Adaptive Non Orthogonal MFSK

M-ary frequency shift keying (MFSK) using one or more orthogonal tones per symbol has been in use in non-coherent 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 2.5 dB lower signal-to-noise ratio (SNR). For some practical configurations we demonstrate as much as 2 dB of gain. We present the performance with maximum-likelihood (ML) receivers as well as least-squares (LS) receivers as well as lower complexity receivers based on compressed sensing (CS). We also demonstrate that such a non-orthogonal system may be used to increase the spectral efficiency of the overall system by adapting the spectral efficiency in response to the link SNR. Such an adaptive non-orthogonal MFSK system requires estimation of the SNR (or Es/N0), and we present both the Cramér-Rao lower bound (CRLB) as well as maximum-likelihood (ML) estimators, which attain the CRLB for both data-aided (DA) SNR estimation as well as non-data-aided (NDA) SNR estimation.