A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. Although almost any modulation can be characterized as amplitude, phase, or frequency modulation or some combination of two or all three of them, the proposed method is independent of traditional modes of amplitude, phase, and frequency modulation and neither explicitly includes nor explicitly excludes them.

The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval. Commonly known data-analysis and statistical techniques (e.g., those of pattern recognition or correlation), implemented in software, can reveal a trend in the histogram associated with some aspect of the shape of the sampled segment of the waveform. In the proposed method, the waveform would be shaped, at the transmitter, such that the trend in the histogram to be generated at the receiver would encode a digital datum (e.g., a one or a zero in the case of binary encoding).

A receiver according to this method could be embodied in analog or digital circuitry. In an analog embodiment, the histogram of the signal would be captured by a tree of window com parator/integrators, there being one branching level of the tree for each of n compartments of the histogram. The final analog calculation of the aspect of shape of the histogram that encodes the desired information would be performed by various hard-wired combinations of n-level summing amplifiers. A digital embodiment would include a single analog-to-digital converter operating at a sampling rate high enough to avoid aliasing. The PDF modulation would be detected by software that would examine the histogram table.

Regardless of the analog or digital nature of the receiver circuitry, the transmitter would best be embodied in a combination of digital and analog circuitry: The waveform-shaping computations for encoding the information to be conveyed would be performed digitally. The resulting numbers would be fed as input to a digital-to-analog converter to generate the analog waveform to be amplified and used to generate the transmitted signal.

The main advantage of the method would lie in its value as the basis of an electronic form of steganography. Because a message would be encoded in statistical characteristics of a waveform, neither the existence nor the contents of the message could easily be discerned by simple inspection of the waveform.

Some types of PDF-modulation waveforms are expected to be resilient in the presence of interference and jamming if properly used in digital-signal-processing radio-relay systems: examples include sawtooth and square waveforms. On the other hand, at low receiver signal-to-noise ratios, decoding can be problematic in cases in which users do not take care to select modulation waveforms that are easily recognizable in the presence of noise.

This work was done by Glenn L. Williams of Glenn Research Center. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Electronics/Computers category.

Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-17650-1.

NASA Tech Briefs Magazine

This article first appeared in the December, 2009 issue of NASA Tech Briefs Magazine.

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