Performance of Percent Gaussian Orthogonal Signaling Waveforms

Abstract

Recent developments of secure digital chaotic spread spectrum communication systems have been based on the generalized ideals of maximum channel capacity and maximal entropy/security, which result in a Gaussian-distributed noiselike signal that is indistinguishable from naturally occurring (bandlimited) thermal noise. An implementation challenge associated with these waveforms is that the signal peak-toaverage power ratio (PAPR) is approximately that of an i.i.d Gaussian distributed random sequence; with infinite tails in the Gaussian distribution, modeled practically by a Gaussian distribution truncated to ±4.8ı, the peak excursions of the output can be 13-15 dB over that of the average signal power. To address this PAPR constraint, a series of "percent Gaussian" orthogonal signaling waveforms were developed, allowing parameterized waveform selection that compactly trade PAPR improvements with cyclostationary feature content; these waveforms are bounded by the Gaussian distributed digital chaos signal and a constant amplitude zero autocorrelation (CAZAC) signal, all of which deliver security advantages over traditional direct sequence spread spectrum (DSSS) waveforms. This paper presents an underlying model for these "percent Gaussian" waveforms, derives a generalized set of symbol error rate metrics. Discussion of the performance bounds is also presented.

Generalized Multi-carrier Chaotic Shift Keying

“…Each of the spreading sequences are generated through statistical transformation of a digital chaotic uniform random phase and a selected amplitude scaling, resulting in Gaussian chaos, direct sequence spread spectrum (DSSS), CAZAC, and variable PAPR waveforms nicknamed percent Gaussian [9].…”

“…Note that collapsing the near-continuous phase distribution of the CAZAC sequence to a uniform distribution on the discrete set ቄ గ ସ ǡ ଷగ ସ ǡ ହగ ସ ǡ గ ସ ቅ creates a semi-coherent DSSS-QPSK sequence. While the statistical distributions of each of the spreading sequences differ, each zero-mean sequence is normalized such that it exhibits unit variance in each of the quadrature channels (total variance = 2); the second order statistics of ห‫ݔ‬ ሺఊሻ ሺߛሻห ଶ are bounded [9] by the CAZAC and Gaussian limiting cases: Ͳ ߪ ௫௫ ଶ ሺߛሻ Ͷ. Each term ܻ in (2) may be decomposed into an independent signal and noise correlation terms.…”

“…The generalized CSK modulation enable encoding of data into more complex multi-carrier CSK signals, where decoding and data decisions are based on the presence of a specific signal within the received ensemble [8]. This approach further allows use of multiple phase-coherent spreading characteristics such as those used previously for Gaussian-distributed digital chaos waveforms, constant amplitude-zero autocorrelation (CAZAC), direct sequence, and parameterized 'percent Gaussian' spreading sequences [9]. These latter sequences yield signal statistics and performance that are bounded by the CAZAC and chaotic waveforms, most notably in their peak-to-average power ratio (PAPR) and susceptibilities to cyclostationary feature detection.…”

Evaluating HPA Effects on Chaotic Sequence Spread Spectrum Detectability

“…These CSSS signals offer advantages for secure communications since the spread signal is statistically indistinguishable from bandlimited white noise, helping it blend into an Additive White Gaussian Noise (AWGN) background, approaching the limits of detectability [1]. Recognizing the challenges of transmitting AWGN-like signals through real-world amplifiers, a recent alternative to CSSS was developed that maintains a sufficiently random phase distribution and near constant envelope magnitude distribution to produce additive white uniform noise [2], retaining many of the CSSS advantages, yet there is a quantifiable increase in detectability due to the non-Gaussian magnitude distribution [3].…”

Total Variation Distance Based Performance Analysis of Covert Communication over AWGN Channels in Non-asymptotic Regime

“…First, Gaussian distribution is optimal in both maximizing the mutual information between the input and output ends of the legitimate receiver over AWGN channels in the asymptotic regime and minimizing KL divergence between the output and the background noise at the adversary (Theorem 5 in [4]). It has found applications in secure chaotic spread spectrum communication systems [18] [19]. Second, TVD at the adversary is relatively easy to analyze when the codewords are Gaussian generated (or nearly Gaussian generated) than a determined codebook.…”