Determination of the Minimum Distance Between Symbols of the Two Non-Orthogonal M-QAM Carriers

Multicarrier communication systems have become ubiquitous, mainly due to the popularization of orthogonal frequency division multiplexing (OFDM), in which carriers are separated in frequency by the inverse of the symbol duration. Recently, more spectrally efficient modulations based on non- orthogonal carriers (non-OFDM) have been put forward and shown numerically to have the same performance as OFDM employing up to 40% less bandwidth. This work addresses the problem of analytically deriving the minimum frequency separation which does not affect the minimum distance between multicarrier symbols. In doing so, it shows that the probability of error remains unaffected up to a certain degree of spectral superposition of the carriers, so that the performance of non- OFDM in terms of bit error rate (BER) remains the same as OFDM. Simulations and comparisons to previous numerical results are used to illustrate this conclusion.