Performance of Percent Gaussian Orthogonal Signaling Waveforms

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 noise like signal that is indistinguishable from naturally occurring (band limited) thermal noise. An implementation challenge associated with these waveforms is that the signal peak-to average 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 ±4.8s, 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.