Modulation Based on Probability Density Functions

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.