Featureless chaotic spread spectrum modulation of arbitrary data constellations

Abstract

Chaotic spread spectrum communication systems provide a number of advantages for secure communications due to the apparent randomness of the underlying spreading signal. Many of these chaotic signals exhibit colored spectra, providing discernible features that enable their detection independent of the transmitted data. A recent digital chaotic circuit [1] has been shown to exhibit a truly white spectrum in addition to apparent time-domain randomness. This maximal entropy characteristic supports Shannon's criteria for maximal channel capacity communication, low probability of interception/ detection (LPI/LPD), and a compact bandlimited white spectrum. Such a signal is featureless, susceptible only by energy detection. The disadvantage of such spread communication systems, one shared equally by all spread spectrum systems, is that the channel capacity is constrained by the bandwidth increases required for spreading gain. A traditional approach to increasing bandwidth efficiency is generalizing the modulated digital signaling constellation to include multiple levels of amplitude and phase modulation, which enhances exploitable cyclostationary features unless compensated. This paper presents a framework for adapting the maximal entropy digital chaotic signal to featureless chaotic spread spectrum modulation of arbitrary discrete-time discrete-amplitude data constellations, permitting higher throughputs in chaotic spread spectrum communication systems without sacrificing any of the maximum entropy characteristics that provide LPI/LPD.

Performance of Percent Gaussian Orthogonal Signaling Waveforms

“…These simulations were also repeated for dual-carrier CQAM [8] variants. Spread ratios from 100 to 1M were used in addition to 16 distinct Ȗ values.…”

“…The analysis and performance models/measurements each validate the usage of this Ȗ parameter as a single reference for scaling that modifies the PAPR of the resulting signal and also can be used to quantify the variations in cyclostationary feature content. The results presented in this paper deal with single-carrier phase shift-keying (PSK) modulations that are spread using the percent Gaussian shaped sequences, although the results have been extended and empirically validated for modulation variants employing chaotic carrier shift keying (CSK) [5,6], pulse rotation modulations (PRM) [7], and featureless chaotic spreading of higher-order digital constellations [8]. All models assume that transmit and coherent receive signals entering the despreader are phase/frequency aligned and timesynchronized, with any deviations quantified as receiver implementation losses.…”

Physical-layer encryption for enhanced cyber-physical security

“…Nonetheless, the waveforms are difficult to exploit due to their maximal entropy characteristic, providing an intrinsic property similar to physical-layer encryption. Characteristics of the chaotic spread-spectrum signals are shown in [7], with specific extensions to dual-carrier self-encrypted signals [8] and constant amplitude zero autocorrelation (CAZAC) signals. These waveforms have been implemented and tested in two different software defined radio platforms, validating both their performance and security.…”

“…Mechanisms have been developed to dynamically vary and dither the symbol rate, making physical layer synchronization by an adversary with complete knowledge of the spreading sequence still a challenge. A second security option is the self-encrypted 'chaotic QAM' modulations, which consist of two (or more) coordinated carriers acting as either constructive or destructive interferers depending on a receiver's access to the private keys [8], squaring the computational complexity of brute force cryptographic searches. In all cases, the despreading operation must still contend with thermal noise and interferers, making the decryption process necessarily lossy.…”

“…One is to use a dual-carrier 'chaotic-shift keying' (CSK) approach where the spreading signals are chosen from a pre-defined set of orthogonal bases; having a set of paired carriers allows one to always remain the same (simplifying tracking), while the other is altered such that matched filter receivers targeting different signals can detect the alteration/pattern. A slight adaptation of this technique proposed in [8] allows the creation of a multi-level secure (MLS) wireless link whereby proprietary/non-proprietary data protections may be inserted. The second method is to induce a sawtooth variation in the amplitudes of the paired carriers such that the total variance remains constant, yet the receiver will recognize a coded event of either alternating 0/1s or other predefined pattern that is used for secondary authentication absent any detectable cyclostationary features.…”