection switch responsive to the stored sub-sampled chaos samples from the registers, where the selection switch is responsive to a selection signal from the symbol mapper that selects one of the registers to output the sequences of stored sub-sampled chaos samples from the system.

Example communication systems and methods are described. In one implementation, a method receives a first chaotic sequence of a first temporal length, and a second chaotic sequence of a second temporal length. The method also receives a data symbol for communication to a destination. Based on the data symbol, the second chaotic sequence is temporally shifted and combined with the first chaotic sequence to generate a composite chaotic sequence. The first chaotic sequence functions as a reference chaotic sequence while the second chaotic sequence functions as a data-carrying auxiliary chaotic sequence.

The present invention teaches a system and method for improved signal recovery for range and coverage extension in a heterogeneous cooperative network of digital chaos transmissions with OFDM component signal transmission. The invention improves upon the state of art in side channel information from the transmit side containing information on the clipped amplitude. In-band transmission of the side information is achieved by exploiting the sparsity of the resulting clip amplitude position with improved levels of compression over the prior art using Gabor Transform Multiple Symbol Encoding transmitter. The information rate of the clipped amplitude is sub-Nyquist relative to the original OFDM component signal transmission, which allows very low power spreading by a cooperative digital chaos sequences at a transmit side and recovery of the clipped amplitude at a receive side. Further, an improved noise resistance side channel performance is achieved by decoding Gabor Transform symbols for symbol recovery.

Example communication systems and methods are described. In one implementation, a method receives a first chaotic sequence of a first temporal length, and a second chaotic sequence of a second temporal length. The method also receives a data symbol for communication to a destination. Based on the data symbol, the second chaotic sequence is temporally shifted and combined with the first chaotic sequence to generate a composite chaotic sequence. The first chaotic sequence functions as a reference chaotic sequence while the second chaotic sequence functions as a data-carrying auxiliary chaotic sequence.

The present invention teaches method and apparatus to transform a featureless, unpredictable, and non-repeatable chaos waveform into digital chaos waveforms that maintain featureless characteristics to serve as a for wireless communications protocol, whereby unintended observers cannot detect or disrupt yet imprint a small measure of predictability and repeatability to aid intend observers in recovering embedded information.

Example communication systems and methods are described. In one implementation, a method receives a first chaotic sequence of a first temporal length, and a second chaotic sequence of a second temporal length. The method also receives a data symbol for communication to a destination. Based on the data symbol, the second chaotic sequence is temporally shifted and combined with the first chaotic sequence to generate a composite chaotic sequence. The first chaotic sequence functions as a reference chaotic sequence while the second chaotic sequence functions as a data-carrying auxiliary chaotic sequence.

A system, method, and computer program product for chaotically generating a pseudorandom number sequence, such as for use in spread spectrum communications systems and in cryptographic systems. Chaotically generated pseudorandom numbers are not cyclostationary in nature, so output values encoded via such non-cyclostationary bases have no clear correlations. Spread signal communications systems using chaotically generated spreading codes thus operate without rate line artifacts, increasing their resistance to signal detection and to determinations of underlying signal chip rates and signal symbol rates. Broadcasts and guided transmissions (including either conductive wire or optical transmission media), in both radio frequency and optical systems are supported. Common spread spectrum communications systems including DSSS and FHSS may be strengthened through the use of chaotically generated spreading codes. Similarly, keys and nonces generated for cryptographic systems may be improved over those based on conventionally generated pseudorandom numbers.

The present invention teaches a system and method for signal recovery for range and coverage extension in a heterogeneous cooperative network of digital chaos transmissions with OFDM component signal transmission. The invention improves upon the state of art in side channel information from the transmit side containing information on the clipped amplitude. In-band transmission of the side information is achieved by exploiting the sparsity of the resulting clip amplitude position in conjunction with hash function to map keys to values, where the values at the position location for the clipped amplitude. The information rate of the clipped amplitude is sub-Nyquist relative to the original OFDM component signal transmission, which allows very low power spreading by a cooperative digital chaos sequences at a transmit side and recovery of the clipped amplitude at a receive side. Further, an improved noise resistance side channel performance is achieved by mapping to clipping amplitudes to scaled digital chaos samples preloaded on the receive device. A network manager or coordinator can update these scaled digital chaos samples during scheduled beacon frames to improvement network performance.

The present invention teaches a system and method for improved signal recovery for range and coverage extension in a heterogeneous cooperative network of digital chaos transmissions with OFDM component signal transmission. The invention improves upon the state of art in side channel information from the transmit side containing information on the clipped amplitude. In-band transmission of the side information is achieved by exploiting the sparsity of the resulting clip amplitude position with improved levels of compression over the prior art using Gabor Transform Multiple Symbol Encoding transmitter. The information rate of the clipped amplitude is sub-Nyquist relative to the original OFDM component signal transmission, which allows very low power spreading by a cooperative digital chaos sequences at a transmit side and recovery of the clipped amplitude at a receive side. Further, an improved noise resistance side channel performance is achieved by decoding Gabor Transform symbols for symbol recovery.

The present invention teaches a system and method for signal recovery for range and coverage extension in a heterogeneous cooperative network of digital chaos transmissions with OFDM component signal transmission. The invention improves upon the state of art in side channel information from the transmit side containing information on the clipped amplitude. In-band transmission of the side information is achieved by exploiting the sparsity of the resulting clip amplitude position in conjunction with hash function to map keys to values, where the values at the position location for the clipped amplitude. The information rate of the clipped amplitude is sub-Nyquist relative to the original OFDM component signal transmission, which allows very low power spreading by a cooperative digital chaos sequences at a transmit side and recovery of the clipped amplitude at a receive side. Further, an improved noise resistance side channel performance is achieved by mapping to clipping amplitudes to scaled digital chaos samples preloaded on the receive device. A network manager or coordinator can update these scaled digital chaos samples during scheduled beacon frames to improvement network performance.