Analytic investigation into the statistical characteristics of the interference due to non-orthogonal time-frequency signaling

The statistical characteristics of non-truncated Intersymbol and Interchannel Interference (ISI/ICI) due to Non-Orthogonal Time-Frequency Signaling (NOTFS) are analytically investigated. The Gaussianity of ISI/ICI is formally discussed in general. This is illustrated for the special case of a single-carrier Faster-than-Nyquist (FTN) signaling using the Root-Raised Cosine (RRC) pulse. Novel closed-form expressions for the ISI second-order statistics are explicitly provided in terms of the system parameters for the same special case. These are partly used to analytically establish that, over all system parameters, the ISI characteristics asymptotically approach those of an exactly Gaussian RV only when the FTN speedup factor approaches infinity. Approximate, yet elegantly compact, closed-form expressions for the Bit Error Rate (BER) for a symbol-by-symbol binary detector using RRC signaling are provided to further shed light, through simulations, on the accuracy and validity of the commonly used Gaussian ISI assumption.