Proof of concept mathemathical model of a modulation breaking the Shannon limit

Abstract

Recent research in the field of spectral analysis shows oversampling helps extract significantly more information than conventional sampling, from the same signal in the same bandwidth. A modulation grouping time domain overlapping symbols is proposed, in order to utilize oversampling. Overlapped symbol groups are decoded with the help of a system of equations, as each symbol has a slightly different time position. Their values can thus be distinctively detected with a low error probability. The Shannon limit is considered in a complete form, i.e. error probability, beside bandwidth and signal to noise ratio determine the maximum rate of a channel. The simulation gives a rate about four times the Shannon limit without considering bits to be wasted on synchronization, which are not considered in the Shannon limit either. The modulation needs time synchronization like most digital modulations, e.g. OFDM, but there are enough bits left for it without falling behind the Shannon limit. The result suggests a new channel limit theorem is needed and more research has to be done on reaching it by oversampling the signal relative to the channel bandwidth.