MFSK using non-orthogonal tones

M-ary Frequency Shift Keying (MFSK) using one or more orthogonal tones per symbol has been in use in noncoherent systems for quite some time. We present an alternate system for non-coherent systems using non-orthogonal tones, spread non-uniformly throughout the bandwidth which outperforms the equivalent orthogonal tone system. We demonstrate that from a theoretical capacity point of view, the same bit rate could be achieved by the proposed system with as much as 2.5dB lower signal to noise ratio (SNR). We present the performance with various receiver types and also present the Cramer-Rao Lower Bound (CRLB) and Maximum Likelihood (ML) estimators of SNR estimation using this modulation scheme.