Channel Capacity Theory

Classical channel capacity theory contains an implicit assumption that the spectrum is at least approximately stationary: that is, that the power placed into each frequency does not vary significantly over time. (This appears in the use of the Fourier transform to prove the sampling theorem.)

Based on a new generalization of Euler’s formula, the foundational mathematics for telecommunications, Astrapi’s Spiral Modulation for the first time fully exploits the capabilities of a continuously non-stationary spectrum. By doing so, it bypasses the domain of applicability for the Shannon-Hartley law and for the first time provides a practical and theoretically sound path to exceeding the Shannon limit on spectral efficiency.

External validation, resulting from a six-month study, has shown that Spiral Modulation can improve signal power efficiency by 3-4 dB (a factor of two or more) for alphabet sizes of 8 and above, compared to the current state-of-the-art.

Beyond that, a potentially much more important performance win from Spiral Modulation is reducing occupied bandwidth. This is utilizes Instantaneous Spectral Analysis.